A better large NN expansion for chiral Yukawa models

We consider the most general renormalizable chiral Yukawa model with $SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w )$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c \rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio $\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$ only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. The large $N=\sqrt{N_{c} N_{w}}$ expansion is expected to be no worse quantitatively in this model that in the purely scalar case and the $N=\infty$ limit is soluble even when the model is regularized non--perturbatively. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to $m_t \le 1~TeV$.Comment: 4p, 1 fig, latex, psfile included, sharfile distribution, Contribution to the LAT92 proceedings, Preprint, RU-92-4

Influence of enzymatic and acidic demethoxylation on structure formation in sugar containing citrus pectin gels

Aim of the present study was to investigate the impact of different demethoxylation methods and the co-occuring side effects on the molecular properties and structure formation in pectin gels. A high-methoxylated citrus pectin (HMP) was demethoxylated using either hydrochloric acid or pectin methylesterases of plant (pPME) or fungal (fPME) origin. pPME treatment causes a more block-wise distribution of free carboxyl groups, fPME or acidic treatment a random distribution. Twelve pectin samples with four different degrees of methoxylation (DM) between 62% and 41% were prepared. The gelation process was studied by oscillatory measurements. In pectin samples from pPME treatment structure formation started at higher temperature and the final gels were more elastic in comparison to pectin from the two other modifications. The impact of the block-wise distribution of the free carboxyl groups became more evident with decreasing DM. The gelling process of pectin samples with random distribution was similar independent of DM.Side effects of all demethoxylation reactions were an altered sodium ion content (high in enzymatically treated pectin, close to zero in acidic treated) and a decrease of the molecular weight with increasing degree of demethoxylation. These side effects additionally altered the gelation process and the final gel properties in different ways

Induced Gravity II: Grand Unification

As an illustration of a renormalizable, asymptotically-free model of induced gravity, we consider an $SO(10)$ gauge theory interacting with a real scalar multiplet in the adjoint representation. We show that dimensional transmutation can occur, spontaneously breaking $SO(10)$ to $SU(5){\otimes}U(1),$ while inducing the Planck mass and a positive cosmological constant, all proportional to the same scale $v$. All mass ratios are functions of the values of coupling constants at that scale. Below this scale (at which the Big Bang may occur), the model takes the usual form of Einstein-Hilbert gravity in de Sitter space plus calculable corrections. We show that there exist regions of parameter space in which the breaking results in a local minimum of the effective action, and a {\bf positive} dilaton $(\hbox{mass})^2$ from two-loop corrections associated with the conformal anomaly. Furthermore, unlike the singlet case we considered previously, some minima lie within the basin of attraction of the ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling constants also lie within the range of convergence of the Euclidean path integral, so there is hope that there will be candidates for sensible vacua. Although open questions remain concerning unitarity of all such renormalizable models of gravity, it is not obvious that, in curved backgrounds such as those considered here, unitarity is violated. In any case, any violation that may remain will be suppressed by inverse powers of the reduced Planck mass.Comment: 44 pages, 5 figures, 2 tables. v2 has new discussion concerning stability of SSB plus related appendix. Additional references added. v3 is version to be published; contains minor revision

Structure formation in sugar containing pectin gels – Influence of Ca2+ on the gelation of low-methoxylated pectin at acidic pH

A new method for the examination of the pectin gelation process is presented as a complementation of the most common determination of the gelling point (cross-over of G′ and G″) from oscillation measurements. It is based on the first derivation dG′/dt from oscillation measurements (named as structuring velocity), and defines an initial as well as a critical structuring temperature. These allow an exact determination of the start of structure formation and description of the structuring process also in gels with pre-gelation that showed no clear GP. Moreover, phases and mechanisms of gelation can be identified and structure developing rates can be calculated. The application of this method on the gelation of low-methoxylated pectin at pH 3 and 30% saccharose with different contents of Ca2+ was tested. The results show differences as well as similarities between the GP and the newly defined structuring parameters that could be partly explained by varying structuring mechanisms at different Ca-content. The initial structuring process started probably with ionic interactions (egg-box junction zones and random crosslinks) via Ca-bridges as well as hydrophobic interactions at temperatures ≥ 60 °C, it was nearly completed around 40 °C. Hydrophilic interactions (below 50 °C) and inter-dimer aggregations (below 25 °C) perhaps dominated the gelation during further cooling. In dependence on the Ca-content, two to three phases could be identified during the structuring process. The properties of the gels after cooling were tested by oscillation measurements as well as the USA-sag method. With increasing calcium content the elastic behaviour of the gels increased but they became also more and more brittle