Mapping exomoon trajectories around Earth-like exoplanets

2021 ◽  
Vol 502 (4) ◽  
pp. 5292-5301
Author(s):  
Euaggelos E Zotos ◽  
Konstantinos E Papadakis ◽  
S Wageh
Keyword(s):  
Phase Space ◽  
Numerical Methods ◽  
Periodic Solutions ◽  
Linear Stability ◽  
Grid Method ◽  
Regular Motion ◽  
The Earth ◽  
Classification Technique ◽  
Predictor Corrector ◽  
Parent Star

ABSTRACT We consider a system in which both the parent star and the Earth-like exoplanet move on circular orbits. Using numerical methods, such as the orbit classification technique, we study all types of trajectories of possible exomoons around the exoplanet. In particular, we scan the phase space around the exoplanet and we distinguish between bounded, collisional, and escaping trajectories, considering both retrograde and prograde types of motion. In the case of bounded regular motion, we also use the grid method and a standard predictor-corrector procedure for revealing the corresponding network of symmetric periodic solutions, while we also compute their linear stability.

Introduction to molecular simulations in soft matter

2017 ◽  
Author(s):  
J.-L. Barrat ◽  
J. J. de Pablo
Keyword(s):  
Phase Space ◽  
Numerical Methods ◽  
Theoretical Basis ◽  
Soft Matter ◽  
Relevant Literature ◽  
Coarse Grained ◽  
Soft Interfaces ◽  
Molecular Scale ◽  
Soft Matter Physics ◽  
The Continuum

We describe the main features of the coarse-grained models that are typically useful in modelling soft interfaces, from force fields to the continuum descriptions involving density fields. We explain the theoretical basis of the main numerical methods that are used to explore the phase space associated with these models. Finally, three recent examples, illustrating the spirit in which relatively simple simulations can contribute to solving pending problems in soft matter physics, are briefly described. Clearly, a short series of lectures can offer, at best, a biased and restricted view of the available approaches. Our aim here will be to provide the reader with such an overview, with a focus on methods and descriptions that ‘bridge the scale’ between the molecular scale and the continuum or quasi-continuum one. The objective to present a guide to the relevant literature—which has now to a large extent appeared in the form of textbooks.

scholarly journals MOST Spacebased Photometry of HD 189733: Precise Timing Measurements for Transits Across an Active Star

2008 ◽  
Vol 4 (S253) ◽  
pp. 459-461
Author(s):  
E. Miller-Ricci ◽  
J. F. Rowe ◽  
D. Sasselov ◽  
J. M. Matthews ◽  
R. Kuschnig ◽  
...  
Keyword(s):  
Orbital Period ◽  
Mass Range ◽  
Active Star ◽  
Precise Timing ◽  
Resonant Orbits ◽  
The Earth ◽  
Test Spot ◽  
Transit Times ◽  
Nearly Continuous ◽  
Parent Star

AbstractWe have measured transit times for HD 189733 passing in front of its bright (V = 7.67) chromospherically active and spotted parent star. Nearly continuous broadband photometry of this system was obtained with the MOST (Microvariability & Oscillations of STars) space telesope during 21 days in August 2006, monitoring 10 consecutive transits. We have used these data to search for deviations from a constant orbital period which can indicate the presence of additional planets in the system that are as yet undetected by Doppler searches. We find no variations above the level of ±45 s, ruling out planets in the Earth-to-Neptune mass range in a number of resonant orbits. We find that a number of complications can arise in measuring transit times for a planet transiting an active star with large star spots. However, such transiting systems are also useful in that they can help to constrain and test spot models. This has implications for the large number of transiting systems expected to be discovered by the CoRoT and Kepler missions.

