Bounding the Heat Trace of a Calabi-Yau Manifold

The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. In conformal field theories defined via sigma models into Calabi-Yau manifolds, relevant operators can be estimated, in the point-particle approximation, by the low-lying spectrum of the scalar Laplacian on the manifold. In the strict large volume limit, the standard asymptotic expansion of Weyl and Minakshisundaram-Pleijel diverges with the higher-order curvature invariants. We propose that it would be sufficient to find an a priori uniform bound on the trace of the heat kernel for large but finite volume. As a first step in this direction, we then study the heat trace asymptotics, as well as the actual spectrum of the scalar Laplacian, in the vicinity of a conifold singularity. The eigenfunctions can be written in terms of confluent Heun functions, the analysis of which gives evidence that regions of large curvature will not prevent the existence of a bound of this type. This is also in line with general mathematical expectations about spectral continuity for manifolds with conical singularities. A sharper version of our results could, in combination with the SCHOK bound, provide a basis for a global restriction on the dimension of the moduli space of Calabi-Yau manifolds.Comment: 32 pages, 3 figure

A note on palindromic δ\delta-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart $\delta$-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact.Comment: 4 page

Marginal deformations of heterotic G2G_2 sigma models

Recently, the infinitesimal moduli space of heterotic $G_2$ compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST operator. This BRST operator is nilpotent if and only if the target space geometry satisfies the heterotic supersymmetry conditions. We relate this to the supergravity approach by showing that the corresponding cohomologies are indeed isomorphic. We work at tree-level in $\alpha'$ perturbation theory and study general geometries, in particular with non-vanishing torsion.Comment: Minor changes: Added references and a section on classical symmetries. 24 pages, 1 figure, 1 tabl

Les privilèges et immunités humanitaires

Depuis nombre d'années, l'organisation non gouvernementale (ONG) humanitaire et ses volontaires se dévouent corps et âme en vue d'atténuer les effets néfastes des tragédies et catastrophes qui assaillent l'humanité. La présente étude s'inscrit dans une perspective de droit nouveau visant à leur accorder des statuts juridiques internationaux particuliers. L'exercice consiste d'abord à recenser les situations problématiques auxquelles se heurtent l'ONG humanitaire et ses volontaires sur le terrain. Celles-ci détermineront essentiellement l'étendue de la protection à leur offrir. S'ensuit une analyse du droit international, général et conventionnel, sous l'angle de la protection qu'il attribue à l'ONG humanitaire et à ses volontaires. Confronté au silence du droit international quant à la détermination de statuts juridiques internationaux particuliers conformes aux besoins ressentis par le milieu, nous proposons l'ébauche d'une convention sur les privilèges et immunités humanitaires.For many years now, the Humanitarian Non-Governmental Organization (NGO) and its volunteers have continuously devoted themselves to providing relief to lessen the distressing effects of calamities and disasters that afflict humankind. This study sheds light on a new legal approach that would recognize an international status for the Humanitarian NGO and its volunteers. First, the problematic situations that they faced on site are considered and they then serve to determine the scope of protection that must be granted. Attention is subsequently focused on International Law to highlight currently afforded protection. Since International Law remains silent as to the determination of an international status that would respond to the previously identified needs, a draft convention on humanitarian privileges and immunities will therefore be proposed

Effects of Turning Radius on Skid-Steered Wheeled Robot Power Consumption on Loose Soil

This research highlights the need for a new power model for skid-steered wheeled robots driving on loose soil and lays the groundwork to develop such a model. State-of-the-art power modeling assumes hard ground; under typical assumptions this predicts constant power consumption over a range of small turning radii where the inner wheels are rotating backwards. However, experimental results performed both in the field and in a controlled laboratory sandbox show that, on sand, power is not in fact constant with respect to turning radius. Power peaks by 20% in a newly identified range of turns where the inner wheels rotate backwards but are being dragged forward. This range of turning radii spans from half the rover width to R', the radius at which the inner wheel is not commanded to turn. Data shows higher motor torque and wheel sinkage in this range. To progress toward predicting the required power for a skid-steered wheeled robot to maneuver on loose soil, a preliminary version of a two-dimensional slip-sinkage model is proposed, along with a model of the force required to bulldoze the pile of sand that accumulates next to the wheels as it they are skidding. However, this is shown to be a less important factor contributing to the increased power in small-radius turns than the added inner wheel torque induced by dragging these wheels through the piles of sand they excavate by counter-rotation (in the identified range of turns). Finally, since a direct application of a power model is to design energy-efficient paths, time dependency of power consumption is also examined. Experiments show reduced rover angular velocity in sand around turning radii where the inner wheels are not rotated and this leads to the introduction to a new parameter to consider in path planning: angular slip

Electrochemical treatment of industrial sulfidic spent caustic streams for sulfide removal and caustic recovery

Alkaline spent caustic streams (SCS) produced in the petrochemical and chemical manufacturing industry, contain high concentrations of reactive sulfide (HS-) and caustic soda (NaOH). Common treatment methods entail high operational costs while not recovering the possible resources that SCS contain. Here we studied the electrochemical treatment of SCS from a chemical manufacturing industry in an electrolysis cell, aiming at anodic HS- removal and cathodic NaOH, devoid of sulfide, recovery. Using a synthetic SCS we first evaluated the HS- oxidation product distribution over time, as well as the HS- removal and the NaOH recovery, as a function of current density. In a second step, we investigated the operational aspects of such treatment for the industrial SCS, under 300 A m(-2) fixed current density. In an electrolysis cell receiving 205 +/- 60 g S L-1 d(-1) HS- over 20 days of continuous operation, HS- was removed with a 38.0 +/- 7.7 % removal and similar to 80 % coulombic efficiency, with a concomitant recovery of a similar to 12 wt.% NaOH solution. The low cell voltage obtained (1.75 +/- 0.12 V), resulted in low energy requirements of 3.7 +/- 0.6 kW h kg(-1) S and 6.3 +/- 0.4 kW h kg(-1) NaOH and suggests techno-economic viability of this process