Study of errors in the integration of the two-body problem using generalized Sundman's anomalies

[EN] As is well known, the numerical integration of the two body problem with constant step presents problems depending on the type of coordinates chosen. It is usual that errors in Runge-Lenz's vector cause an artificial and secular precession of the periaster although the form remains symplectic, theoretically, even when using symplectic methods. Provided that it is impossible to preserve the exact form and all the constants of the problem using a numerical method, a possible option is to make a change in the variable of integration, enabling the errors in the position of the periaster and in the speed in the apoaster to be minimized for any eccentricity value between 0 and 1. The present work considers this casuistry. We provide the errors in norm infinite, of different quantities such as the Energy, the module of the Angular Moment vector and the components of Runge-Lenz's vector, for a large enough number of orbital revolutions.Lopez Orti, JA.; Marco Castillo, FJ.; Martínez Uso, MJ. (2014). Study of errors in the integration of the two-body problem using generalized Sundman's anomalies. SEMA SIMAI Springer Series. 4:105-112. doi:10.1007/978-3-319-06953-1_11S1051124Brower, D., Clemence, G.M.: Celestial Mechanics. Academic, New York (1965)Brumberg, E.V.: Length of arc as independent argument for highly eccentric orbits. Celest. Mech. 53, 323–328 (1992)Fehlberg, E., Marsall, G.C.: Classical fifth, sixth, seventh and eighth Runge–Kutta formulas with stepsize control. Technical report, NASA, R-287 (1968)Ferrándiz, J.M., Ferrer, S., Sein-Echaluce, M.L.: Generalized elliptic anomalies. Celest. Mech. 40, 315–328 (1987)Gragg, W.B.: Repeated extrapolation to the limit in the numerical solution of ordinary differential equations. SIAM J. Numer. Anal. 2, 384–403 (1965)Janin, G.: Accurate computation of highly eccentric satellite orbits. Celest. Mech. 10, 451–467 (1974)Janin, G., Bond, V.R.: The elliptic anomaly. Technical memorandum, NASA, n. 58228 (1980)Levallois, J.J., Kovalevsky, J.: Géodésie Générale, vol. 4. Eyrolles, Paris (1971)López, J.A., Agost, V., Barreda, M.: A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics. Int. J. Comput. Math. 89, 433–442 (2012)López, J.A., Marco, F.J., Martínez, M.J.: A study about the integration of the elliptical orbital motion based on a special one-parametric family of anomalies. Abstr. Appl. Anal. 2014, ID 162060, 1–11 (2014)Nacozy, P.: The intermediate anomaly. Celest. Mech. 16, 309–313 (1977)Sundman, K.: Memoire sur le probleme des trois corps. Acta Math. 36, 105–179 (1912)Tisserand, F.F.: Traité de Mecanique Celeste. Gauthier-Villars, Paris (1896)Velez, C.E., Hilinski, S.: Time transformation and Cowell’s method. Celest. Mech. 17, 83–99 (1978

Long-term wind resource assessment for small and medium-scale turbines using operational forecast data and measure-correlate-predict

Output from a state-of-the-art, 4 km resolution, operational forecast model (UK4) was investigated as a source of long-term historical reference data for wind resource assessment. The data were used to implement measure-correlate-predict (MCP) approaches at 37 sites throughout the United Kingdom (UK). The monthly and hourly linear correlation between the UK4-predicted and observed wind speeds indicates that UK4 is capable of representing the wind climate better than the nearby meteorological stations considered. Linear MCP algorithms were implemented at the same sites using reference data from UK4 and nearby meteorological stations to predict the long-term (10-year) wind resource. To obtain robust error statistics, MCP algorithms were applied using onsite measurement periods of 1-12 months initiated at 120 different starting months throughout an 11 year data record. Using linear regression MCP over 12 months, the average percentage errors in the long-term predicted mean wind speed and power density were 3.0% and 7.6% respectively, using UK4, and 2.8% and 7.9% respectively, using nearby meteorological stations. The results indicate that UK4 is highly competitive with nearby meteorological observations as an MCP reference data source. UK4 was also shown to systematically improve MCP predictions at coastal sites due to better representation of local diurnal effects

Measurement of the branching fraction for Υ(1S)→τ+τ−\Upsilon (1S) \to \tau^+ \tau^-

We have studied the leptonic decay of the $\Upsilon (1S)$ resonance into tau pairs using the CLEO II detector. A clean sample of tau pair events is identified via events containing two charged particles where exactly one of the particles is an identified electron. We find $B(\Upsilon(1S) \to \tau^+ \tau^-) = (2.61~\pm~0.12~{+0.09\atop{-0.13}})$. The result is consistent with expectations from lepton universality.Comment: 9 pages, RevTeX, two Postscript figures available upon request, CLNS 94/1297, CLEO 94-20 (submitted to Physics Letters B

