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

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

A new method was developed for the calculation of optimum constant admittance solutions for the minimization of the sound radiated from an arbitrary axisymmetric body. This method utilizes both the integral equation technique used in the calculation of the optimum non-constant admittance liners and the independent solution generated as a by product of these calculations. The results generated by both these methods are presented for three duct geometries: (1) a straight duct; (2) the QCSEE inlet; and (3) the QCSEE inlet less its centerbody

The phase structure of the 3-d Thirring model

We study the phase structure of the Thirring model in 3-d and find it to be compatible with the existence of a non gaussian fixed point of RG. A Finite Size Scaling argument is included in the equation of state in order to avoid the assumptions usually needed to extrapolate to the thermodynamical limit.Comment: Talk presented at LATTICE96(other models

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

Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories

A long time ago, it has been conjectured that a Hamiltonian with a potential of the form x^2+i v x^3, v real, has a real spectrum. This conjecture has been generalized to a class of so-called PT symmetric Hamiltonians and some proofs have been given. Here, we show by numerical investigation that the divergent perturbation series can be summed efficiently by an order-dependent mapping (ODM) in the whole complex plane of the coupling parameter v^2, and that some information about the location of level crossing singularities can be obtained in this way. Furthermore, we discuss to which accuracy the strong-coupling limit can be obtained from the initially weak-coupling perturbative expansion, by the ODM summation method. The basic idea of the ODM summation method is the notion of order-dependent "local" disk of convergence and analytic continuation by an order-dependent mapping of the domain of analyticity augmented by the local disk of convergence onto a circle. In the limit of vanishing local radius of convergence, which is the limit of high transformation order, convergence is demonstrated both by numerical evidence as well as by analytic estimates.Comment: 11 pages; 12 figure

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.

Branching rate expansion around annihilating random walks

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.Comment: 5 pages, 5 figure

Higher-Order Corrections to Instantons

The energy levels of the double-well potential receive, beyond perturbation theory, contributions which are non-analytic in the coupling strength; these are related to instanton effects. For example, the separation between the energies of odd- and even-parity states is given at leading order by the one-instanton contribution. However to determine the energies more accurately multi-instanton configurations have also to be taken into account. We investigate here the two-instanton contributions. First we calculate analytically higher-order corrections to multi-instanton effects. We then verify that the difference betweeen numerically determined energy eigenvalues, and the generalized Borel sum of the perturbation series can be described to very high accuracy by two-instanton contributions. We also calculate higher-order corrections to the leading factorial growth of the perturbative coefficients and show that these are consistent with analytic results for the two-instanton effect and with exact data for the first 200 perturbative coefficients.Comment: 7 pages, LaTe

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