Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\mathbb{R}^N\setminus\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is $L$-harmonic, $Lu=0$, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behavior can be presented in a unified way through a suitable global approximation

ON GAUGINO CONDENSATION WITH FIELD-DEPENDENT GAUGE COUPLINGS

We study in detail gaugino condensation in globally and locally supersymmetric Yang-Mills theories. We focus on models for which gauge-neutral matter couples to the gauge bosons only through nonminimal gauge kinetic terms, for the cases of one and several condensing gauge groups. Using only symmetry arguments, the low-energy expansion, and general properties of supersymmetry, we compute the low energy Wilson action, as well as the (2PI) effective action for the composite {\it classical} superfield U\equiv\langle \Tr\WW \rangle, with $W_\alpha$ the supersymmetric gauge field strength. The 2PI effective action provides a firmer foundation for the approach of Veneziano and Yankielowicz, who treated the composite superfield, $U$, as a quantum degree of freedom. We show how to rederive the Wilson action by minimizing the 2PI action with respect to $U$. We determine, in both formulations and for global and local supersymmetry, the effective superpotential, $W$, the non-perturbative contributions to the low-energy K\"ahler potential $K$, and the leading higher supercovariant derivative terms in an expansion in inverse powers of the condensation scale. As an application of our results we include the string moduli dependence of the super- and K\"ahler potentials for simple orbifold models.Comment: 54 pages, plain te

Brans-Dicke-type theories and avoidance of the cosmological singularity

We tudy flat Friedmann-Robertson-Walker cosmology in Brans-Dicke-type theories of gravitation with minimal coupling between the scalar field and the matter fields in the Einstein frame (general relativity with an extra scalar field) for arbitrary values of the Brans-Dicke parameter $\omega>-{3/2}$. It is shown that the cosmological singularity occuring in the Einstein frame formulation of this theory is removed in the Jordan frame in the range $-{3/2}<\omega<\leq-{4/3}$. This result is interpreted in the ligth of a viewpoint (first presented in reference gr-qc/9905071) asserting that both Jordan frame and Einstein frame formulations of general relativity are physically equivalent. The implications of the obtained result for string theory are outlined.Comment: 9 pages, LaTeX, no figures. Improved version accepted for publication in PR

Radiative Electroweak Symmetry-Breaking Revisited

In the absence of a tree-level scalar-field mass, renormalization-group methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series within the effective potential for $SU(2)\times U(1)$ electroweak symmetry. This improvement of the effective potential function is seen to reduce residual dependence on the renormalization mass scale. The all-orders summation of leading logarithm terms involving the dominant three couplings contributing to radiative corrections is suggestive of a potential characterized by a plausible Higgs boson mass of 216 GeV. However, the tree potential's local minimum at $\phi =0$ is restored if QCD is sufficiently strong.Comment: revtex, 4 pages, 1 eps figure embedded in manuscript. Updated version contains additional comments and corrects minor error

Ion species fractions in the far-field plume of a high-specific impulse Hall thruster

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76418/1/AIAA-2003-5001-731.pd

Dual geometries and spacetime singularities

The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity). This dual representation provides a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.Comment: 11 pages, LaTeX, no figures, version accepted for publication in PR