Newtonian Calculation Research Articles

General relativistic calculation of magnetic field and power loss for a misaligned pulsar

In this study, we model a pulsar as a general relativistic oblique rotator, where the oblique rotator is a rotationally deformed neutron star whose rotation and magnetic axis is inclined at an angle. The oblique rotator spins down, losing rotational energy through the magnetic poles. The magnetic field is assumed to be dipolar; however, the star has a non-zero azimuthal component due to the misalignment. The magnetic field induces an electric field for a force-free condition. The magnetic field decreases as the misalignment increases and is minimum along the equatorial plane of the star. In contrast, the electric field remains almost constant initially but decreases rapidly at a high misalignment angle. The charge separation at the star surface is qualitatively similar to that of Newtonian calculation. We find that the power loss for a general relativistic rotator is minimum for either an aligned or an orthogonal rotator, which is in contrasts with Newtonian approach of calculation where the power loss increases with an increase in the misalignment angle.

Density and viscosity of a polyol ester lubricant: Measurement and molecular dynamics simulation.

Polyol ester (POE) is the main component of many refrigeration lubricants. In this work, the density and the viscosity of a typical, pure polyol ester, pentaerythritol tetrahexanoate (PEC6), were measured over 258.15 K to 373.15 K and predicted with molecular dynamics simulations. Nonequilibrium molecular dynamics (NEMD) was employed to compute the shear viscosities for different shear rates. The Eyring model was used to fit the shear viscosities and to extrapolate to the Newtonian viscosity. A protocol was proposed to perform a NEMD-Eyring fit for a low-error, reproducible and robust Newtonian viscosity calculation. Three force fields, i.e., OPLS, LOPLS, and DREIDING, were tested in terms of their density and viscosity prediction accuracy. OPLS gave the best density prediction (within ± 0.2 %), while LOPLS showed the best viscosity prediction accuracy (within - 4 % to 20 %). This work illustrates the value of molecular simulation in predicting lubricant properties and its potential in guiding the design of POE lubricants for desired properties.

Relativistic cosmological large scale structures at one-loop

The large scale structure bispectrum in the squeezed limit couples large with small scales. Since relativity is important at large scales and non-linear loop corrections are important at small scales, the proper calculation of the observed bispectrum in this limit requires a non-linear relativistic calculation. We compute the matter bispectrum in general relativity in the weak field approximation. The calculation is as involved as existing second-order results. We find several differences with the Newtonian calculation such as the non-cancellation of IR divergences, the need to renormalize the background, and the fact that initial conditions must be set at second order in perturbation theory. For the bispectrum, we find relativistic corrections to be as large as the newtonian result in the squeezed limit. In that limit relativistic one-loop contributions, which we compute for the first time, can be as large as tree level results and have the same 1/k2 dependence as a primordial local non-Gaussianity signal where k is the momentum approaching zero. Moreover, we find the time dependence of the relativistic corrections to the bispectrum to be the same as that of a primordial non-Gaussianity signal.

Soldner Had Found in 1802 the Deflection of the Light by the Sun as the General Relativity Shows

Systematically, it is written in the literature that only the general relativity (GR) allows finding the just value of the deflection of the light by the sun. Yet, we noted, by reading over the original text of SOLDNER of 1801: “Ueber die Ablenkung eines Lichtstrals von seiner geradlinigen Bewegung, durch die Attraktion eines Weltkörpers, the welchem er nahe vorbei geht” (that we think it is important to put in English in full in Appendix) that, contrary to what we read since about 100 years, he found the right value. Soldner had started from a Newtonian gravitational calculation and, with the value of 1801, find 1.64”. This calculation, with the actual values, allows finding the right value of 1.752”. There are reasons to explain the wrong calculations which we usually make. However, there is no epistemological reason for questioning the general relativity. Some observations are only explained by the GR. But the Newtonian calculations are much simpler. We can continue to say that the theory of Newton is incomplete but we cannot say it is false.

