Browsing by Subject "Green function"

Now showing 1 - 7 of 7

Open Access
Asymptotics of extremal polynomials for some special cases
(2017-05) Alpan, Gökalp
We study the asymptotics of orthogonal and Chebyshev polynomials on fractals. We consider generalized Julia sets in the sense of Br uck-B uger and weakly equilibrium Cantor sets which was introduced in [62]. We give characterizations for Parreau-Widom condition and optimal smoothness of the Green function for the weakly equilibrium Cantor sets. We also show that, for small parameters, the corresponding Hausdor measure and the equilibrium measure of a set from this family are mutually absolutely continuous. We prove that the sequence of Widom-Hilbert factors for the equilibrium measure of a non-polar compact subset of R is bounded below by 1. We give a su cient condition for this sequence to be unbounded above. We suggest de nitions for the Szeg}o class and the isospectral torus for a generic subset of R
Open Access
Efficient computation of surface fields excited on a dielectric-coated circular cylinder
(IEEE, 2000-10) Erturk, V. B.; Rojas, R. G.
An efficient method to evaluate the surface fields excited on an electrically large dielectric-coated circular cylinder is presented. The efficiency of the method results from the circumferentially propagating representation of the Green’s function as well as its efficient numerical evaluation along a steepest descent path. The circumferentially propagating series representation of the appropriate Green’s function is obtained from its radially propagating counterpart via Watson’s transformation and then the path of integration is deformed to the steepest descent path on which the integrand decays most rapidly. Numerical results are presented that indicate that the representations obtained here are very efficient and valid even for arbitrary small separations of the source and field points. This work is especially useful in the moment-method analysis of conformal microstrip antennas where the mutual coupling effects are important.
Open Access
Extension operators for spaces of infinitely differentiable functions
(2005) Altun, Muhammed
We start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the compact set, where the functions are defined, has Markov property. In this work, we examine some model compact sets having no Markov property, but where a linear continuous extension operator exists for the space of Whitney functions given on these sets. Using local interpolation of Whitney functions we can generalize the PawÃlucki-Ple´sniak extension operator. We also give an upper bound for the Green function of domains complementary to generalized Cantor-type sets, where the Green function does not have the H¨older continuity property. And, for spaces of Whitney functions given on multidimensional Cantor-type sets, we give the conditions for the existence and non-existence of a linear continuous extension operator.
Open Access
Fano effect in a double T-shaped interferometer
(Springer, 2009) Moldoveanu, V.; Dinu, I. V.; Tanatar, Bilal
We study the coherent transport in a one-dimensional lead with two side-coupled quantum dots using the Keldysh's Green function formalism.The effect of the interdot Coulomb interaction is taken into account by computing the firstand second order contributions to the self-energy.We show that the Fano interference due to the resonance of one dotis strongly affected by the fixed parameters that characterize the second dot. If the second dot is tuned close to resonance an additionalpeak develops between the peak and dip of the Fano line shape of the current. In contrast, when the second dotis off-resonance and its occupation number is close to unity the interdot Coulomb interaction merely shifts the Fano line and no other maxima appear.The system we consider is more general than the single-dot interferometer studied experimentally by Kobayashi et al. [Phys. Rev. B 70, 035319 (2004)] and may be used for controlling quantum interference and studying decoherence effects in mesoscopic transport.
Open Access
Modeling photoelectron spectra of conjugated oligomers with time-dependent density functional theory
(American Chemical Society, 2010) Salzner, U.
With the aim of producing accurate band structures of conjugated systems by employing the states of cations, TDDFT calculations on conjugated oligomer radical cations of thiophene, furan, and pyrrole with one to eight rings were carried out. Benchmarking of density functional theory and ab initio methods on the thiophene monomer shows that the ΔSCF ionization potential (IP) is most accurate at the B3LYP/6-311G* level. Improvement of the basis set beyond 6-311G* leads to no further changes. The IP is closer to experiment at B3LYP/6-311G* than at CCSD(T)/CCPVQZ. For longer oligomers the ΔSCF IPs decrease too fast with increasing chain length with all density functionals. CCSD/6-311G* performs well if the geometries are optimized at the CCSD level. With MP2 geometries IPs decrease too fast. Peak positions in photoelectron spectra were determined by adding appropriate TDDFT excitation energies of radical cations to the ΔSCF IPs. The agreement with experiment and with Green function calculations shows that TDDFT excited states of radical cations at the B3LYP/6-311G* level are very accurate and that absorption energies can be employed to predict photoelectron spectra.
Open Access
On the Poisson representation of a function harmonic in the upper half-plane
(Springer, 2002) Gergün, S.; Ostrovskii, I.
New conditions for the validity of the Poisson representation (in usual and generalized form) for a function harmonic in the upper half-plane are obtained. These conditions differ from known ones by weaker growth restrictions inside the half-plane and stronger restrictions on the behavior on the real axis.
Open Access
Smoothness of the Green function for a special domain
(Polska Akademia Nauk, 2012) Celik, S.; Goncharov, A.
We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions gℂ\K is estimated. Markov's constants of the corresponding set are evaluated. © Instytut Matematyczny PAN, 2012.