HI in the Outskirts of Nearby Galaxies

The HI in disk galaxies frequently extends beyond the optical image, and can trace the dark matter there. I briefly highlight the history of high spatial resolution HI imaging, the contribution it made to the dark matter problem, and the current tension between several dynamical methods to break the disk-halo degeneracy. I then turn to the flaring problem, which could in principle probe the shape of the dark halo. Instead, however, a lot of attention is now devoted to understanding the role of gas accretion via galactic fountains. The current $\rm \Lambda$ cold dark matter theory has problems on galactic scales, such as the core-cusp problem, which can be addressed with HI observations of dwarf galaxies. For a similar range in rotation velocities, galaxies of type Sd have thin disks, while those of type Im are much thicker. After a few comments on modified Newtonian dynamics and on irregular galaxies, I close with statistics on the HI extent of galaxies.Comment: 38 pages, 17 figures, invited review, book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

Constraining the electric charges of some astronomical bodies in Reissner-Nordstrom spacetimes and generic r^-2-type power-law potentials from orbital motions

We put model-independent, dynamical constraints on the net electric charge Q of some astronomical and astrophysical objects by assuming that their exterior spacetimes are described by the Reissner-Nordstroem metric, which induces an additional potential U_RN \propto Q^2 r^-2. Our results extend to other hypothetical power-law interactions inducing extra-potentials U_pert = r^-2 as well (abridged).Comment: LaTex2e, 16 pages, 3 figures, no tables, 128 references. Version matching the one at press in General Relativity and Gravitation (GRG). arXiv admin note: substantial text overlap with arXiv:1112.351

Interaction design and usability of learning spaces in 3D multi-user virtual worlds

Three-dimensional virtual worlds are multimedia, simulated environments, often managed over the Web, which users can 'inhabit' and interact via their own graphical self-representations known as 'avatars'. 3D virtual worlds are being used in many applications: education/training, gaming, social networking, marketing and commerce. Second Life is the most widely used 3D virtual world in education. However, problems associated with usability, navigation and wayfinding in 3D virtual worlds may impact on student learning and engagement. Based on empirical investigations of learning spaces in Second Life, this paper presents design guidelines to improve the usability and ease of navigation in 3D spaces. Methods of data collection include semi-structured interviews with Second Life students, educators and designers. The findings have revealed that design principles from the fields of urban planning, Human-Computer Interaction, Web usability, geography and psychology can influence the design of spaces in 3D multi-user virtual environments

A unified approach to singular problems arising in the membrane theory

summary:We consider the singular boundary value problem $$(t^nu'(t))'+ t^nf(t,u(t))=0, \quad \lim _{t\to 0+}t^nu'(t)=0, \quad a_0u(1)+a_1u'(1-)=A,$$ where $f(t,x)$ is a given continuous function defined on the set $(0,1]\times (0,\infty )$ which can have a time singularity at $t=0$ and a space singularity at $x=0$. Moreover, $n\in \Bbb N$, $n\ge 2$, and $a_0$, $a_1$, $A$ are real constants such that $a_0\in (0,\infty )$, whereas $a_1,A\in [0,\infty )$. The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in characterizing positive solutions. We illustrate the analytical findings by numerical simulations based on polynomial collocation