scholarly journals On Some Damped 2 Body Problems

2021 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Singular Potential ◽  
Central Charge ◽  
The Sun ◽  
Initial State ◽  
High Scale ◽  
All Solutions ◽  
Electrical Devices ◽  
New Phenomena ◽  
Formal Calculation ◽  
Dissipative Model

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear which were investigated thoroughly by R. Ortega and his co-authors between 2014 and 2017, in particular all solutions are bounded and tend to $0$ for $t$ large, some of them with asymptotically spiraling exponentially fast convergence to the center. We provide explicit estimates for the bounds in the general case that we refine under specific restrictions on the initial state, and we give a formal calculation which could be used to determine practically some special asymptotically spiraling orbits. Besides, a related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology

scholarly journals On Some Damped 2 Body Problems

2020 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Singular Potential ◽  
Blow Up ◽  
Central Charge ◽  
The Sun ◽  
Bounded Solutions ◽  
High Scale ◽  
Electrical Devices ◽  
Moving Particle ◽  
New Phenomena ◽  
Dissipative Model

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center. A related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology.

scholarly journals On Some Damped 2 Body Problems

2020 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Singular Potential ◽  
Blow Up ◽  
Central Charge ◽  
The Sun ◽  
Bounded Solutions ◽  
High Scale ◽  
Electrical Devices ◽  
Moving Particle ◽  
New Phenomena ◽  
Dissipative Model

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center. A related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology.

scholarly journals On a Linearly Damped 2 Body Problem

2020 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Body Problem ◽  
Singular Potential ◽  
Blow Up ◽  
Atomic Model ◽  
The Sun ◽  
Moving Particle ◽  
New Phenomena

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in nite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover some formal calculations suggest the existence of special orbits with an asymptotically spiraling convergence to the center.

scholarly journals On a Linearly Damped 2 Body Problem

2020 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Finite Time ◽  
Body Problem ◽  
Singular Potential ◽  
Blow Up ◽  
Fast Convergence ◽  
Atomic Model ◽  
The Sun ◽  
Bounded Solutions ◽  
Moving Particle ◽  
New Phenomena

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center.

Calculating the periods of radio signal transmission between two spacecrafts through the Venus atmosphere in the problem of studying its composition

2019 ◽  
Author(s):  
K.S. Fedyaev ◽  
V.V. Koryanov ◽  
S.A. Bober ◽  
V.A. Zubko ◽  
A.A. Belyaev
Keyword(s):  
Radio Signal ◽  
Initial Conditions ◽  
Libration Point ◽  
Signal Transmission ◽  
Energy Costs ◽  
The Sun ◽  
Initial State ◽  
Collinear Libration Point ◽  
Small Spacecraft ◽  
Atmosphere Of Venus

The paper considers calculating the periods of radio signal transmission through the atmosphere of Venus between a small spacecraft placed in a limited orbit in the vicinity of the collinear libration point of the Sun-Venus system and a Venus orbiter. The problem arises in the framework of the project under discussion to study the atmosphere of Venus. The possibility of transfers of these spacecrafts to the required orbits under various initial conditions is also studied. The impulses required for transferring to the specified orbits at the selected initial state vector, the most suitable for solving this problem are calculated. The duration and the number of transmission periods depending on the location of one of the spacecrafts in a limited orbit in the vicinity of the libration point L1 or L2 of the Sun-Venus system are analyzed. The influence of the shape of the orbiter near-Venusian orbit on the character and duration of the periods of transmission through the atmosphere of Venus is investigated. It is concluded that the location of a small spacecraft in a limited orbit in the vicinity of the L1 libration point of the Sun-Venus system is more advantageous compared to L2 both in terms of the duration and the number of the transmission periods as well as terms of the necessary energy costs.

scholarly journals Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Axel Cortes Cubero
Keyword(s):  
Effective Charge ◽  
Central Charge ◽  
Large Mass ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Temperature Dependent ◽  
Initial State ◽  
Conformal Field ◽  
Quantum Quench ◽  
Short Times

