17,272 research outputs found
Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering
The process of gravitational scattering of planetesimals by a massive
protoplanetary embryo is explored theoretically. We propose a method to
describe the evolution of the disk surface density, eccentricity, and
inclination caused by the embryo-planetesimal interaction. It relies on the
analytical treatment of the scattering in two extreme regimes of the
planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and
dispersion-dominated (dynamically ``hot''). In the former, planetesimal
scattering can be treated as a deterministic process. In the latter, scattering
is mostly weak because of the large relative velocities of interacting bodies.
This allows one to use the Fokker-Planck approximation and the two-body
approximation to explore the disk evolution. We compare the results obtained by
this method with the outcomes of the direct numerical integrations of
planetesimal orbits and they agree quite well. In the intermediate velocity
regime an approximate treatment of the disk evolution is proposed based on
interpolation between the two extreme regimes. We also calculate the rate of
embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that
it is in agreement with both the simulations and earlier calculations. Finally
we discuss the question of the direction of the embryo-planetesimal interaction
in the dispersion-dominated regime and demonstrate that it is repulsive. This
means that the embryo always forms a gap in the disk around it, which is in
contrast with the results of other authors. The machinery developed here will
be applied to realistic protoplanetary systems in future papers.Comment: 40 pages, 9 figures, submitted to A
Good rotations
Numerical integrations in celestial mechanics often involve the repeated
computation of a rotation with a constant angle. A direct evaluation of these
rotations yields a linear drift of the distance to the origin. This is due to
roundoff in the representation of the sine s and cosine c of the angle theta.
In a computer, one generally gets c^2 + s^2 1, resulting in a mapping that
is slightly contracting or expanding. In the present paper we present a method
to find pairs of representable real numbers s and c such that c^2 + s^2 is as
close to 1 as possible. We show that this results in a drastic decrease of the
systematic error, making it negligible compared to the random error of other
operations. We also verify that this approach gives good results in a realistic
celestial mechanics integration.Comment: 24 pages, 3 figure
Laser frequency combs and ultracold neutrons to probe braneworlds through induced matter swapping between branes
This paper investigates a new experimental framework to test the braneworld
hypothesis. Recent theoretical results have shown the possibility of matter
exchange between branes under the influence of suitable magnetic vector
potentials. It is shown that the required conditions might be achieved with
present-day technology. The experiment uses a source of pulsed and coherent
electromagnetic radiation and relies on the Hansch frequency comb technique
well-known in ultrahigh-precision spectroscopy. A good matter candidate for
testing the hypothesis is a polarized ultracold neutron gas for which the
number of swapped neutrons is measured.Comment: 14 pages, 4 figures. Published version. Published in Phys. Rev.
An ab initio study of magneto-electric coupling of
The present paper proposes the direct calculation of the microscopic
contributions to the magneto-electric coupling, using ab initio methods. The
electrostrictive and the Dzyaloshinskii-Moriya contributions were evaluated
individually. For this purpose a specific method was designed, combining DFT
calculations and embedded fragments, explicitely correlated, quantum chemical
calculations. This method allowed us to calculate the evolution of the magnetic
couplings as a function of an applied electric field. We found that in the Dzyaloshinskii-Moriya contribution to the magneto-electric effect
is three orders of magnitude weaker than the electrostrictive contribution.
Strictive effects are thus dominant in the magnetic exchange evolution under an
applied electric field, and by extension on the magneto-electric effect. These
effects remain however quite small and the modifications of the magnetic
excitations under an applied electric field will be difficult to observe
experimentally. Another important conclusion is that the amplitude of the
magneto-electric effect is very small. Indeed, it can be shown that the linear
magneto-electric tensor is null due to the inter-layer symmetry operations.Comment: J. Phys. Cond. Matter 201
Robustness: a New Form of Heredity Motivated by Dynamic Networks
We investigate a special case of hereditary property in graphs, referred to
as {\em robustness}. A property (or structure) is called robust in a graph
if it is inherited by all the connected spanning subgraphs of . We motivate
this definition using two different settings of dynamic networks. The first
corresponds to networks of low dynamicity, where some links may be permanently
removed so long as the network remains connected. The second corresponds to
highly-dynamic networks, where communication links appear and disappear
arbitrarily often, subject only to the requirement that the entities are
temporally connected in a recurrent fashion ({\it i.e.} they can always reach
each other through temporal paths). Each context induces a different
interpretation of the notion of robustness.
We start by motivating the definition and discussing the two interpretations,
after what we consider the notion independently from its interpretation, taking
as our focus the robustness of {\em maximal independent sets} (MIS). A graph
may or may not admit a robust MIS. We characterize the set of graphs \forallMIS
in which {\em all} MISs are robust. Then, we turn our attention to the graphs
that {\em admit} a robust MIS (\existsMIS). This class has a more complex
structure; we give a partial characterization in terms of elementary graph
properties, then a complete characterization by means of a (polynomial time)
decision algorithm that accepts if and only if a robust MIS exists. This
algorithm can be adapted to construct such a solution if one exists
The measured compositions of Uranus and Neptune from their formation on the CO iceline
The formation mechanisms of the ice giants Uranus and Neptune, and the origin
of their elemental and isotopic compositions, have long been debated. The
density of solids in the outer protosolar nebula is too low to explain their
formation, and spectroscopic observations show that both planets are highly
enriched in carbon, very poor in nitrogen, and the ices from which they
originally formed might had deuterium-to-hydrogen ratios lower than the
predicted cometary value, unexplained properties observed in no other planets.
Here we show that all these properties can be explained naturally if Uranus and
Neptune both formed at the carbon monoxide iceline. Due to the diffusive
redistribution of vapors, this outer region of the protosolar nebula
intrinsically has enough surface density to form both planets from carbon-rich
solids but nitrogen-depleted gas, in abundances consistent with their observed
values. Water rich interiors originating mostly from transformed CO ices
reconcile the D/H value of Uranus and Neptune's building blocks with the
cometary value. Finally, Our scenario generalizes a well known hypothesis that
Jupiter formed on an iceline (water snowline) for the two ice giants, and might
be a first step towards generalizing this mechanism for other giant planets.Comment: The Astrophysical Journal (in press), 8 pages, 5 figure
Predicting spinor condensate dynamics from simple principles
We study the spin dynamics of quasi-one-dimensional F=1 condensates both at
zero and finite temperatures for arbitrary initial spin configurations. The
rich dynamical evolution exhibited by these non-linear systems is explained by
surprisingly simple principles: minimization of energy at zero temperature, and
maximization of entropy at high temperature. Our analytical results for the
homogeneous case are corroborated by numerical simulations for confined
condensates in a wide variety of initial conditions. These predictions compare
qualitatively well with recent experimental observations and can, therefore,
serve as a guidance for on-going experiments.Comment: 4 pages, 2 figures. v3: matches version appeared in PR
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