Kinematics effects of atmospheric friction in spacecraft flybys

[EN] Gravity assist manoeuvres are one of the most successful techniques in astrodynamics. In these trajectories the spacecraft comes very close to the surface of the Earth, or other Solar system planets or moons, and, as a consequence, it experiences the effect of atmospheric friction by the outer layers of the Earth¿s atmosphere or ionosphere. In this paper we analyze a standard atmospheric model to estimate the density profile during the two Galileo flybys, the NEAR and the Juno flyby. We show that, even allowing for a margin of uncertainty in the spacecraft cross-section and the drag coefficient, the observed 8 mm/s anomalous velocity decrease during the second Galileo flyby of December 8th 1992 cannot be attributed only to atmospheric friction. On the other hand, for perigees on the border between the thermosphere and the exosphere the friction only accounts for a fraction of a millimeter per second in the final asymptotic velocity. 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.Acedo Rodríguez, L. (2017). Kinematics effects of atmospheric friction in spacecraft flybys. Advances in Space Research. 59(7):1715-1723. doi:10.1016/j.asr.2017.01.008S1715172359

Quantum Mechanics of the Solar System

[EN] According to the correspondence principle, as formulated by Bohr, both in the old and the modern quantum theory, the classical limit should be recovered for large values of the quantum numbers in any quantum system. However, this classical limit of quantum theory is not so straightforward as in the interface of other generalizations of classical mechanics and other domains. In particular, relativistic kinematics and mechanics reduce to Newtonian equations by simple algebra in the case of bodies moving with small velocities compared to the speed of light in vacuum. In this paper we consider the correspondence limit to the two-body problem in gravitational physics, the limit in which both the principal and the angular quantum numbers, N, L are very large. In this limit, we compare with the classical elliptical orbits and we find that the macroscopic coherent quantum states correspond to the statistical average of every classical state compatible with conservation laws for the total energy and angular momentum. We also consider the perturbed Kepler problem with a central perturbation force proportional to the inverse of the cube of the distance to the central body. The exact solution for the quantum eigenstates shows that the first order perturbation to the energy eigenvalues are obtained classically as the temporal orbital average of the perturbation potential.Acedo Rodríguez, L. (2014). Quantum Mechanics of the Solar System. Latin-American Journal of Physics Education. 8(2):255-262. http://hdl.handle.net/10251/81331S2552628

Brain oscillations in a random neural network

[EN] It is well-known that rhythmic patterns of neural activity appear both in the normal and abnormal function of the brain. Apart from the standard bands of electric oscillations found in the electroencephalogram (EEG): from alpha (8-12 Hz) to delta waves (1-4 Hz), synchronized firing of neural populations characterize some complex cognitive functions such as memory, attention and consciousness. In the case of electrocardiogram (ECG) it is usually recognized that oscillations can be understood as the limit cycle of an underlying non-linear process in heart dynamics. However, the situation is not so clear for EEG and the origin and purpose of neural oscillations are still the subject of a heated debate. Our model is a version of the standard SIRS model from epidemiology in which susceptible, infected and recovered sites represent quiescent, firing and refractory neurons, respectively. Here we show that, in a SIRS random network epidemic model for neural activity, self-sustained oscillations appear in a restricted parameter region of the transition probabilities. This could explain the role of synchronized oscillations as a discriminant process for internal or external stimuli in brain dynamics. (C) 2011 Elsevier Ltd. All rights reserved.This work was supported by grant from the Universidad Politecnica de Valencia PAID-06-09 ref: 2588 and FIS Research Grant PI10/01433 from the Instituto de Salud Carlos III.Acedo Rodríguez, L.; Moraño Fernández, JA. (2013). Brain oscillations in a random neural network. Mathematical and Computer Modelling. 57(7-8):1768-1772. https://doi.org/10.1016/j.mcm.2011.11.02817681772577-

