scholarly journals Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals

2011 ◽  
Vol 46 (2) ◽  
pp. 63-73
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Time Intervals ◽  
Good Consistency ◽  
Newtonian Case ◽  
Long Time

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

scholarly journals Application of the Spectral Analysis for Modeling the Rotations of the Moon

2010 ◽  
Vol 45 (4) ◽  
pp. 153-162 ◽  
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Spectral Analysis ◽  
Numerical Solution ◽  
Rotational Motion ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Physical Libration ◽  
Newtonian Case ◽  
Rotational Motions

Application of the Spectral Analysis for Modeling the Rotations of the Moon The main purposes of this research are the development of the optimal spectral analysis schemes for the investigation of the rotational motion of the Moon and then the comparison between the result of the optimal spectral analysis of the rotational motions of the Earth and the Moon. Dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9 year time interval. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) represented by Cassini relations and the semi-analytical solutions of the lunar physical libration problem (Eckhardt, 1981), (Moons, 1982), (Moons, 1984), (Pešek, 1982). The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the optimal spectral analysis methods for the Newtonian case. All the periodic terms representing the behavior of the residuals are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2010) is constructed, which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2010. The discrepancies between the new numerical solution and MRS2010 do not surpass 20 mas over 418.9 year time interval. The result of the comparison demonstrates that MRS2010 series represent more accurately the Moon rotation than SMR series.

scholarly journals Rers2014 and Mrs2014: New High-Precision Rigid Earth Rotation and Moon Rotation Series

2015 ◽  
Vol 50 (1) ◽  
pp. 35-40
Author(s):  
V.V. Pashkevich
Keyword(s):  
Numerical Solution ◽  
Numerical Investigation ◽  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Euler Angles ◽  
Time Intervals ◽  
The Earth ◽  
Long Time ◽  
Rigid Earth

Abstract Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 ìas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

scholarly journals New Results on the Motions of Asteroids in Resonances

1992 ◽  
Vol 152 ◽  
pp. 145-152 ◽  
Author(s):  
R. Dvorak
Keyword(s):  
Initial Conditions ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Close Approach ◽  
Integration Time ◽  
Time Interval ◽  
Time Intervals ◽  
3 Dimensional ◽  
Special Cases ◽  
Good Agreement

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

scholarly journals Design and interpretation of cell trajectory assays

2013 ◽  
Vol 10 (88) ◽  
pp. 20130630 ◽  
Author(s):  
Lucie G. Bowden ◽  
Matthew J. Simpson ◽  
Ruth E. Baker
Keyword(s):  
Cell Biology ◽  
Time Interval ◽  
Short Time Interval ◽  
Trajectory Data ◽  
Time Intervals ◽  
Different Types ◽  
Long Time ◽  
A Cell ◽  
Cell Trajectory ◽  
Short Time

Cell trajectory data are often reported in the experimental cell biology literature to distinguish between different types of cell migration. Unfortunately, there is no accepted protocol for designing or interpreting such experiments and this makes it difficult to quantitatively compare different published datasets and to understand how changes in experimental design influence our ability to interpret different experiments. Here, we use an individual-based mathematical model to simulate the key features of a cell trajectory experiment. This shows that our ability to correctly interpret trajectory data is extremely sensitive to the geometry and timing of the experiment, the degree of motility bias and the number of experimental replicates. We show that cell trajectory experiments produce data that are most reliable when the experiment is performed in a quasi-one-dimensional geometry with a large number of identically prepared experiments conducted over a relatively short time-interval rather than a few trajectories recorded over particularly long time-intervals.

ON THE REGULARITY OF THREE-DIMENSIONAL ROTATING EULER–BOUSSINESQ EQUATIONS

1999 ◽  
Vol 09 (07) ◽  
pp. 1089-1121 ◽  
Author(s):  
A. BABIN ◽  
A. MAHALOV ◽  
B. NICOLAENKO
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Boussinesq Equations ◽  
Stable Stratification ◽  
Primitive Equations ◽  
Time Interval ◽  
Regular Solutions ◽  
Time Intervals ◽  
Long Time

The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α≥ 3/4. Existence on a long-time interval T*of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T*→∞ as the frequency of gravity waves →∞).

