Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

Energy Conditions and Segre Classification of Phantom Fields

Recent discoveries in the field of observational cosmology have provided increasing evidence that the Universe is undergoing a late time acceleration, which has also stimulated speculations on the nature of the dark component responsible for such a phenomenon. Among several candidates discussed in the current literature, phantom fields, an exotic scalar field with a negative kinetic term and that violates most of the classical energy conditions, appear as a real possibility according to recent observational analysis. In this paper we examine the invariant characterization for the energy-momentum tensor of phantom fields through the Segre algebraic classification in the framework of general relativity. We also discuss some constraints which are imposed on the values of $V(\phi)$ from the classical energy conditions.Comment: 4 pages, 1 figure, to appear in Phys. Lett.

Social Entrepreneurship That Truly Benefits the Poor: An Integrative Justice Approach

The phenomenal growth of social entrepreneurship over thelast decade has ably demonstrated how technology, innovation, and anentrepreneurial spirit can afford better solutions to the vexing social andenvironmental problems of our time than can traditional aid and charitybasedefforts. In most cases, but not always, the poor and disadvantagedhave benefited from the growth of social entrepreneurship. In order toensure that social entrepreneurship does indeed benefit the poor, it isimperative that there be normative guidelines for fair and just engagementwith impoverished populations. A model that has been presented in themarketing and public policy literature is the integrative justice model (IJM)for impoverished populations. While the IJM was developed primarily in thecontext of multinational corporations (MNCs) operating in emerging markets,its applicability extends beyond MNCs. This article attempts to apply theIJM principles in the context of social entrepreneurship in order to providesocial entrepreneurial organizations (SEOs) with a normative frameworkaimed at ensuring that the poor truly benefit from their activities. Basedon this framework, the article suggests certain areas to which SEOs oughtto be particularly attentive in their practice. The article also makes somesuggestions for further research

Anomalous exchange interaction between intrinsic spins in conducting graphene systems

We address the nature and possible observable consequences of singular one-electron states that appear when strong defects are introduced in the metallic family of graphene, namely, metallic carbon nanotubes and nanotori. In its simplest form, after creating two defects on the same sublattice, a state may emerge at the Fermi energy presenting very unusual properties: It is unique, normalizable, and features a wave function equally distributed around both defects. As a result, the exchange coupling between the magnetic moments generated by the two defects is anomalous. The intrinsic spins couple ferromagnetically, as expected, but do not present an antiferromagnetic excited state at any distance. We propose the use of metallic carbon nanotubes as a novel electronic device based on this anomalous coupling between spins which can be useful for the robust transmission of magnetic information at large distances.Comment: 5 pages 5 fugure

How `sticky' are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range $\lambda$ at a given packing fraction and reduced temperature can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter $\tau$. Such an equivalence cannot hold for the radial distribution function since this function has a delta singularity at contact in the SHS case, while it has a jump discontinuity at $r=\lambda$ in the SW case. Therefore, the equivalence is explored with the cavity function $y(r)$. Optimization of the agreement between y_{\sw} and y_{\shs} to first order in density suggests the choice for $\tau$. We have performed Monte Carlo (MC) simulations of the SW fluid for $\lambda=1.05$, 1.02, and 1.01 at several densities and temperatures $T^*$ such that $\tau=0.13$, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)]. Although, at given values of $\eta$ and $\tau$, some local discrepancies between y_{\sw} and y_{\shs} exist (especially for $\lambda=1.05$), the SW data converge smoothly toward the SHS values as $\lambda-1$ decreases. The approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y_{\shs} the solution of the Percus--Yevick equation as well as the rational-function approximation, the radial distribution function $g(r)$ of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1) corrected, Fig. 14 redone, to be published in JC

Directional Detection of Dark Matter with MIMAC

Directional detection is a promising search strategy to discover galactic Dark Matter. We present a Bayesian analysis framework dedicated to Dark Matter phenomenology using directional detection. The interest of directional detection as a powerful tool to set exclusion limits, to authentify a Dark Matter detection or to constrain the Dark Matter properties, both from particle physics and galactic halo physics, will be demonstrated. However, such results need highly accurate track reconstruction which should be reachable by the MIMAC detector using a dedicated readout combined with a likelihood analysis of recoiling nuclei.Comment: 4 pages, 2 figures, to appear in the proceedings of the TAUP 2011 conference held in Munich (5 - 9 September, 2011