Global representations of the Heat and Schr\"odinger equation with singular potential

We study the $n$-dimensional Schr\"odinger equation with singular potential $V_\lambda(x)=\lambda |x|^{-2}$. Its solution space is studied as a global representation of $\widetilde{SL(2,\R)}\times O(n)$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of $K$-finite vectors is calculated, obtaining conditions for $\lambda$ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of $\lambda$ is studied as a representation of the $2n+1$-dimensional Heisenberg group

Southwest Border Violence: Issues in Identifying and Measuring Spillover Violence

[Excerpt] There has been a recent increase in the level of drug trafficking-related violence within and between the drug trafficking organizations in Mexico. This violence has generated concern among U.S. policy makers that the violence in Mexico might spill over into the United States. Currently, U.S. federal officials deny that the recent increase in drug trafficking-related violence in Mexico has resulted in a spillover into the United States, but they acknowledge that the prospect is a serious concern. Currently, no comprehensive, publicly available data exist that can definitively answer the question of whether there has been a significant spillover of drug trafficking-related violence into the United States. Although anecdotal reports have been mixed, U.S. government officials maintain that there has not yet been a significant spillover. In an examination of data that could provide insight into whether there has been a significant spillover in drug trafficking-related violence from Mexico into the United States, CRS analyzed violent crime data from the Federal Bureau of Investigation’s Uniform Crime Report program. The data, however, do not allow analysts to determine what proportion of the violent crime rate is related to drug trafficking or, even more specifically, what proportion of drug trafficking-related violent crimes can be attributed to spillover violence. In conclusion, because the trends in the overall violent crime rate may not be indicative of trends in drug trafficking-related violent crimes, CRS is unable to draw definitive claims about trends in drug trafficking-related violence spilling over from Mexico into the United States. This report will be updated as circumstances warrant

Position, spin and orbital angular momentum of a relativistic electron

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K.Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S.M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)].Comment: 10 pages, 1 table, to appear in Phys. Rev.

AFM pulling and the folding of donor-acceptor oligorotaxanes: phenomenology and interpretation

The thermodynamic driving force in the self-assembly of the secondary structure of a class of donor-acceptor oligorotaxanes is elucidated by means of molecular dynamics simulations of equilibrium isometric single-molecule force spectroscopy AFM experiments. The oligorotaxanes consist of cyclobis(paraquat-\emph{p}-phenylene) rings threaded onto an oligomer of 1,5-dioxynaphthalenes linked by polyethers. The simulations are performed in a high dielectric medium using MM3 as the force field. The resulting force vs. extension isotherms show a mechanically unstable region in which the molecule unfolds and, for selected extensions, blinks in the force measurements between a high-force and a low-force regime. From the force vs. extension data the molecular potential of mean force is reconstructed using the weighted histogram analysis method and decomposed into energetic and entropic contributions. The simulations indicate that the folding of the oligorotaxanes is energetically favored but entropically penalized, with the energetic contributions overcoming the entropy penalty and effectively driving the self-assembly. In addition, an analogy between the single-molecule folding/unfolding events driven by the AFM tip and the thermodynamic theory of first-order phase transitions is discussed and general conditions, on the molecule and the cantilever, for the emergence of mechanical instabilities and blinks in the force measurements in equilibrium isometric pulling experiments are presented. In particular, it is shown that the mechanical stability properties observed during the extension are intimately related to the fluctuations in the force measurements.Comment: 42 pages, 17 figures, accepted to the Journal of Chemical Physic

Aerobic power, huddling and the efficiency of torpor in the South American marsupial, Dromiciops gliroides.

During periods of cold, small endotherms depend on a continuous supply of food and energy to maintain euthermic body temperature (T(b)), which can be challenging if food is limited. In these conditions, energy-saving strategies are critical to reduce the energetic requirements for survival. Mammals from temperate regions show a wide arrange of such strategies, including torpor and huddling. Here we provide a quantitative description of thermoregulatory capacities and energy-saving strategies in Dromiciops gliroides, a Microbiotherid marsupial inhabiting temperate rain forests. Unlike many mammals from temperate regions, preliminary studies have suggested that this species has low capacity for control and regulation of body temperature, but there is still an incomplete picture of its bioenergetics. In order to more fully understand the physiological capacities of this "living fossil", we measured its scope of aerobic power and the interaction between huddling and torpor. Specifically, we evaluated: (1) the relation between basal (BMR) and maximum metabolic rate (MMR), and (2) the role of huddling on the characteristics of torpor at different temperatures. We found that BMR and MMR were above the expected values for marsupials and the factorial aerobic scope (from [Formula: see text]CO(2)) was 6.0±0.45 (using [Formula: see text]CO(2)) and 6.2±0.23 (using [Formula: see text]O(2)), an unusually low value for mammals. Also, repeatability of physiological variables was non-significant, as in previous studies, suggesting poor time-consistency of energy metabolism. Comparisons of energy expenditure and body temperature (using attached data-loggers) between grouped and isolated individuals showed that at 20°C both average resting metabolic rate and body temperature were higher in groups, essentially because animals remained non-torpid. At 10°C, however, all individuals became torpid and no differences were observed between grouped and isolated individuals. In summary, our study suggests that the main response of Dromiciops gliroides to low ambient temperature is reduced body temperature and torpor, irrespective of huddling. Low aerobic power and low time-consistency of most thermoregulatory traits of Dromiciops gliroides support the idea of poor thermoregulatory abilities in this species

Solitonic dispersive hydrodynamics: theory and observation

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.Comment: 8 pages, 5 figure

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A Compensatory Liability Regime to Promote the Exchange of Microbial Genetic Resources for Research and Benefit Sharing

Female rhesus macaques were immunized with HIV virus-like particles (HIV-VLPs) or HIV DNA administered as sequential combinations of mucosal (intranasal) and systemic (intramuscular) routes, according to homologous or heterologous prime-boost schedules. The results show that in rhesus macaques only the sequential intranasal and intramuscular administration of HIV-VLPs, and not the intranasal alone, is able to elicit humoral immune response at the systemic as well as the vaginal level.funding agencies|Simian Vaccine Evaluation Unit (SVEU) of the Division of AIDS||European Community|201433|</p