Electromagnetic waves in a uniform gravitational field and Planck's postulate

The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earths surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The resulting gravitational time dilation near these masses gives rise to a frequency change of any periodic process, including electromagnetic oscillations as the wave propagates across the gravitational field. This phenomenon can be tackled with classical electrodynamics assuming a curved spacetime background and Maxwells equations in a generally covariant form. In this paper, we show that in a classical field theoretical context the gravitational redshift can be interpreted as the propagation of electromagnetic waves in a medium with corresponding conductivity ¿ = g/(¿ 0c 3), where g is the gravitational acceleration and ¿ 0 is the vacuum magnetic permeability. Moreover, the energy density of the wave remains proportional to its frequency in agreement with Plancks postulate. © 2012 IOP Publishing Ltd.Acedo Rodríguez, L.; Tung, MM. (2012). Electromagnetic waves in a uniform gravitational field and Planck's postulate. European Journal of Physics. 33(5):1073-1082. doi:10.1088/0143-0807/33/5/1073S10731082335Pound, R. V., & Rebka, G. A. (1959). Gravitational Red-Shift in Nuclear Resonance. Physical Review Letters, 3(9), 439-441. doi:10.1103/physrevlett.3.439Okun, L. B., Selivanov, K. G., & Telegdi, V. L. (2000). On the interpretation of the redshift in a static gravitational field. American Journal of Physics, 68(2), 115-119. doi:10.1119/1.19382Vessot, R. F. C., Levine, M. W., Mattison, E. M., Blomberg, E. L., Hoffman, T. E., Nystrom, G. U., … Wills, F. D. (1980). Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser. Physical Review Letters, 45(26), 2081-2084. doi:10.1103/physrevlett.45.2081Schaffer, S. (1979). John Michell and Black Holes. Journal for the History of Astronomy, 10(1), 42-43. doi:10.1177/002182867901000104Desloge, E. A. (1989). Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field. American Journal of Physics, 57(12), 1121-1125. doi:10.1119/1.15802Desloge, E. A. (1990). The gravitational red shift in a uniform field. American Journal of Physics, 58(9), 856-858. doi:10.1119/1.16349Kobakhidze, A. (2011). Gravity is not an entropic force. Physical Review D, 83(2). doi:10.1103/physrevd.83.02150

