The maximal D=7 supergravities

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and three-form tensor fields that transform into each other under an intricate set of nonabelian gauge transformations. The embedding tensor encodes the proper distribution of the degrees of freedom among these fields. In addition to the kinetic terms the vector and tensor fields contribute to the Lagrangian with a unique gauge invariant Chern-Simons term. This new formulation encompasses all possible gaugings. Examples include the sphere reductions of M theory and of the type IIA/IIB theories with gauge groups SO(5), CSO(4,1), and SO(4), respectively.Comment: 42 page

Viscous fingering of miscible slices

Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem i.e. the log-mobility ratio R, the length of the slice l, the Peclet number Pe and the ratio between transverse and axial dispersion coefficients $\epsilon$. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.Comment: 10 pages, 13 figure

Density and T1T_1 of surface and bulk spins in diamond in high magnetic field gradients

We report on surface and bulk spin density measurements of diamond, using ultra-sensitive magnetic force microscopy with magnetic field gradients up to 0.5 T/$\mu$m. At temperatures between 25 and 800 mK, we measure the shifts in the resonance frequency and quality factor of a cantilever with a micromagnet attached to it. A recently developed theoretical analysis allows us to extract a surface spin density of 0.072 spins/nm$^2$ and a bulk spin density of 0.4 ppm from this data. In addition, we find an increase of the $T_1$ time of the surface spins in high magnetic field gradients due to the suppression of spin diffusion. Our technique is applicable to a variety of samples other than diamond, and could be of interest for several research fields where surface, interface or impurity bulk spin densities are an important factor.Comment: 7 pages, 6 figure

D=11 Supermembrane wrapped on calibrated submanifolds

We construct the Hamiltonian of the D=11 Supermembrane with topological conditions on configuration space. It may be interpreted as a supermembrane theory where all configurations are wrapped in an irreducible way on a calibrated submanifold of a compact sector of the target space. We prove that the spectrum of its Hamiltonian is discrete with finite multiplicity. The construction is explicitly perfomed for a compact sector of the target space being a $2g$ dimensional flat torus and the base manifold of the Supermembrane a genus $g$ compact Riemann surface. The topological conditions on configuration space work in such a way that the $g=2$ case may be interpreted as the intersection of two D=11 Supermembranes over $g=1$ surfaces, with their corresponding topological conditions. The discreteness of the spectrum is preserved by the intersection procedure. Between the configurations satisfying the topological conditions there are minimal configurations which describe minimal immersions from the base manifold to the compact sector of the target space. They allow to map the D=11 Supermembrane with topological conditions to a symplectic noncommutative Yang-Mills theory. We analyze geometrical properties of these configurations in the context of Supermembranes and D-branes theories. We show that this class of configurations also minimizes the Hamiltonian of D-branes theories.Comment: 24 page

Modelling Entrepreneurship: Unifying the Equilibrium and Entry/Exit Approach

This research report provides a framework for modelling rates of entrepreneurship. The proposed framework may be helpful in separating the effects of a range of different variables, all possibly affecting the rate to which people choose to become or remain self-employed. We unify two approaches with respect to the modelling of the rates of entrepreneurship. The first approach is the 'equilibrium approach', seeking to estimate the long and short-run developments of the number of self-employed. The second approach is the entry/exit approach, seeking to determine the determinants of gross entry and exit rates and their interdependencies. The empirical application to Dutch data indicates how the method works and what sorts of results may be expected.

Modelling Entrepreneurship: unifying the equilibrium and entry/exit approach

Two approaches can be distinguished with respect to modelling entrepreneurship: (i) the approach focusing on the net development of the number of entrepreneurs in an equilibrium framework and (ii) the approach focusing on the entries and exits of entrepreneurs. In this paper we unify these approaches to arrive at a model explaining the equilibrium and actual number of entrepreneurs and the entry and exit rate of entrepreneurs simultaneously and consistently. We applied our unified approach to the Netherlands, using self-employment data for the 1960-99 period. We found error-correction of about 20% per year and a very different situation in terms of disequilibrium before and after the early 1980s. Periods of high unemployment appear to be characterised by both high entry and high exit rates.

On Some Stability Properties of Compactified D=11 Supermembranes

We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{1}\times S^{1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.Comment: 12 pages,Latex2e lamuphys, Invited talk at International Seminar "Supersymetry and Quantum Symmetries", Dubn

The role and value of water in natural capital restoration on the Agulhas Plain

The Agulhas Plain is a low-lying coastal area within the Cape Floristic Region classified as one of the six plant kingdoms of the world. The area is heavily invaded by alien vegetation that infringes upon the sustainable supply of ecosystem goods and services provided by the native fynbos vegetation. Natural capital restoration is expected to recover the supply of ecosystem goods and services, and in particular to increase the amount of water available for consumption. The study conducts cost-benefit analyses to assess whether alien clearing and restoration would add value to the Agulhas Plain. The analyses indicate that the cost of alien clearing and restoration in the area cannot be justified if the additional water released holds no benefit to the Plain. A brief assessment shows that the actual average value of water on the Agulhas Plain, as estimated by other studies, is higher than the economic cost of making the water available through alien clearing and restoration. Thus this would make alien clearing and restoration economically justified.Cost-benefit analysis, Invasive vegetation, Natural capital restoration, Water

A note on the Seiberg-Witten solution of N=2 Super Yang-Mills Theory

We examine the Seiberg-Witten treatment of N=2 super Yang-Mills theory, and note that in the strong coupling region of moduli space, some massive particle excitations appear to have negative norm. We discuss the significance of our observation.Comment: 4 pages, latex, no figures. The discussion has been revise

Spectral properties in supersymmetric matrix models

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.Comment: 40 pages, 5 figure