2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals

We prove that the 2-hermitean matrix model and the complex-matrix model obey the same loop equations, and as a byproduct, we find a formula for Itzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) are rewritten as gaussian integrals over triangular matrices and then computed explicitly. That formula is an efficient alternative to the former Shatashvili's formula.Comment: 29 pages, Late

Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium

The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition implies that the fluid flow moves only along the angular direction, i.e. there is no convection. Using this simplification, some recent studies have provided us with uniqueness and existence results for asymptotically flat vacuum exterior fields given the interior sources. Here, the generalisation of the problem to include general sources is studied. It is proven that the convective motions have no direct influence on the exterior field, and hence, that the aforementioned results on uniqueness and existence of exterior fields apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum Gra

On gonihedric loops and quantum gravity

We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model and studied analytically. Second, the gravitational version of this loop model is studied via matrix models techniques. Both methods lead to the conclusion that the model has $c_{matter}=0$ for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition

On global models for isolated rotating axisymmetric charged bodies; uniqueness of the exterior field

A relatively recent study by Mars and Senovilla provided us with a uniqueness result for the exterior vacuum gravitational field generated by an isolated distribution of matter in axial rotation in equilibrium in General Relativity. The generalisation to exterior electrovacuum gravitational fields, to include charged rotating objects, is presented here.Comment: LaTeX, 21 pages, uses iopart styl

Correlation Functions of Complex Matrix Models

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions are a sum of expressions attached to a set of fully packed oriented loops configurations; for rotational invariant systems, explicit expressions can be written for each configuration and more specifically for the Gaussian potential, we obtain the large $N$ expansion ('t Hooft expansion) and the so-called BMN limit.Comment: latex BMN.tex, 7 files, 6 figures, 30 pages (v2 for spelling mistake and added reference) [http://www-spht.cea.fr/articles/T05/174

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.Comment: 58 pages; Acknowledgements added; small corrections in appendix A; minor changes & Note Adde

Defining Rules for Kinematic Shapes with Variable Spatial Relations

Designing mechanisms can be a challenging problem, because the underlying kinematics involved are typically not intuitively incorporated into common techniques for design representation. Kinematic shapes and kinematic grammars build on the shape grammar and making grammar formalisms to enable a visually intuitive approach to model and explore mechanisms. With reference to the lower kinematic pairs this paper introduces kinematic shapes. These are connected shapes with parts which have variable spatial relations that account for the relative motion of the parts. The paper considers how such shapes can be defined, the role of elements shared by connected parts, and the motions that result. It also considers how kinematic shape rules can be employed to generate and explore the motion of mechanisms

On the sub-micron aerosol size distribution in a coastal-rural site at El Arenosillo Station (SW – Spain)

This study focuses on the analysis of the sub-micron aerosol characteristics at El Arenosillo Station, a rural and coastal environment in South-western Spain between 1 August 2004 and 31 July 2006 (594 days). The mean total concentration (<i>N</i><sub>T</sub>) was 8660 cm<sup>−3</sup> and the mean concentrations in the nucleation (<i>N</i><sub>NUC</sub>), Aitken (<i>N</i><sub>AIT</sub>) and accumulation (<i>N</i><sub>ACC</sub>) particle size ranges were 2830 cm<sup>−3</sup>, 4110 cm<sup>−3</sup> and 1720 cm<sup>−3</sup>, respectively. Median size distribution was characterised by a single-modal fit, with a geometric diameter, median number concentration and geometric standard deviation of 60 nm, 5390 cm<sup>−3</sup> and 2.31, respectively. Characterisation of primary emissions, secondary particle formation, changes to meteorology and long-term transport has been necessary to understand the seasonal and annual variability of the total and modal particle concentration. Number concentrations exhibited a diurnal pattern with maximum concentrations around noon. This was governed by the concentrations of the nucleation and Aitken modes during the warm seasons and only by the nucleation mode during the cold seasons. Similar monthly mean total concentrations were observed throughout the year due to a clear inverse variation between the monthly mean <i>N</i><sub>NUC</sub> and <i>N</i><sub>ACC</sub>. It was related to the impact of desert dust and continental air masses on the monthly mean particle levels. These air masses were associated with high values of <i>N</i><sub>ACC</sub> which suppressed the new particle formation (decreasing <i>N</i><sub>NUC</sub>). Each day was classified according to a land breeze flow or a synoptic pattern influence. The median size distribution for desert dust and continental aerosol was dominated by the Aitken and accumulation modes, and marine air masses were dominated by the nucleation and Aitken modes. Particles moved offshore due to the land breeze and had an impact on the particle burden at noon, especially when the wind was blowing from the NW sector in the morning during summer time. This increased <i>N</i><sub>NUC</sub> and <i>N</i><sub>AIT</sub> by factors of 3.1 and 2.4, respectively. Nucleation events with the typical "banana" shape were characterised by a mean particle nucleation rate of 0.74 cm<sup>−3</sup> s<sup>−1</sup>, a mean growth rate of 1.96 nm h<sup>−1</sup> and a mean total duration of 9.25 h (starting at 10:55 GMT and ending at 20:10 GMT). They were observed for 48 days. Other nucleation events were identified as those produced by the emissions from the industrial areas located at a distance of 35 km. They were observed for 42 days. Both nucleation events were strongly linked to the marine air mass origin

A matrix model for the topological string II: The spectral curve and mirror geometry

In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.Comment: 1+37 page