The Flyby Anomaly in an Extended Whitehead’s Theory

In this paper, we consider an extended version of Whitehead s theory of gravity in connection with the flyby anomaly. Whitehead s theory is a linear approximation defined in a background Minkowski spacetime, which gives the same solutions as standard general relativity for the Schwarzschild and Kerr metrics cast in Kerr Schild coordinates. For a long time and because it gives the same results for the three classical tests perihelion advance, light bending and gravitational redshift it was considered a viable alternative to general relativity, but as it is really a linear approximation, it fails in more stringent tests. The model considered in this paper is a formal generalization of Whitehead s theory, including all possible bilinear forms. In the resulting theory, a circulating vector field of force in the low velocities approximation for a rotating planet is deduced, in addition to Newtonian gravity. This extra force gives rise to small variations in the asymptotic velocities of flybys around the Earth to be compared to the recently reported flyby anomaly.Acedo Rodríguez, L. (2015). The Flyby Anomaly in an Extended Whitehead’s Theory. Galaxies. 3(3):113-128. doi:10.3390/galaxies3030113S11312833A Generalized Whiteheadian Theory of Gravity: The Kerr Solution, unpublished paper, 1986 http://www.ctr4process.org/publications/ProcessStudies/PSS/2004-6-Russell-Wasserman-A_Generalized_Whiteheadian_Theory _of_Gravity.pdfKerr, R. P., & Schild, A. (1965). Some algebraically degenerate solutions of Einstein’s gravitational field equations. Proceedings of Symposia in Applied Mathematics, 199-209. doi:10.1090/psapm/017/0216846Shapiro, I. I. (1964). Fourth Test of General Relativity. Physical Review Letters, 13(26), 789-791. doi:10.1103/physrevlett.13.789Everitt, C. W. F., DeBra, D. B., Parkinson, B. W., Turneaure, J. P., Conklin, J. W., Heifetz, M. I., … Wang, S. (2011). Gravity Probe B: Final Results of a Space Experiment to Test General Relativity. Physical Review Letters, 106(22). doi:10.1103/physrevlett.106.221101Everitt, C. W. F., Adams, M., Bencze, W., Buchman, S., Clarke, B., Conklin, J. W., … Worden, P. W. (2009). Gravity Probe B Data Analysis. Space Science Reviews, 148(1-4), 53-69. doi:10.1007/s11214-009-9524-7Gibbons, G., & Will, C. M. (2008). On the multiple deaths of Whitehead’s theory of gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 39(1), 41-61. doi:10.1016/j.shpsb.2007.04.004Bain, J. (1998). Whitehead’s Theory of Gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 29(4), 547-574. doi:10.1016/s1355-2198(98)00022-7Reinhardt, M., & Rosenblum, A. (1974). Whitehead contra Einstein. Physics Letters A, 48(2), 115-116. doi:10.1016/0375-9601(74)90425-3Hunter, A., & Fowler, A. (1934). The Solar Limb Effect. Monthly Notices of the Royal Astronomical Society, 94(7), 594-602. doi:10.1093/mnras/94.7.594Adam, M. G., Ibbetson, P. A., & Petford, A. D. (1976). The Solar Limb Effect: Observations of Line Contours and Line Shifts. Monthly Notices of the Royal Astronomical Society, 177(3), 687-708. doi:10.1093/mnras/177.3.687Anderson, J. D., Campbell, J. K., Ekelund, J. E., Ellis, J., & Jordan, J. F. (2008). Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth. Physical Review Letters, 100(9). doi:10.1103/physrevlett.100.091102Iorio, L. (2015). Gravitational anomalies in the solar system? International Journal of Modern Physics D, 24(06), 1530015. doi:10.1142/s0218271815300153Poincaré, M. H. (1906). Sur la dynamique de l’électron. Rendiconti del Circolo matematico di Palermo, 21(1), 129-175. doi:10.1007/bf03013466Carlip, S. (2000). Aberration and the speed of gravity. Physics Letters A, 267(2-3), 81-87. doi:10.1016/s0375-9601(00)00101-8A new look inside the theory of the linear approximation: Gravity assists and Flybys http://www.lluisbel.com/upload/OnHold/FlyBys.pdfChapront, J., Chapront-Touzé, M., & Francou, G. (2002). A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements. Astronomy & Astrophysics, 387(2), 700-709. doi:10.1051/0004-6361:20020420DE430 Lunar Orbit, Physical Librations, and Surface Coordinates http://proba2.sidc.be/aux/data/spice/docs/DE430_Lunar_Ephemeris_and_Orientation.pdfAdler, S. L. (2009). Can the flyby anomaly be attributed to earth-bound dark matter? Physical Review D, 79(2). doi:10.1103/physrevd.79.023505Pinheiro, M. J. (2014). The flyby anomaly and the effect of a topological torsion current. Physics Letters A, 378(41), 3007-3011. doi:10.1016/j.physleta.2014.09.003Acedo, L. (2014). The