New sum rule identities and duality relation for the Potts nn-point correlation function

It is shown that certain sum rule identities exist which relate correlation functions for $n$ Potts spins on the boundary of a planar lattice for $n\geq 4$. Explicit expressions of the identities are obtained for $n=4,5$. It is also shown that the identities provide the missing link needed for a complete determination of the duality relation for the $n$-point correlation function. The $n=4$ duality relation is obtained explicitly. More generally we deduce the number of correlation identities for any $n$ as well as an inversion relation and a conjecture on the general form of the duality relation.Comment: 11 pages in RevTeX, 4 PS figures, submitted to PR

Systematic study of the symmetry energy coefficient in finite nuclei

The symmetry energy coefficients in finite nuclei have been studied systematically with a covariant density functional theory (DFT) and compared with the values calculated using several available mass tables. Due to the contamination of shell effect, the nuclear symmetry energy coefficients extracted from the binding energies have large fluctuations around the nuclei with double magic numbers. The size of this contamination is shown to be smaller for the nuclei with larger isospin value. After subtracting the shell effect with the Strutinsky method, the obtained nuclear symmetry energy coefficients with different isospin values are shown to decrease smoothly with the mass number $A$ and are subsequently fitted to the relation $\dfrac{4a_{\rm sym}}{A}=\dfrac{b_v}{A}-\dfrac{b_s}{A^{4/3}}$. The resultant volume $b_v$ and surface $b_s$ coefficients from axially deformed covariant DFT calculations are $121.73$ and $197.98$ MeV respectively. The ratio $b_s/b_v=1.63$ is in good agreement with the value derived from the previous calculations with the non-relativistic Skyrme energy functionals. The coefficients $b_v$ and $b_s$ corresponding to several available mass tables are also extracted. It is shown that there is a strong linear correlation between the volume $b_v$ and surface $b_s$ coefficients and the ratios $b_s/b_v$ are in between $1.6-2.0$ for all the cases.Comment: 16 pages, 6 figure

Stochastic model of temporal changes of wind spectra in the free atmosphere

Data for wind profile spectra changes with respect to time from Cape Kennedy, Florida for the time period from 28 November 1964 to 11 May 1967 have been analyzed. A universal statistical distribution of the spectral change which encompasses all vertical wave numbers, wind speed categories, and elapsed time has been developed for the standard deviation of the time changes of detailed wind profile spectra as a function of wave number

A Three-Pole Substrate Integrated Waveguide Bandpass Filter Using New Coupling Scheme

A novel three-pole substrate integrated waveguide (SIW) bandpass filter (BPF) using new coupling scheme is proposed in this paper. Two high order degenerate modes (TE102 and TE201) of a square SIW cavity and a dominant mode (TE101) of a rectangular SIW cavity are coupled to form a three-pole SIW BPF. The coupling scheme of the structure is given and analyzed. Due to the coupling between two cavities, as well as the coupling between source and load, three transmission zeros are created in the stopband of the filter. The proposed three-pole SIW BPF is designed and fabricated. Good agreement between simulated and measured results verifies the validity of the design methodology well

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.