Computation of Turbulent Flow in a Thin Liquid Layer of Fluid Involving a Hydraulic Jump

1991 ◽  
Vol 113 (3) ◽  
pp. 411-418 ◽  
Author(s):  
M. M. Rahman ◽  
A. Faghri ◽  
W. L. Hankey
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Grid Method ◽  
Optimization Procedure ◽  
Solid Boundary ◽  
Plane Flow ◽  
Recirculating Flow ◽  
Flow Configurations ◽  
Rapid Deceleration ◽  
Predictor Corrector

Numerically computed flow fields and free surface height distributions are presented for the flow of a thin layer of liquid adjacent to a solid horizontal surface that encounters a hydraulic jump. Two kinds of flow configurations are considered: two-dimensional plane flow and axisymmetric radial flow. The computations used a boundary-fitted moving grid method with a k-ε model for the closure of turbulence. The free surface height was determined by an optimization procedure which minimized the error in the pressure distribution on the free surface. It was also checked against an approximate procedure involving integration of the governing equations and use of the MacCormack predictor-corrector method. The computed film height also compared reasonably well with previous experiments. A region of recirculating flow as found to be present adjacent to the solid boundary near the location of the jump, which was caused by a rapid deceleration of the flow.

scholarly journals Structure of Regions of Regular Motion in the Phase Space of Channeled Electrons

2020 ◽  
Vol 14 (2) ◽  
pp. 306-311
Author(s):  
V. V. Syshchenko ◽  
A. I. Tarnovsky ◽  
A. Yu. Isupov ◽  
I. I. Solovyev
Keyword(s):  
Phase Space ◽  
Regular Motion

Instabilities of exact, time-periodic solutions of the incompressible Euler equations

2000 ◽  
Vol 404 ◽  
pp. 269-287 ◽  
Author(s):  
JOSEPH A. BIELLO ◽  
KENNETH I. SALDANHA ◽  
NORMAN R. LEBOVITZ
Keyword(s):  
Periodic Solutions ◽  
Linear Stability ◽  
Euler Equations ◽  
Parameter Space ◽  
Spatial Scales ◽  
Inviscid Flow ◽  
Steady Flows ◽  
Periodic Flows ◽  
Finite Dimensional ◽  
Time Periodic Solutions

We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.

LINEAR STABILITY ANALYSIS GENERALIZED TO A THERMALLY-DRIVEN FLOW

1999 ◽  
Vol 09 (02) ◽  
pp. 415-425
Author(s):  
JEAN-MICHEL CORNET ◽  
CLAUDE-HENRI LAMARQUE
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
The Other ◽  
Basic Solution ◽  
Driven Cavity ◽  
Convective Flows ◽  
Other Hand ◽  
Thermally Driven

We intend to establish a methodology suited to the search of the first bifurcations of convective flows using a linear stability analysis so that it permits us to define a relationship between amplitude and frequency of the perturbation. We use a particular combination of various numerical methods to compute on one hand the basic solution. On the other hand the perturbation is applied to the search for the bifurcations in a thermally-driven cavity.

THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW

2004 ◽  
Vol 14 (11) ◽  
pp. 3821-3846 ◽  
Author(s):  
GAMAL M. MAHMOUD ◽  
TASSOS BOUNTIS
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Chaotic Behavior ◽  
Nonlinear Oscillators ◽  
Complex Variables ◽  
Point Of View ◽  
Stability And Control ◽  
Ginzburg Landau Equations ◽  
The Stability ◽  
And Control

Dynamical systems in the real domain are currently one of the most popular areas of scientific study. A wealth of new phenomena of bifurcations and chaos has been discovered concerning the dynamics of nonlinear systems in real phase space. There is, however, a wide variety of physical problems, which, from a mathematical point of view, can be more conveniently studied using complex variables. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. In this survey, we shall focus on such classes of autonomous, parametrically excited and modulated systems of complex nonlinear oscillators. We first describe appropriate perturbation approaches, which have been specially adapted to study periodic solutions, their stability and control. The stability analysis of these fundamental periodic solutions, though local by itself, can yield considerable information about more global properties of the dynamics, since it is in the vicinity of such solutions that the largest regions of regular or chaotic motion are observed, depending on whether the periodic solution is, respectively, stable or unstable. We then summarize some recent studies on fixed points, periodic solutions, strange attractors, chaotic behavior and the problem of chaos control in systems of complex oscillators. Some important applications in physics, mechanics and engineering are mentioned. The connection with a class of complex partial differential equations, which contains such famous examples, as the nonlinear Schrödinger and Ginzburg–Landau equations is also discussed. These complex equations play an important role in many branches of physics, e.g. fluids, superconductors, plasma physics, geophysical fluids, modulated optical waves and electromagnetic fields.

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