Renormalization of the transformation operators of quantum electrodynamics

1954 ◽  
Vol 227 (1168) ◽  
pp. 94-102
Keyword(s):  
Quantum Electrodynamics ◽  
Matrix Theory ◽  
Transformation Operator ◽  
Time Interval ◽  
Matrix Elements ◽  
Finite Time Interval ◽  
Time Intervals ◽  
Starting Point ◽  
The Matrix ◽  
Long Time

The transformation operator of electrodynamics for a finite time interval with uncertain boundaries is represented by a continuous switching on and off of the charge. It is shown that its divergencies are the same as those appearing in the S matrix theory, and a covariant procedure is given for isolating their infinite parts. Provided Gupta’s renormalized Lagrangian is used as a starting point all the infinities may be removed. The coefficients of the counter terms are power series in the time-dependent charge with coefficients that are independent of the time interval being considered. The practice of approximating the matrix elements of the transformation operators for long time intervals by matrix elements of the S matrix is discussed and justified. In an appendix the extension of these results to the renormalizable meson theories is discussed.

scholarly journals Corrosion and Inhibition Effects of Mild Steel in Hydrochloric Acid Solutions Containing Organophosphonic Acid

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Manish Gupta ◽  
Jyotsna Mishra ◽  
K. S. Pitre
Keyword(s):  
Corrosion Rate ◽  
Mild Steel ◽  
Electrochemical Techniques ◽  
Time Interval ◽  
Time Intervals ◽  
Voltammetric Method ◽  
Average Value ◽  
Long Time ◽  
In The Beginning ◽  
Short Time

A study has been made on the mechanism of corrosion of mild steel and the effect of nitrilo trimethylene phosphonic (NTMP) acid as a corrosion inhibitor in acidic medium, that is, 10% HC1 using the weight loss method and electrochemical techniques, that is, potentiodynamic and galvanostatic polarization measurements. Although corrosion is a long-time process, but it takes place at a faster rate in the beginning which goes on decreasing with due course of time. The above-mentioned methods of corrosion rate determination furnish an average value for a long-time interval. Looking at the versatility and minimum detection limit of the voltammetric method, the authors have developed a new voltammetric method for the determination of corrosion rate at short-time intervals. The results of corrosion of mild steel in 10% HC1 solution with and without NTMP inhibitor at short-time intervals have been reported. The corrosion inhibition efficiency of NTMP is 93% after 24 h.

scholarly journals Decay of turbulence in the final period

1948 ◽  
Vol 194 (1039) ◽  
pp. 527-543 ◽  
Keyword(s):  
Correlation Coefficient ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Initial Period ◽  
Energy Decay ◽  
Transitional Period ◽  
Asymptotic State ◽  
Time Interval ◽  
Velocity Correlation ◽  
Time Intervals

The final period of decay of a turbulent motion occurs when the effects of inertia forces are negligible. Under these conditions the instantaneous velocity distribution in the turbulence field may be solved as an initial value problem. It is shown that homogeneous turbulence tends to an asymptotic statistical state which is independent of the initial conditions. In this asymptotic state the energy of turbulence is proportional to t -5/2 and the longitudinal double-velocity correlation coefficient for two points distance r apart is e -r2/svt , where t is the time of decay. The asymptotic time-interval correlation coefficient is found to be different from unity for very large time intervals only, showing the aperiodic character of the motion. The whole field of motion comes gradually to rest, smaller eddies decaying more rapidly than larger eddies, and the above stable eddy distribution is established when only the largest eddies of the original turbulence remain. Relevant measurements have been made in the field of isotropic turbulence downstream from a grid of small mesh. The above energy decay and space-interval correlation relations are found to be valid at distances from the grid greater than 400-mesh lengths and at a mesh Reynolds number of 650. The duration of the transitional period, in which the energy decay law is changing from that appropriate to the initial period of decay to the above asymptotic law, increases very rapidly with R M . There is a brief discussion of the criterion for the existence of final period decay, although clarification must wait until the existence and termination of the initial period of decay are better understood.

scholarly journals Dispersive fractalisation in linear and nonlinear Fermi–Pasta–Ulam–Tsingou lattices

2021 ◽  
pp. 1-26
Author(s):  
PETER J. OLVER ◽  
ARI STERN
Keyword(s):  
Initial Conditions ◽  
Step Function ◽  
Continuum Models ◽  
Time Intervals ◽  
Piecewise Constant ◽  
Periodic Linear ◽  
Long Time ◽  
Nonlinear Force ◽  
Linear And Nonlinear ◽  
Nonlinear Continuum

We investigate, both analytically and numerically, dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi–Pasta–Ulam–Tsingou systems. When subject to periodic boundary conditions and discontinuous initial conditions, e.g., a step function, both the linearised and nonlinear continuum models for FPUT exhibit fractal solution profiles at irrational times (as determined by the coefficients and the length of the interval) and quantised profiles (piecewise constant or perturbations thereof) at rational times. We observe a similar effect in the linearised FPUT chain at times t where these models have validity, namely t = O(h−2), where h is proportional to the intermass spacing or, equivalently, the reciprocal of the number of masses. For nonlinear periodic FPUT systems, our numerical results suggest a somewhat similar behaviour in the presence of small nonlinearities, which disappears as the nonlinear force increases in magnitude. However, these phenomena are manifested on very long time intervals, posing a severe challenge for numerical integration as the number of masses increases. Even with the high-order splitting methods used here, our numerical investigations are limited to nonlinear FPUT chains with a smaller number of masses than would be needed to resolve this question unambiguously.

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