flyby anomaly: A case for strong gravitomagnetism? Advances in Space Research, 54(4), 788-796. doi:10.1016/j.asr.2014.04.014Iorio, L. (2014). A flyby anomaly for Juno? Not from standard physics. Advances in Space Research, 54(11), 2441-2445. doi:10.1016/j.asr.2014.06.035Iorio, L. (2009). The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly. Scholarly Research Exchange, 2009, 1-8. doi:10.3814/2009/807695Ciufolini, I., Paolozzi, A., Koenig, R., Pavlis, E. C., Ries, J., Matzner, R., … Paris, C. (2013). Fundamental Physics and General Relativity with the LARES and LAGEOS satellites. Nuclear Physics B - Proceedings Supplements, 243-244, 180-193. doi:10.1016/j.nuclphysbps.2013.09.005Ciufolini, I., Paolozzi, A., Pavlis, E., Ries, J., Gurzadyan, V., Koenig, R., … Sindoni, G. (2012). Testing General Relativity and gravitational physics using the LARES satellite. The European Physical Journal Plus, 127(11). doi:10.1140/epjp/i2012-12133-8Renzetti, G. (2012). Are higher degree even zonals really harmful for the LARES/LAGEOS frame-dragging experiment? Canadian Journal of Physics, 90(9), 883-888. doi:10.1139/p2012-081Renzetti, G. (2013). First results from LARES: An analysis. New Astronomy, 23-24, 63-66. doi:10.1016/j.newast.2013.03.001Renzetti, G. (2014). Some reflections on the Lageos frame-dragging experiment in view of recent data analyses. New Astronomy, 29, 25-27. doi:10.1016/j.newast.2013.10.008Iorio, L., Luca Ruggiero, M., & Corda, C. (2013). Novel considerations about the error budget of the LAGEOS-based tests of frame-dragging with GRACE geopotential models. Acta Astronautica, 91, 141-148. doi:10.1016/j.actaastro.2013.06.002Iorio, L., Lichtenegger, H. I. M., Ruggiero, M. L., & Corda, C. (2010). Phenomenology of the Lense-Thirring effect in the solar system. Astrophysics and Space Science, 331(2), 351-395. doi:10.1007/s10509-010-0489-5Iorio, L. (2008). An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging. Space Science Reviews, 148(1-4), 363-381. doi:10.1007/s11214-008-9478-1Páramos, J., & Hechenblaikner, G. (2013). Probing the flyby anomaly with the future STE-QUEST mission. Planetary and Space Science, 79-80, 76-81. doi:10.1016/j.pss.2013.02.005Iorio, L. (2010). Juno, the angular momentum of Jupiter and the Lense–Thirring effect. New Astronomy, 15(6), 554-560. doi:10.1016/j.newast.2010.01.004Tommei, G., Dimare, L., Serra, D., & Milani, A. (2014). On the Juno radio science experiment: models, algorithms and sensitivity analysis. Monthly Notices of the Royal Astronomical Society, 446(3), 3089-3099. doi:10.1093/mnras/stu2328Helled, R., Anderson, J. D., Schubert, G., & Stevenson, D. J. (2011). Jupiter’s moment of inertia: A possible determination by Juno. Icarus, 216(2), 440-448. doi:10.1016/j.icarus.2011.09.016The Determination of Jupiter’s Angular Momentum from the Lense-Thirring Precession of the Juno Spacecraft http://adsabs.harvard.edu/abs/2011AGUFM.P41B1620FIorio, L. (2013). A possible new test of general relativity with Juno. Classical and Quantum Gravity, 30(19), 195011. doi:10.1088/0264-9381/30/19/19501

Mathematical Modelling in Engineering & Human Behaviour 2018

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods

Aportaciones a la corología del género Quercus en el Sistema Ibérico meridional

Se aportan citas de varios taxones del género Quercus poco conocidos o novedosos en el extremo meridional del Sistema Ibérico.SUMMARY: New records of several rare taxa of the genus Quercus found in the southern extreme of the Iberian Mountains are here reported

The challenge of modelling aggregated human behaviour

Mathematical modelling is a blooming area of applied mathematics, and it is not yet sixty years old. At its beginning, engineers were the main practitioners of this new area of mathematics, developing mathematical models for solving engineering problems in natural sciences. More recently, financial engineering is dealing with mathematical models based on market behaviour, where implicitly human behaviour is involved in an aggregated way, through the dynamic change of the underlying asset price. In the recent past of the conference (Mathematical Modelling in Engineering & Human Behaviour), mathematical modelling of social behaviour, such as addictions, social disorders, or educational achievement, has emerged.Jódar Sánchez, LA.; Cortés, J.; Acedo Rodríguez, L. (2013). The challenge of modelling aggregated human behaviour. Mathematical and Computer Modelling. 57(7-8):1617-1618. doi:10.1016/j.mcm.2012.05.002S16171618577-