The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

Defect Motion and Lattice Pinning Barrier in Josephson-Junction Ladders

We study motion of domain wall defects in a fully frustrated Josephson-unction ladder system, driven by small applied currents. For small system sizes, the energy barrier E_B to the defect motion is computed analytically via symmetry and topological considerations. More generally, we perform numerical simulations directly on the equations of motion, based on the resistively-shunted junction model, to study the dynamics of defects, varying the system size. Coherent motion of domain walls is observed for large system sizes. In the thermodynamical limit, we find E_B=0.1827 in units of the Josephson coupling energy.Comment: 7 pages, and to apear in Phys. Rev.

Development of airborne hemispheric spectrometer

A new concept of hyperspectral instrument is presented. Novel design of hyperspectral skydome allows retrieval of atmospheric constituents and properties from a snapshot of spectral solar radiation over entire sky, regardless of platform motion either on ground or aircraft. Design and description of subsystems of the instrument are given followed by preliminary tolerance analysis, whose results are to be added in the retrieval algorithm along with hardware specifications. Extended application of the hyperspectral skydome is being carried out filling in the gap in the imaging spectrometry

Local well-posedness of the generalized Cucker-Smale model

In this paper, we study the local well-posedness of two types of generalized Cucker-Smale (in short C-S) flocking models. We consider two different communication weights, singular and regular ones, with nonlinear coupling velocities $v|v|^{\beta-2}$ for $\beta > \frac{3-d}{2}$. For the singular communication weight, we choose $\psi^1(x) = 1/|x|^{\alpha}$ with $\alpha \in (0,d-1)$ and $\beta \geq 2$ in dimension $d > 1$. For the regular case, we select $\psi^2(x) \geq 0$ belonging to (L_{loc}^\infty \cap \mbox{Lip}_{loc})(\mathbb{R}^d) and $\beta \in (\frac{3-d}{2},2)$. We also remark the various dynamics of C-S particle system for these communication weights when $\beta \in (0,3)$