Exact on-event expressions for discrete potential systems

The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell-Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations

Compatible actions and non-abelian tensor products

For a pair of groups $G, H$ we study pairs of actions $G$ on $H$ and $H$ on $G$ such that these pairs are compatible and non-abelian tensor products $G \otimes H$ are defined.Comment: 9 page

Azimuthally Symmetric Theory of Gravitation (I)

From a purely none-general relativistic standpoint, we solve the empty space Poisson equation ($\nabla^{2}\Phi=0$) for an azimuthally symmetric setting, i.e., for a spinning gravitational system like the Sun. We seek the general solution of the form $\Phi=\Phi(r,\theta)$. This general solution is constrained such that in the zeroth order approximation it reduces to Newton's well known inverse square law of gravitation. For this general solution, it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body. We show that to second order approximation, this azimuthally symmetric gravitational field is capable of explaining at least two things (1) the observed perihelion shift of solar planets (2) that the mean Earth-Sun distance must be increasing -- this resonates with the observations of two independent groups of astronomers (Krasinsky & Brumberg 2004; Standish 2005) who have measured that the mean Earth-Sun distance must be increasing at a rate of about $7.0\pm0.2 m/cy$ (Standish 2005) to $15.0\pm0.3 m/cy$ (Krasinsky & Brumberg 2004). In-principle, we are able to explain this result as a consequence of loss of orbital angular momentum -- this loss of orbital angular momentum is a direct prediction of the theory. Further, we show that the theory is able to explain at a satisfactory level the observed secular increase Earth Year ($1.70\pm0.05 ms/yr$; Miura et al. 2009}). Furthermore, we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least $8.00\pm2.00 s/cy$.Comment: 2 figures, 2 tables, 13 pages. Accepted to MNRAS 2009 December 9. Received 2009 December 9; in original form 2009 September 5: ref. MN-09-1767-MJ.R3

Spin gap behavior in Cu2_2Sc2_2Ge4_4O13_{13} by 45^{45}Sc nuclear magnetic resonance

We report the results of a $^{45}$Sc nuclear magnetic resonance (NMR) study on the quasi-one-dimensional compound Cu$_2$Sc$_2$Ge$_4$O$_{13}$ at temperatures between 4 and 300 K. This material has been a subject of current interest due to indications of spin gap behavior. The temperature-dependent NMR shift exhibits a character of low-dimensional magnetism with a negative broad maximum at $T_{max}$ $\simeq$ 170 K. Below $$, the NMR shifts and spin lattice relaxation rates clearly indicate activated responses, confirming the existence of a spin gap in Cu$_2$Sc$_2$Ge% $_4$O$_{13}$. The experimental NMR data can be well fitted to the spin dimer model, yielding a spin gap value of about 275 K which is close to the 25 meV peak found in the inelastic neutron scattering measurement. A detailed analysis further points out that the nearly isolated dimer picture is proper for the understanding of spin gap nature in Cu$_2$Sc$_2$Ge$_4$O$_{13}$.Comment: 4 pages, 6 figures, submitted to Phys. Rev.

Tracking intracavernously injected adipose-derived stem cells to bone marrow.

The intracavernous (i.c.) injection of stem cells (SCs) has been shown to improve erectile function in various erectile dysfunction (ED) animal models. However, the tissue distribution of the injected cells remains unknown. In this study we tracked i.c.-injected adipose-derived stem cells (ADSCs) in various tissues. Rat paratesticular fat was processed for ADSC isolation and culture. The animals were then subject to cavernous nerve (CN) crush injury or sham operation, followed by i.c. injection of 1 million autologous or allogeneic ADSCs that were labeled with 5-ethynyl-2-deoxyuridine (EdU). Another group of rats received i.c. injection of EdU-labeled allogeneic penile smooth muscle cells (PSMCs). At 2 and 7 days post injection, penises and femoral bone marrow were processed for histological analyses. Whole femoral bone marrows were also analyzed for EdU-positive cells by flow cytometry. The results show that ADSCs exited the penis within days of i.c. injection and migrated preferentially to bone marrow. Allogenicity did not affect the bone marrow appearance of ADSCs at either 2 or 7 days, whereas CN injury reduced the number of ADSCs in bone marrow significantly at 7 but not 2 days. The significance of these results in relation to SC therapy for ED is discussed

Gravitational Properties of Monopole Spacetimes Near the Black Hole Threshold

Although nonsingular spacetimes and those containing black holes are qualitatively quite different, there are continuous families of configurations that connect the two. In this paper we use self-gravitating monopole solutions as tools for investigating the transition between these two types of spacetimes. We show how causally distinct regions emerge as the black hole limit is achieved, even though the measurements made by an external observer vary continuously. We find that near-critical solutions have a naturally defined entropy, despite the absence of a true horizon, and that this has a clear connection with the Hawking-Bekenstein entropy. We find that certain classes of near-critical solutions display naked black hole behavior, although they are not truly black holes at all. Finally, we present a numerical simulation illustrating how an incident pulse of matter can induce the dynamical collapse of a monopole into an extremal black hole. We discuss the implications of this process for the third law of black hole thermodynamics.Comment: 23 pages, 4 figures RevTe

Gravitational Leakage into Extra Dimensions: Probing Dark Energy Using Local Gravity

The braneworld model of Dvali-Gabadadze-Porrati (DGP) is a theory where gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe. Cosmology in this model has been shown to support both "conventional" and exotic explanations of the dark energy responsible for today's cosmic acceleration. We present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity. In particular, we show that orbits nearby a mass source suffer a universal anomalous precession as large as 5 microarcseconds/year, dependent only on the graviton's effective linewidth and the global geometry of the full, five-dimensional universe. Thus, this theory offers a local gravity correction sensitive to factors that dictate cosmological history.Comment: 18 pages, 1 figure, revtex. Reference updated. Footnote change