Improved Action Functionals in Non-Perturbative Quantum Gravity

Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt-Deser-Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless phi**4 theory in a Universe with Robertson-Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Lambda.Comment: Latex file. Record without file already exists on SLAC-SPIRES, and hence that record and the one for the present arxiv submission should become one record onl

Asteroseismic stellar activity relations

In asteroseismology an important diagnostic of the evolutionary status of a star is the small frequency separation which is sensitive to the gradient of the mean molecular weight in the stellar interior. It is thus interesting to discuss the classical age-activity relations in terms of this quantity. Moreover, as the photospheric magnetic field tends to suppress the amplitudes of acoustic oscillations, it is important to quantify the importance of this effect by considering various activity indicators. We propose a new class of age-activity relations that connects the Mt. Wilson $S$ index and the average scatter in the light curve with the small frequency separation and the amplitude of the p-mode oscillations. We used a Bayesian inference to compute the posterior probability of various empirical laws for a sample of 19 solar-like active stars observed by the Kepler telescope. We demonstrate the presence of a clear correlation between the Mt. Wilson $S$ index and the relative age of the stars as indicated by the small frequency separation, as well as an anti-correlation between the $S$ index and the oscillation amplitudes. We argue that the average activity level of the stars shows a stronger correlation with the small frequency separation than with the absolute age that is often considered in the literature. The phenomenological laws discovered in this paper have the potential to become new important diagnostics to link stellar evolution theory with the dynamics of global magnetic fields. In particular we argue that the relation between the Mt. Wilson $S$ index and the oscillation amplitudes is in good agreement with the findings of direct numerical simulations of magneto-convection.Comment: 5 pages, 4 figures, 2 tables. Accepted for publication in A&

Long time dynamics of highly concentrated solitary waves for the nonlinear Schroedinger equation

In this paper we study the behavior of solutions of a nonlinear Schroedinger equation in presence of an external potential, which is allowed to be singular at one point. We show that the solution behaves like a solitary wave for long time even if we start from a unstable solitary wave, and its dynamics coincide with that of a classical particle evolving according to a natural effective Hamiltonian

On the spectrum of the transfer operators of a one-parameter family with intermittency transition

We study the transfer operators for a family $F_r:[0,1] \to [0,1]$ depending on the parameter $r\in [0,1]$, which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a suitable Hilbert space, we can define a family of infinite matrices associated to the operators and study their spectrum by numerical methods.Comment: 6 pages, 3 figure

Analysis of the Two Isoforms of the Human Alkyl Adenine DNA Glycosylase (HAAG) Gene: A Comparative Study of its Isoforms, its Protein and its Resistance to DNA Damage Agents

This study was conducted at the University of Massachusetts Medical Center in the Volkert laboratory. Human alkyl adenine DNA glycosylase (hAAG) is a DNA repair enzyme that repairs alkylated DNA bases. hAAG was cloned in 1991 and a second isoform was classified in 1994. The difference between the two isoforms of hAAG is an alternate spliced first exon. Both isoforms of the hAAG gene were present in the Volkert laboratory collection, however the second isoform (hAAG-2) was phenotypically different than the first and became the first focus of this study. Using the improperly functioning isoform as a template, and constructing a 5\u27 primer with the identical upstream sequence as the functioning isoform (hAAG-1), a phenotypically similar gene was constructed by PCR. The new isoform (hAAG-2) was cloned into an expression vector and its activity as a DNA repair agent was studied. A second version of hAAG-2 was also constructed, incorporating a histidine tag for protein purification and identification purposes. Efforts included using the ability of hAAG to complement glycosylase deficient alkA tagA E. coli double mutant strains to assess and to compare the ability of the two isoforms of hAAG and to determine if the histidine tag affected function. The ability of hAAG to rescue cells from exposure to a variety of DNA damaging agents was studied by inducing each isoform and analyzing the sensitivity of the cells to increased doses of DNA damaging agents. Both hAAG-1 and hAAG-2 were able to restore the wild type resistance of the alkA and tag genes when exposed to the alkylating agents MNNG and MMS. In order to study the ability of hAAG to repair alkyl lesions larger than methyl groups, it was necessary to inactivate the uvrA dependent nucleotide excision repair gene. In E. coli, methyl lesions are repaired primarily by glycosylases, while nucleotide excision repairs bulky lesions. Thus, in order to detect hAAG activity on these types of damage, it was necessary to inactivate the bacterial uvrA gene. Each isoform of hAAG was transformed into a triple mutant strain deficient in alkA tagA and uvrA, then exposed to CNU, BCNU, and Mitomycin C. Each of these DNA damaging agent caused increased toxicity in the presence of hAAG. hAAG-1 expressed in the alkA tag double mutant strain was exposed to Mitomycin C and showed greater resistance than hAAG-1 expressed in the alkA tag uvrA triple mutant. In fact, in the nucleotide excision proficient strain, expression increased Mitomycin C resistance above that seen in the control, suggesting that glycosylase activity may function in a partnership with nucleotide excision repair and that the two isoforms of hAAG have subtle differences. An ompT protease knockout host strain was constructed using P1-transduction and used to examine protein products. hAAG-2 was inserted into the pBlueScript plasmid so that the gene could be regulated by the T7 promoter for use beyond the scope of this thesis. A protein synthesis time course assay was conducted to determine the expression levels of hAAG-1 and hAAG-2 when induced by IPTG. Immunoblot detection of the histidine tag was used to measure expression levels of each isoform

A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter $G$ and cosmological term $\Lambda$. In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for $G$ and $\Lambda$ near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of $G$ and $\Lambda$ near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.Comment: 10 pages, RevTex4, no figures, to appear on GR

Renormalization Group in Quantum Mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form of the action is not preserved by the flow. To cure this problem we consider a more general action than usual which is stable by the renormalization group flow. It allows us to obtain a new consistent renormalization group equation for the action.Comment: 20 page