Frequency dependent dielectric constants and its numerical computation through Kramers-Kronig relations and Hilbert transform.

The dielectric constant and loss are important (real and imaginary components) properties of interest to electrical engineers because these two parameters, among others, decide the suitability of a material for a given application. The nature of some physical important parameters is such that frequency dependent real and imaginary components cannot be specified independently from each other. The Kramers-Kronig relations provide the coupling between real and imaginary components. Occasions arise when only one of the components can be readily obtained from theoretical or experimental procedures. The mathematical technique used by Kramers-Kronig relations, which allows one component to be defined in terms of the other is Hilbert transform since &egr;\u27(o) and &egr;″(o) can be shown to be Hilbert transform pairs. The particle formation of this Hilbert transform pair is not an easy task in most instances. One cannot produce an analytical function in order to obtain its Hilbert transformation over a large frequency range. An efficient algorithm is developed to obtain the complex dielectric permittivity of materials over a large frequency range. In this thesis, the algorithm has been verified for both theoretically generated data (Debye equation) and measured data for various high temperature dielectric materials. This procedure calculates the one component of the dielectric constant from its other component by use of the Hilbert transform properties of Kramers-Kronig relation and FFT techniques. Different laboratory equipments and measuring techniques were used in this project and described in detail.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .W44. Source: Masters Abstracts International, Volume: 43-01, page: 0287. Adviser: Govinda Raju. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Measurement of direct photon production at Tevatron fixed target energies

Measurements of the production of high transverse momentum direct photons by a 515 GeV/c piminus beam and 530 and 800 GeV/c proton beams in interactions with beryllium and hydrogen targets are presented. The data span the kinematic ranges of 3.5 < p_T < 12 GeV/c in transverse momentum and 1.5 units in rapidity. The inclusive direct-photon cross sections are compared with next-to-leading-order perturbative QCD calculations and expectations based on a phenomenological parton-k_T model.Comment: RevTeX4, 23 pages, 32 figures, submitted to Phys. Rev.

Evidence for Parton kT Effects in High pT Particle Production

Inclusive pizero and direct-photon cross sections in the kinematic range 3.5 < pT < 12 GeV/c with central rapidities are presented for 530 and 800 GeV/c proton beams and a 515 GeV/c pi- beam incident on beryllium targets. Current Next-to-Leading-Order perturbative QCD calculations fail to adequately describe the data for conventional choices of scales. Kinematic distributions from these hard scattering events provide evidence that the interacting partons carry significant initial-state parton transverse momentum (kT). Incorporating these kT effects phenomenologically greatly improves the agreement between calculations and the measured cross sections.Comment: 11 pages including 6 pages of figures with caption

Production of pizero and eta mesons at large transverse momenta in pi-p and pi-Be interactions at 515 GeV/c

We present results on the production of high transverse momentum pizero and eta mesons in pi-p and pi-Be interactions at 515 GeV/c. The data span the kinematic ranges 1 < p_T < 11 GeV/c in transverse momentum and -0.75 < y < 0.75 in rapidity. The inclusive pizero cross sections are compared with next-to-leading order QCD calculations and to expectations based on a phenomenological parton-k_T model.Comment: RevTeX4, 15 pages, 15 figures, to be submitted to Phys. Rev.

Event-by-event fluctuations of the kaon to pion ratio in central Pb+Pb collisions at 158 GeV per Nucleon

We present the first measurement of fluctuations from event to event in the production of strange particles in collisions of heavy nuclei. The ratio of charged kaons to charged pions is determined for individual central Pb+Pb collisions. After accounting for the fluctuations due to detector resolution and finite number statistics we derive an upper limit on genuine non-statistical fluctuations, perhaps related to a first or second order QCD phase transition. Such fluctuations are shown to be very small.Comment: 4 pages, 2 figure

Two-proton correlations from 158 AGeV Pb+Pb central collisions

The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added about the structure on the tail of the correlation function. The systematic error is revised. To appear in Phys. Lett.

Baryon Stopping and Charged Particle Distributions in Central Pb+Pb Collisions at 158 GeV per Nucleon

Net proton and negative hadron spectra for central \PbPb collisions at 158 GeV per nucleon at the CERN SPS were measured and compared to spectra from lighter systems. Net baryon distributions were derived from those of net protons, utilizing model calculations of isospin contributions as well as data and model calculations of strange baryon distributions. Stopping (rapidity shift with respect to the beam) and mean transverse momentum \meanpt of net baryons increase with system size. The rapidity density of negative hadrons scales with the number of participant nucleons for nuclear collisions, whereas their \meanpt is independent of system size. The \meanpt dependence upon particle mass and system size is consistent with larger transverse flow velocity at midrapidity for \PbPb compared to \SS central collisions.Comment: This version accepted for publication in PRL. 4 pages, 3 figures. Typos corrected, some paragraphs expanded in response to referee comments, to better explain details of analysi

Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon

We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.Comment: 6 pages, 2 figures, submitted to Phys. Lett.

Experimental Study of the Shortest Reset Word of Random Automata

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with $n$ states and 2 input letters with high probability is sublinear with respect to $n$ and can be estimated as $1.95 n^{0.55}.