اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTidal friction in close-in satellites and exoplanets. The Darwin theory re-visited
61
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This report is a review of Darwins classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.
قيم البحث
اقرأ أيضاً
Extrasolar satellites are generally too small to be detected by nominal searches. By analogy to the most active body in the Solar System, Io, we describe how sodium (Na I) and potassium (K I) $textit{gas}$ could be a signature of the geological activ
ity venting from an otherwise hidden exo-Io. Analyzing $sim$ a dozen close-in gas giants hosting robust alkaline detections, we show that an Io-sized satellite can be stable against orbital decay below a planetary tidal $mathcal{Q}_p lesssim 10^{11}$. This tidal energy is focused into the satellite driving a $sim 10^{5 pm 2}$ higher mass loss rate than Ios supply to Jupiters Na exosphere, based on simple atmospheric loss estimates. The remarkable consequence is that several exo-Io column densities are on average $textit{more than sufficient}$ to provide the $sim$ 10$^{10 pm 1}$ Na cm$^{-2}$ required by the equivalent width of exoplanet transmission spectra. Furthermore, the benchmark observations of both Jupiters extended ($sim 1000$ R$_J$) Na exosphere and Jupiters atmosphere in transmission spectroscopy yield similar Na column densities that are purely exogenic in nature. As a proof of concept, we fit the high-altitude Na at WASP 49-b with an ionization-limited cloud similar to the observed Na profile about Io. Moving forward, we strongly encourage time-dependent ingress and egress monitoring along with spectroscopic searches for other volcanic volatiles.
Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the change of
emission level with spin polarization and for new measurements of transient emission. The rate constants given are in variance to those reported previously.
The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one operator, the
unintegrated chiral superpotential. In the quantum theory this term receives an admixture by a second operator, the Yang-Mills part of the Lagrangian. It has long been debated whether this anomalous contribution is affected by higher loop corrections. We present a first principles calculation at the second non-trivial order in perturbation theory using supersymmetric dimensional reduction as a regulator and renormalisation by Z-factors. Singular higher loop corrections to the renormalisation factor of the Yang-Mills term are required if the conformal properties of two-point functions are to be met. These singularities take the form determined in preceding work on rather general grounds. Moreover, we also find non-vanishing finite terms. The core part of the problem is the evaluation of a four-loop two-point correlator which is accomplished by the Laporta algorithm. Apart from several examples of the T1 topology with two lines of non-integer dimension we need the first few orders in the epsilon expansion of three master integrals. The approach is self-contained in that all the necessary information can be derived from the power counting finiteness of some integrals.
We consider the influence maximization problem (selecting $k$ seeds in a network maximizing the expected total influence) on undirected graphs under the linear threshold model. On the one hand, we prove that the greedy algorithm always achieves a $(1
- (1 - 1/k)^k + Omega(1/k^3))$-approximation, showing that the greedy algorithm does slightly better on undirected graphs than the generic $(1- (1 - 1/k)^k)$ bound which also applies to directed graphs. On the other hand, we show that substantial improvement on this bound is impossible by presenting an example where the greedy algorithm can obtain at most a $(1- (1 - 1/k)^k + O(1/k^{0.2}))$ approximation. This result stands in contrast to the previous work on the independent cascade model. Like the linear threshold model, the greedy algorithm obtains a $(1-(1-1/k)^k)$-approximation on directed graphs in the independent cascade model. However, Khanna and Lucier showed that, in undirected graphs, the greedy algorithm performs substantially better: a $(1-(1-1/k)^k + c)$ approximation for constant $c > 0$. Our results show that, surprisingly, no such improvement occurs in the linear threshold model. Finally, we show that, under the linear threshold model, the approximation ratio $(1 - (1 - 1/k)^k)$ is tight if 1) the graph is directed or 2) the vertices are weighted. In other words, under either of these two settings, the greedy algorithm cannot achieve a $(1 - (1 - 1/k)^k + f(k))$-approximation for any positive function $f(k)$. The result in setting 2) is again in a sharp contrast to Khanna and Luciers $(1 - (1 - 1/k)^k + c)$-approximation result for the independent cascade model, where the $(1 - (1 - 1/k)^k + c)$ approximation guarantee can be extended to the setting where vertices are weighted. We also discuss extensions to more generalized settings including those with edge-weighted graphs.
We describe the formalism, and present the results, for a triple-Regge analysis of the available pp and pbar{p} high-energy data which explicitly accounts for absorptive corrections. In particular, we allow for the gap survival probability, S^2, in s
ingle proton diffractive dissociation. Since for pp scattering the value of S^2 is rather small, the triple-Pomeron vertex obtained in this analysis is larger than that obtained in the old analyses where the suppression caused by the absorptive corrections was implicitly included in an effective vertex. We show that the bare triple-Pomeron coupling that we extract from the pp and pbar{p} data is consistent with that obtained in a description of the gamma p -> J/psi + Y HERA data. The analyses of the data prefer a zero slope, corresponding to the small size of the bare vertex, giving the hope of a smooth matching to the perturbative QCD treatment of the triple-Pomeron coupling.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