Measurement of the Decay Asymmetry Parameters in Λc+→Λπ+\Lambda_c^+ \to \Lambda\pi^+ and Λc+→Σ+π0\Lambda_c^+ \to \Sigma^+\pi^0

We have measured the weak decay asymmetry parameters (\aLC ) for two \LC\ decay modes. Our measurements are \aLC = -0.94^{+0.21+0.12}_{-0.06-0.06} for the decay mode $\Lambda_c^+ \to \Lambda\pi^+$ and \aLC = -0.45\pm 0.31 \pm 0.06 for the decay mode $\Lambda_c \to \Sigma^+\pi^0$. By combining these measurements with the previously measured decay rates, we have extracted the parity-violating and parity-conserving amplitudes. These amplitudes are used to test models of nonleptonic charmed baryon decay.Comment: 11 pages including the figures. Uses REVTEX and psfig macros. Figures as uuencoded postscript. Also available as http://w4.lns.cornell.edu/public/CLNS/1995/CLNS95-1319.p

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange

Study of the B^0 Semileptonic Decay Spectrum at the Upsilon(4S) Resonance

We have made a first measurement of the lepton momentum spectrum in a sample of events enriched in neutral B's through a partial reconstruction of B0 --> D*- l+ nu. This spectrum, measured with 2.38 fb**-1 of data collected at the Upsilon(4S) resonance by the CLEO II detector, is compared directly to the inclusive lepton spectrum from all Upsilon(4S) events in the same data set. These two spectra are consistent with having the same shape above 1.5 GeV/c. From the two spectra and two other CLEO measurements, we obtain the B0 and B+ semileptonic branching fractions, b0 and b+, their ratio, and the production ratio f+-/f00 of B+ and B0 pairs at the Upsilon(4S). We report b+/b0=0.950 (+0.117-0.080) +- 0.091, b0 = (10.78 +- 0.60 +- 0.69)%, and b+ = (10.25 +- 0.57 +- 0.65)%. b+/b0 is equivalent to the ratio of charged to neutral B lifetimes, tau+/tau0.Comment: 14 page, postscript file also available at http://w4.lns.cornell.edu/public/CLN

Observation of the Ξc+\Xi_c^+ Charmed Baryon Decays to Σ+K−π+\Sigma^+ K^-\pi^+, Σ+Kˉ∗0\Sigma^+ \bar{K}^{*0}, and ΛK−π+π+\Lambda K^-\pi^+\pi^+

We have observed two new decay modes of the charmed baryon $\Xi_c^+$ into $\Sigma^+ K^-\pi^+$ and $\Sigma^+ \bar{K}^{*0}$ using data collected with the CLEO II detector. We also present the first measurement of the branching fraction for the previously observed decay mode $\Xi_c^+\to\Lambda K^-\pi^+\pi^+$. The branching fractions for these three modes relative to $\Xi_c^+\to\Xi^-\pi^+\pi^+$ are measured to be $1.18 \pm 0.26 \pm 0.17$, $0.92 \pm 0.27 \pm 0.14$, and $0.58 \pm 0.16 \pm 0.07$, respectively.Comment: 12 page uuencoded postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Conformal collider physics: Energy and charge correlations

We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision. We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers. For ${\cal N}=1$ superconformal theories the one point function for states created by the R-current or the stress tensor are determined by the two parameters $a$ and $c$ characterizing the conformal anomaly. Demanding that the measured energies are positive we get bounds on $a/c$. We also give a prescription for computing the energy and charge correlation functions in theories that have a gravity dual. The prescription amounts to probing the falling string state as it crosses the $AdS$ horizon with gravitational shock waves. In the leading, two derivative, gravity approximation the energy is uniformly distributed on the sphere at infinity, with no fluctuations. We compute the stringy corrections and we show that they lead to small, non-gaussian, fluctuations in the energy distribution. Corrections to the one point functions or antenna patterns are related to higher derivative corrections in the bulk.Comment: 73 pages, 8 figures; v2: minor changes and added references; v3: more references adde

Should science educators deal with the science/religion issue?

I begin by examining the natures of science and religion before looking at the ways in which they relate to one another. I then look at a number of case studies that centre on the relationships between science and religion, including attempts to find mechanisms for divine action in quantum theory and chaos theory, creationism, genetic engineering and the writings of Richard Dawkins. Finally, I consider some of the pedagogical issues that would need to be considered if the science/religion issue is to be addressed in the classroom. I conclude that there are increasing arguments in favour of science educators teaching about the science/religion issue. The principal reason for this is to help students better to learn science. However, such teaching makes greater demands on science educators than has generally been the case. Certain of these demands are identified and some specific suggestions are made as to how a science educator might deal with the science/religion issue. © 2008 Taylor & Francis