At thermal equilibrium, the concept of effective central charge for massive deformations of two-dimensional conformal field theories (CFT) is well understood, and can be defined by comparing the partition function of the massive model to that of a CFT. This temperature-dependent effective charge interpolates monotonically between the central charge values corresponding to the IR and UV fixed points at low and high temperatures, respectively. We propose a non-equilibrium, time-dependent generalization of the effective central charge for integrable models after a quantum quench, c_{\rm eff}(t), obtained by comparing the return amplitude to that of a CFT quench. We study this proposal for a large mass quench of a free boson, where the effective charge is seen to interpolate between c_{\rm eff}=0 at t=0t=0, and c_{\rm eff}\sim 1 at t\to\inftyt→∞, as is expected. We use our effective charge to define an “Ising to Tricritical Ising" quench protocol, where the charge evolves from c_{\rm eff}=1/2 at t=0t=0, to c_{\rm eff}=7/10 at t\to\inftyt→∞, the corresponding values of the first two unitary minimal CFT models. We then argue that the inverse “Tricritical Ising to Ising" quench is impossible with our methods. These conclusions can be generalized for quenches between any two adjacent unitary minimal CFT models. We finally study a large mass quench into the “staircase model" (sinh-Gordon with a particular complex coupling). At short times after the quench, the effective central charge increases in a discrete “staircase" structure, where the values of the charge at the steps can be computed in terms of the central charges of unitary minimal CFT models. When the initial state is a pure state, one always finds that c_{\rm eff}(t\to\infty)\geq c_{\rm eff}(t=0), though c_{\rm eff}(t), generally oscillates at finite times. We explore how this constraint may be related to RG flow irreversibility.

Chromospheric activity as a function of age in main-sequence stars

1966 ◽  
Vol 24 ◽  
pp. 40-43
Author(s):  
O. C. Wilson ◽  
A. Skumanich
Keyword(s):  
Main Sequence ◽  
The Sun ◽  
Main Sequence Stars ◽  
Tentative Conclusion ◽  
Chromospheric Activity ◽  
General Field ◽  
Large Clusters

Evidence previously presented by one of the authors (1) suggests strongly that chromospheric activity decreases with age in main sequence stars. This tentative conclusion rests principally upon a comparison of the members of large clusters (Hyades, Praesepe, Pleiades) with non-cluster objects in the general field, including the Sun. It is at least conceivable, however, that cluster and non-cluster stars might differ in some fundamental fashion which could influence the degree of chromospheric activity, and that the observed differences in chromospheric activity would then be attributable to the circumstances of stellar origin rather than to age.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Seti Space Missions

1997 ◽  
Vol 161 ◽  
pp. 761-776 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Electromagnetic Waves ◽  
Space Missions ◽  
Gravitational Lens ◽  
The Sun ◽  
Space Antenna ◽  
Focal Distance ◽  
Large Space ◽  
The Earth ◽  
Space Antennas ◽  
New Space

AbstractSETI from space is currently envisaged in three ways: i) by large space antennas orbiting the Earth that could be used for both VLBI and SETI (VSOP and RadioAstron missions), ii) by a radiotelescope inside the Saha far side Moon crater and an Earth-link antenna on the Mare Smythii near side plain. Such SETIMOON mission would require no astronaut work since a Tether, deployed in Moon orbit until the two antennas landed softly, would also be the cable connecting them. Alternatively, a data relay satellite orbiting the Earth-Moon Lagrangian pointL2would avoid the Earthlink antenna, iii) by a large space antenna put at the foci of the Sun gravitational lens: 1) for electromagnetic waves, the minimal focal distance is 550 Astronomical Units (AU) or 14 times beyond Pluto. One could use the huge radio magnifications of sources aligned to the Sun and spacecraft; 2) for gravitational waves and neutrinos, the focus lies between 22.45 and 29.59 AU (Uranus and Neptune orbits), with a flight time of less than 30 years. Two new space missions, of SETI interest if ET’s use neutrinos for communications, are proposed.

A Search for Dyson Spheres around Late-Type Stars in the Solar Neighborhood II

1997 ◽  
Vol 161 ◽  
pp. 707-709 ◽  
Author(s):  
Jun Jugaku ◽  
Shiro Nishimura
Keyword(s):  
Solar Neighborhood ◽  
The Sun ◽  
Late Type ◽  
Solar Type

AbstractWe continued our search for partial (incomplete) Dyson spheres associated with 50 solar-type stars (spectral classes F, G, and K) within 25 pc of the Sun. No candidate objects were found.

Sign in / Sign up

Export Citation Format

Share Document