The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime

The renormalization group (RG) is used to study the asymptotically free $\phi_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop effective potential as well as its explicit forms in the case of strong gravitational fields and strong scalar fields. Using zeta function techniques, the one-loop and corresponding RG improved vacuum energies are found for the Kaluza-Klein backgrounds $R^4\times S^1\times S^1$ and $R^4\times S^2$. They are given in terms of exponentially convergent series, appropriate for numerical calculations. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification can be qualitatively different when the RG improved energy is used.Comment: LaTeX, 15 pages, 4 figure

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

PYROELECTRIC PROPERTIES OF CHIRAL SMECTIC PHASES

On a mesuré la réponse pyroélectrique des cristaux liquides ferroélectriques (L-p-décyloxy-, L-p-nonyloxybenzilidène p'-amino cinnamate de méthyl-2 butyle et mélange) à des impulsions thermiques de durées de 2 x 10-4 et 3 x 10-8 s. A partir des données obtenues on a calculé les variations du coefficient pyroélectrique γ(T) en fonction de la température. La dispersion de γ et de la polarisation spontanée Ps en fonction de la fréquence a été obtenue et est en accord avec les mesures de dispersion de la susceptibilité diélectrique pour des fréquences dans la gamme 104-2 x 105 Hz. On a mesuré le temps de relaxation de la polarisation spontanée (τ) et on a trouvé une divergence de τ près de la température de transition smectique C-smectique A. On a aussi montré que des impuretés dipolaires ont une influence visible sur les valeurs de γmax et de Pmaxs pour les cristaux étudiés.The temperature dependences of the pyroelectric coefficient γ(T) of ferroelectric liquid crystalline L-p-decyloxy- and L-p-nonyloxybenzylidene-p'-amino-2-methylbutylcinnamate and their mixture were calculated from the measurements of their responses to heat pulses with durations of 2 x 10-4 and 3 x 10-8 s. The frequency dispersion of γ and the spontaneous polarization Ps was discovered which is consistent with the corresponding dispersion of dielectric permittivity over a frequency range 104-2 x 105 Hz. The direct measurements of the relaxation time for spontaneous polarization (τ) were performed and sharp increase in τ near the SmC-SmA phase transition was observed. The effect of dipolar admixtures on γmax and Pmaxs was also discussed

Key parameters for size- and shape-controlled synthesis of vaterite particles

Calcium carbonate (CaCO3) has attracted scientific attention due to its essential role in both inorganic and bioorganic chemistry. Vaterite is the least thermodynamically stable CaCO3 polymorph and has elicited great interest as an advanced biomaterial for tissue engineering, drug delivery, and a broad range of personal care products. Numerous methods of vaterite particle synthesis with different sizes and morphologies, have highlighted the submicron porous particles of spherical or ellipsoidal shape as the most useful ones. In this regard, the current study is aimed at development of a reliable method for synthesis of such structures. Herein, submicron vaterite partitles are synthesized by dropwise precipitation from saturated sodium carbonate and calcium chloride solutions in the presence of ethylene glycol while manipulating the concentration ratios of reagents. We demonstrate that our novel technique named "dropwise precipitation" leads to changing calcium concentrations in the reaction solution at each moment affecting the crystallization process. The proposed technique allows routine obtainment of vaterite particles of a required shape, either spherical or ellipsoidal, and a controlled size in the range from 0.4 to 2.7 mu m and (0.4 x 0.7) to (0.7 x 1.1) mu m, respectively. The key parameters influencing the size, shape, and percent of vaterite fraction for synthesized CaCO3 particles are discussed