Clustering of quintessence on horizon scales and its imprint on HI intensity mapping

Quintessence can cluster only on horizon scales. What is the effect on the observed matter distribution? To answer this, we need a relativistic approach that goes beyond the standard Newtonian calculation and deals properly with large scales. Such an approach has recently been developed for the case when dark energy is vacuum energy, which does not cluster at all. We extend this relativistic analysis to deal with dynamical dark energy. Using three quintessence potentials as examples, we compute the angular power spectrum for the case of an HI intensity map survey. Compared to the concordance model with the same small-scale power at z = 0, quintessence boosts the angular power by up to ∼ 15% at high redshifts, while power in the two models converges at low redshifts. The difference is mainly due to the background evolution, driven mostly by the normalization of the power spectrum today. The dark energy perturbations make only a small contribution on the largest scales, and a negligible contribution on smaller scales. Ironically, the dark energy perturbations remove the false boost of large-scale power that arises if we impose the (unphysical) assumption that the dark energy is smooth.

Large-scale clustering of galaxies in general relativity

Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in a synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local ${f}_{\mathrm{NL},\mathrm{eff}}\ensuremath{\lesssim}0.5$. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in a synchronous-comoving gauge.

Filling the disk hollow following binary black hole merger: The transient accretion afterglow

Tidal torques from a binary black hole empty out the central regions in any circumbinary gaseous accretion disk. The balance between tidal torques and viscosity maintain the inner edge of the disk at a radius $r\ensuremath{\sim}1.5a--2a$, where $a$ is the binary semimajor axis. Eventually, the inspiraling binary decouples from the disk and merges, leaving behind a central hollow (``donut hole'') in the disk orbiting the remnant black hole. We present a simple, time-dependent, Newtonian calculation that follows the secular (viscous) evolution of the disk as it fills up the hollow down to the black hole innermost stable circular orbit and then relaxes to stationary equilibrium. We use our model to calculate the electromagnetic radiation (``afterglow'') spectrum emitted during this transient accretion epoch. Observing the temporal increase in the total electromagnetic flux and the hardening of the spectrum as the donut hole fills may help confirm a binary black hole merger detected by a gravitational wave interferometer. We show how the very existence of the initial hollow can lead to super-Eddington accretion during this secular phase if the rate is not very far below Eddington prior to decoupling. Our model, though highly idealized, may be useful in establishing some of the key parameters, thermal emission features and scalings that characterize this transient. It can serve as a guide in the design and calibration of future radiation-magnetohydrodynamic simulations in general relativity.

A Numerical Solution of the Inverse Problem in Classical Celestial Mechanics, with Application to Mercury's Motion

It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points is described and its high accuracy verified. The osculating elements are also accurately computed. This solution is implemented in the Gauss iterative algorithm for solving nonlinear least-squares problems. This algorithm is summarized, and its efficiency for the inverse problem in celestial mechanics is checked on a 3-bodies problem. Then it is used to assess the accuracy to which a Newtonian calculation may reproduce the DE403 ephemeris that involves general-relativistic corrections. The parameter optimization allows one to reduce the norm and angular differences between the Newtonian calculation and DE403 by a factor 10 (Mercury, Pluto) to 100 (Venus). The maximum angular difference of the heliocentric positions of Mercury is ca. 220″ per century before the optimization, and ca. 20″ after it. The latter is still far above the observational accuracy. On the other hand, Mercury's longitude of the perihelion is not affected by the optimization: it keeps the linear advance of 43″ per century.

Proper initial conditions for long-term integrations of the solar system

An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment of the initial conditions is illustrated in the transition from the DE406 complete long-range ephemeris to a Newtonian model considering only the Sun and the four major planets. It is also used to best reproduce this same DE406 ephemeris, based on post-Newtonian equations for a system of mass points and including the Moon and asteroids, by using a Newtonian calculation corrected by the Schwarzschild effects of the Sun and restricted to the ten major bodies of the solar system.

Explosion of a rotating neutron star near the minimum mass

A Newtonian calculation is presented for the explosion of an unstable neutron star about the minimum mass, and the amount of neutrino, gravitational, and electromagnetic radiation emitted is estimated. The dynamical evolution of the star is followed by solving the Newtonian equations or motion for a homogeneous, uniformly rotating spheroid with internal pressure and gravity. At the outset, the oblate star is in hydrostatic equilibrium at the minimum mass along an equilibrium curve of fixed angular momentum. The explosion is almost instantaneous, with an intense burst of antineutrinos signaling the onset of abrupt acceleration. Antineutrino luminosities of 10 to the 50th to 10 to the 52nd ergs/s and bulk kinetic energies of order 10 to the 49th ergs are obtained. The results indicate that the gravitational radiation (GR) energy release from the explosion is rather small at E(GR)/M(B) less than 10 to the -14th with an amplitude at maximum acceleration of less than about 5 x 10 to the -23rd sine-squared Theta for a source at a distance of 10 kpc. 19 refs.

