Development of an analytical technique for the optimization of jet engine and duct acoustic liners

A special integral representation of the external solutions of the Helmholtz equation is described. The analytical technique developed for the generation of the optimum acoustic admittance for an arbitrary axisymmetric body is also presented along with some numerical procedures and some preliminary results for a straight duct

Self-Consistent Theory of Normal-to-Superconducting Transition

I study the normal-to-superconducting (NS) transition within the Ginzburg-Landau (GL) model, taking into account the fluctuations in the $m$-component complex order parameter \psi\a and the vector potential $\vec A$ in the arbitrary dimension $d$, for any $m$. I find that the transition is of second-order and that the previous conclusion of the fluctuation-driven first-order transition is an artifact of the breakdown of the \eps-expansion and the inaccuracy of the $1/m$-expansion for physical values \eps=1, $m=1$. I compute the anomalous $\eta(d,m)$ exponent at the NS transition, and find $\eta (3,1)\approx-0.38$. In the $m\to\infty$ limit, $\eta(d,m)$ becomes exact and agrees with the $1/m$-expansion. Near $d=4$ the theory is also in good agreement with the perturbative \eps-expansion results for $m>183$ and provides a sensible interpolation formula for arbitrary $d$ and $m$.Comment: 9 pages, TeX + harvmac.tex (included), 2 figures and hard copies are available from [email protected] To appear in Europhysics Letters, January, 199

Critical exponents of the O(N) model in the infrared limit from functional renormalization

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.Comment: final version, 7 pages 7 figures, to appear in Phys. Rev.

The anomalous Cepheid XZ Ceti

XZ Ceti is the only known anomalous Cepheid in the Galactic field. Being the nearest and brightest such variable star, a detailed study of XZ Ceti may shed light on the behaviour of anomalous Cepheids whose representatives have been mostly detected in external galaxies. CCD photometric and radial velocity observations have been obtained. The actual period and amplitude of pulsation were determined by Fourier analysis. The long time scale behaviour of the pulsation period was studied by the method of the O-C diagram using the archival Harvard photographic plates and published photometric data. XZ Ceti differs from the ordinary classical Cepheids in several respects. Its most peculiar feature is cycle-to-cycle variability of the light curve. The radial velocity phase curve is not stable either. The pulsation period is subjected to strong changes on various time scales including a very short one. The ratio of amplitudes determined from the photometric and radial velocity observations indicates that this Cepheid performs an overtone pulsation, in accord with the other known anomalous Cepheid in our Galaxy, BL Boo (V19 in the globular cluster NGC 5466). Continued observations are necessary to study the deviations from regularity, to determine their time scale, as well as to confirm binarity of XZ Ceti and to study its role in the observed peculiar behaviour.Comment: 7 pages, 4 figures. accepted for Astron. Astrophy

Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde

New applications of the renormalization group method in physics -- a brief introduction

The renormalization group method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The theme issue provides articles reviewing recent progress made using the renormalization group method in atomic, condensed matter, nuclear and particle physics. In the following we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.Comment: Introduction for a theme issue of the Phil. Trans.

Path integral regularization of pure Yang-Mills theory

In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.Comment: LaTeX file, 24 pages, improved version, to be published in Phys. Rev.