Polynomial approximations to Bessel functions

Bessel functions appear in numerous physical problems, and play an important role in many electromagnetic scattering problems. There is no closed form expression for Bessel functions so that approximations suitable for numerical evaluation are necessary in applications. Gross [1] has derived interesting polynomial approximations to the zerothand first-order Bessel functions of the first kind for small arguments, that arise from an integral that occurs in an electromagnetic scattering problem. We study here in detail properties of these approximations. First we extend the analysis in [1] to derive corresponding polynomial approximations for Bessel functions of any integer order. Second we show that as the degree of the polynomial approximation increases, it converges to the Taylor series expansion. Third we compare the accuracy of the polynomial approximations to that of the truncated Taylor series of the same order

Image recovery from irregularly located spectral samples

Recovery of magnetic resonance images from irregular sampling sets is investigated from the point of view of moment discretization of the Fredholm equation of the first kind. The limited spatial extent of the object is known a priori and the sampling schemes considered each have mean density lower than that imposed by the Nyquist limit. The recovery formula obtained has the same form as a standard irregular sampling technique. A practical means of performing the recovery for very large data sets by utilising the block Toeplitz structure of the matrix involved is presented

Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing

The Hartley transform is a mathematical transformation which is closely related to the better known Fourier transform. The properties that differentiate the Hartley Transform from its Fourier counterpart are that the forward and the inverse transforms are identical and also that the Hartley transform of a real signal is a real function of frequency. The Whitened Hartley spectrum, which stems from the Hartley transform, is a bounded function that encapsulates the phase content of a signal. The Whitened Hartley spectrum, unlike the Fourier phase spectrum, is a function that does not suffer from discontinuities or wrapping ambiguities. An overview on how the Whitened Hartley spectrum encapsulates the phase content of a signal more efficiently compared with its Fourier counterpart as well as the reason that phase unwrapping is not necessary for the Whitened Hartley spectrum, are provided in this study. Moreover, in this study, the product–convolution relationship, the time-shift property and the power spectral density function of the Hartley transform are presented. Finally, a short-time analysis of the Whitened Hartley spectrum as well as the considerations related to the estimation of the phase spectral content of a signal via the Hartley transform, are elaborated

Partonic flow and ϕ\phi-meson production in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We present first measurements of the $\phi$-meson elliptic flow ($v_{2}(p_{T})$) and high statistics $p_{T}$ distributions for different centralities from $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at RHIC. In minimum bias collisions the $v_{2}$ of the $\phi$ meson is consistent with the trend observed for mesons. The ratio of the yields of the $\Omega$ to those of the $\phi$ as a function of transverse momentum is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/$c$, but disagrees at higher momenta. The nuclear modification factor ($R_{CP}$) of $\phi$ follows the trend observed in the $K^{0}_{S}$ mesons rather than in $\Lambda$ baryons, supporting baryon-meson scaling. Since $\phi$-mesons are made via coalescence of seemingly thermalized $s$ quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC.Comment: 6 pages, 4 figures, submit to PR

Measurement of Transverse Single-Spin Asymmetries for Di-Jet Production in Proton-Proton Collisions at s=200\sqrt{s} = 200 GeV

We report the first measurement of the opening angle distribution between pairs of jets produced in high-energy collisions of transversely polarized protons. The measurement probes (Sivers) correlations between the transverse spin orientation of a proton and the transverse momentum directions of its partons. With both beams polarized, the wide pseudorapidity ($-1 \leq \eta \leq +2$) coverage for jets permits separation of Sivers functions for the valence and sea regions. The resulting asymmetries are all consistent with zero and considerably smaller than Sivers effects observed in semi-inclusive deep inelastic scattering (SIDIS). We discuss theoretical attempts to reconcile the new results with the sizable transverse spin effects seen in SIDIS and forward hadron production in pp collisions.Comment: 6 pages total, 1 Latex file, 3 PS files with figure

Longitudinal Double-Spin Asymmetry and Cross Section for Inclusive Jet Production in Polarized Proton Collisions at √s = 200 GeV

We report a measurement of the longitudinal double-spin asymmetry ALL and the differential cross section for inclusive midrapidity jet production in polarized proton collisions at √s=200  GeV. The cross section data cover transverse momenta

Neutral kaon interferometry in Au+Au collisions at √s\u3csub\u3eNN\u3c/sub\u3e = 200 GeV

We present the first statistically meaningful results from two-Ks0 interferometry in heavy-ion collisions at √sNN = 200 GeV. A model that takes the effect of the strong interaction into account has been used to fit the measured correlation function. The effects of single and coupled channels were explored. At the mean transverse mass ⟨mT⟩ = 1.07 GeV, we obtain the values R = 4.09±0.46(stat)±0.31(sys) fm and λ=0.92±0.23(stat)±0.13(sys), where R and λ are the invariant radius and chaoticity parameters, respectively. The results are qualitatively consistent with mT systematics established with pions in a scenario characterized by a strong collective flow

Strange Baryon Resonance Production in √s\u3csub\u3eNN\u3c/sub\u3e = 200 GeV p+p and Au+Au Collisions

We report the measurements of Σ(1385) and Λ(1520) production in p+p and Au+Au collisions at √sNN=200  GeV from the STAR Collaboration. The yields and the pT spectra are presented and discussed in terms of chemical and thermal freeze-out conditions and compared to model predictions. Thermal and microscopic models do not adequately describe the yields of all the resonances produced in central Au+Au collisions. Our results indicate that there may be a time span between chemical and thermal freeze-out during which elastic hadronic interactions occur

Energy dependence of charged pion, proton and anti-proton transverse momentum spectra for Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV

We study the energy dependence of the transverse momentum (pT) spectra for charged pions, protons and anti-protons for Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV. Data are presented at mid-rapidity (|y| < 0.5) for 0.2 < pT < 12 GeV/c. In the intermediate pT region (2 < pT < 6 GeV/c), the nuclear modification factor is higher at 62.4 GeV than at 200 GeV, while at higher pT (pT >7 GeV/c) the modification is similar for both energies. The p/pi+ and pbar/pi- ratios for central collisions at \sqrt{s_NN} = 62.4 GeV peak at pT ~ 2 GeV/c. In the pT range where recombination is expected to dominate, the p/pi+ ratios at 62.4 GeV are larger than at 200 GeV, while the pbar/pi- ratios are smaller. For pT > 2 GeV/c, the pbar/pi- ratios at the two beam energies are independent of pT and centrality indicating that the dependence of the pbar/pi- ratio on pT does not change between 62.4 and 200 GeV. These findings challenge various models incorporating jet quenching and/or constituent quark coalescence.Comment: 19 pages and 6 figure

Iterative projection algorithms for solving inverse problems

Inverse problems abound in the ocean sciences, as they do in almost every area of science and technology. Solutions to inverse problems are notoriously difficult, computationally expensive, and noise sensitive. Iterative projection algorithms have proved to he particularly useful for solving some image reconstruction problem with incomplete data. These techniques are outlined with a view to promoting their application in the ocean sciences