Laplace and the Speed of Sound

Previous articleNext article No AccessLaplace and the Speed of SoundBernard S. FinnBernard S. Finn Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Isis Volume 55, Number 1Mar., 1964 Publication of the History of Science Society Article DOIhttps://doi.org/10.1086/349791 Views: 30Total views on this site Citations: 15Citations are reported from Crossref Copyright 1964 History of Science Society, Inc.PDF download Crossref reports the following articles citing this article:Wali Khan Mashwani, Ihsan Mehmood, Maharani Abu Bakar, Ismail Koçcak, Hassène Gritli A Modified Bat Algorithm for Solving Large-Scale Bound Constrained Global Optimization Problems, Mathematical Problems in Engineering 2021 (Feb 2021): 1–14.https://doi.org/10.1155/2021/6636918Ching Koon Yau, Christopher G. Jesudason Mathematical modeling of the effects of attenuation and system electronic coupling on the determination of speed of sound in ultrasonic interferometry, Journal of Mathematical Chemistry 56, no.88 (Mar 2018): 2392–2417.https://doi.org/10.1007/s10910-018-0897-2Mário J. de Oliveira Elementary Concepts and Fundamental Laws of the Theory of Heat, Brazilian Journal of Physics 48, no.33 (Mar 2018): 299–313.https://doi.org/10.1007/s13538-018-0563-yCharles Coulston Gillispie, Raffaele Pisano Final Remarks on the Scientific Relationship Between Père et Fils, (Nov 2013): 337–411.https://doi.org/10.1007/978-94-017-8011-7_11Alejandro Jenkins Self-oscillation, Physics Reports 525, no.22 (Apr 2013): 167–222.https://doi.org/10.1016/j.physrep.2012.10.007Charles Coulston Gillispie, Raffaele Pisano Final Remarks on the Scientific Relationship Between Père et Fils, (Mar 2012): 337–411.https://doi.org/10.1007/978-94-007-4144-7_11G. Benedetto, R. M. Gavioso, R. Spagnolo Precision measurement of the speed of sound and thermodynamic properties of gases, La Rivista del Nuovo Cimento 22, no.66 (Apr 2008): 1–42.https://doi.org/10.1007/BF02872245Jürgen Mittelstraß L, (Jan 1995): 520–729.https://doi.org/10.1007/978-3-476-98727-3_5Ivor Grattan-Guinness Bibliography, (Jan 1990): 1415–1544.https://doi.org/10.1007/978-3-0348-7811-1_22Ivor Grattan-Guinness Bibliography, (Jan 1990): 1415–1544.https://doi.org/10.1007/978-3-0348-9125-7_22D. H. Arnold The m�canique physique of sim�on denis Poisson: The evolution and isolation in France of his approach to physical theory (1800?1840), Archive for History of Exact Sciences 29, no.44 (Jan 1984): 287–307.https://doi.org/10.1007/BF00348404 Bibliography, (Jan 1984): 515–541.https://doi.org/10.1016/S0304-0208(08)70666-2Gisela Kutzbach Early Applications of the Principles of Adiabatic Change and Vertical Convection, (Jan 1979): 19–44.https://doi.org/10.1007/978-1-940033-80-8_2Stephen G. Brush The Wave Theory of Heat: A Forgotten Stage in the Transition from the Caloric Theory to Thermodynamics, The British Journal for the History of Science 5, no.22 (Jan 2009): 145–167.https://doi.org/10.1017/S0007087400010906Robert P. Multhauf, Bernard S. Finn, Aleida V. H. Cattell, Gertrude B. Calvert, and Diana D. Menkes Ninetieth Critical Bibliography of the History of Science and Its Cultural Influences (To 1 January 1965), Isis 56, no.44 (Oct 2015): 490–657.https://doi.org/10.1086/350074