Universality classes for horizon instabilities

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.Comment: 23 pages, latex2e, 4 figure

Multibody Multipole Methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: 1) a deterministic series expansion-based method; 2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic

Monitoring Progress Toward Fulfilling Rights in Early Childhood Under the Convention on the Rights of the Child to Improve Outcomes for Children and Families

Can the United Nations Convention on the Rights of the Child (UN-CRC), to which 193 countries are signatory, be used as a tool to support developmental health in the early years? Improving early childhood development (ECD) requires finding ways for social determinants and child rights approaches to work together, which, to date, has not occurred. However, in 2005, the UN-CRC Monitoring Committee issued General Comment 7: Implementing Rights in Early Childhood (GC7) in response to the observation that children under the age of 8 were often overlooked in countries' reporting of progress toward implementing UN-CRC. This chapter shows how a commitment from the UN-CRC Monitoring Committee and key relevant international agencies (WHO, UNICEF) to a long-term program of monitoring compliance with GC7, in conjunction with monitoring of ECD developmental outcomes in all signatory countries, could help move global society toward equity in developmental health from the start of life. © Oxford University Press, 2014

Stability analysis of surface ion traps

Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle $\theta$ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. We obtain stability diagrams for the coupled system for various values of $\theta$, generalizing the standard $q$-$a$ stability diagrams. We use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and obtain some of the stability boundaries independently by using the method of infinite determinants. We cross-check the consistency of the results of these methods. Our results show that while the primary stability region is quite robust to changes in $\theta$, a secondary stability region is highly variable, joining the primary stability region at the special case of $\theta=45^{\circ}$, which results in a significantly enlarged stability region for this particular angle. We conclude that while the stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are safe in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region

Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation

Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled DC electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode frequencies, and adjust the orientation of trap axes. Microfabricated capacitors on DC electrodes suppress radio-frequency pickup and excess micromotion, while a top-level ground layer simplifies modeling of electric fields and protects trap structures underneath. A localized aperture in the substrate provides access to the trapping region from an oven below, permitting deterministic loading of particular isotopic/elemental sequences via species-selective photoionization. The shapes of the aperture and radio-frequency electrodes are optimized to minimize perturbation of the trapping pseudopotential. Laboratory experiments verify simulated potentials and characterize trapping lifetimes, stray electric fields, and ion heating rates, while measurement and cancellation of spatially-varying stray electric fields permits the formation of nearly-equally spaced ion chains.Comment: 17 pages (including references), 7 figure

RG-Flows, AdS/CFT Correspondence and Stability of Non-Dilatonic Branes

The possibility of having multiple renormalization group (RG) flows (one of which is supersymmetric) between two fixed points is investigated in the context of anti de Sitter / conformal field theory (AdS/CFT) correspondence. An analysis of a toy-model potential suggests that such flows are likely to exist. Superpotential methods are used in the context of finite temperature AdS/CFT to derive a black brane solution which approximates various finite temperature RG-flows in AdS/CFT near the horizon. This solution is also used in formulating a notion of univerality classes of instabilities of black braves. Instabilities of D3, M2 and M5-branes are investigated numerically, and the results confirm the predictions of the proposal of universality classes