Rocking and rolling: a can that appears to rock might actually roll

A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the container slaps the table before rocking up to the opposite tilt. A keen eye notices that the after-slap rising tilt is not generally just diametrically opposite the initial tilt but is veered to one side or the other. Cushman and Duistermaat (2006) recently noticed such veering when a flat disk with rolling boundary conditions is dropped nearly flat. Here, we generalize these rolling disk results to arbitrary axi-symmetric bodies and to frictionless sliding. More specifically, we study motions that almost but do not quite involve a face-down collision of the round container's bottom with the table-top. These motions involve a sudden rapid motion of the contact point around the circular base. Surprisingly, like for the rolling disk, the net angle of motion of this contact point is nearly independent of initial conditions. This angle of turn depends simply on the geometry and mass distribution but not on the moment of inertia about the symmetry axis. We derive simple asymptotic formulas for this "angle of turn" of the contact point and check the result with numerics and with simple experiments. For tall containers (height much bigger than radius) the angle of turn is just over $\pi$ and the sudden rolling motion superficially appears as a nearly symmetric collision leading to leaning on an almost diametrically opposite point on the bottom rim.Comment: 10 pages, 5 figure

Whitepaper on Super-weakly Interacting Massive Particles for Snowmass 2013

Super-weakly interacting massive particles produced in the late decays of weakly interacting massive particles (WIMPs) are generic in large regions of supersymmetric parameter space and other frameworks for physics beyond the standard model. If their masses are similar to that of the decaying WIMP, then they could naturally account for all of the cosmological dark matter abundance. Their astrophysical consequences and collider signatures are distinct and different from WIMP candidates. In particular, they could modify Big Bang Nucleosynthesis, distort the Cosmic Microwave Background, reduce galactic substructure and lower central densities of low-mass galaxies.Comment: 4 pages, 2 figures, white paper for Snowmass 201

Trade liberalization, poverty, and food security in India:

food security, Nutrition, Computable general equilibrium (CGE), Globalization, Markets, trade,

Trade Liberalization, Poverty and Food Security in India

This paper attempts to assess the impact of trade liberalization on growth, poverty, and food security in India with the help of a national level computable general equilibrium (CGE) model. It shows that GDP growth and income poverty reduction that might occur following trade liberalization need not necessarily result in an improvement in the food security / nutritional status of the poor. Evidence from simulations of (partial) trade reforms reflecting a possible Doha-like scenario show that the bottom 30% of the population in both rural and urban areas suffer a decline in calorie and protein intake, in contrast to the rest of the population, even as all households increase their intake of fats. Thus, the outcome on food security / status with regard to individual nutrients depends crucially on the movements in the relative prices of different commodities along with the change in income levels. These results show that trade policy analysis should consider indicators of food security in addition to overall growth and poverty traditionally considered in such studies.Doha negotiations, India trade policy, poverty, food security, CGE model

Shallow Deep Transitions of Neutral and Charged Donor States in Semiconductor Quantum Dots

We carry out a detailed investigation of neutral ($D^0$) and charged ($D^-$) impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The investigation is carried out within the effective mass theory (EMT). We take recourse to local density approximation (LDA) and the Harbola-Sahni (HS) schemes for treating many-body effects. We experiment with a variety of confining potentials: square, harmonic and triangular. We observe that the donor level undergoes shallow to deep transition as the dot radius ($R$) is reduced. On further reduction of the dot radius it becomes shallow again. We term this non-monotonic behaviour \textbf{SHADES}. This suggests the possibility of carrier {\textbf{\textit{``freeze out''}}} for both $D^0$ and $D^-$. Further, our study of the optical gaps also reveals a {\textbf{SHADES}} transition.Comment: 19 pages, 8 figures, Revised Versio