853 research outputs found
Is the Eureka cluster a collisional family of Mars Trojan asteroids?
We explore the hypothesis that the Eureka family of sub-km asteroids in the
L5 region of Mars could have formed in a collision. We estimate the size
distribution index from available information on family members; model the
orbital dispersion of collisional fragments; and carry out a formal calculation
of the collisional lifetime as a function of size. We find that, as initially
conjectured by Rivkin et al (2003), the collisional lifetime of objects the
size of (5261) Eureka is at least a few Gyr, significantly longer than for
similar-sized Main Belt asteroids. In contrast, the observed degree of orbital
compactness is inconsistent with all but the least energetic family-forming
collisions. Therefore, the family asteroids may be ejecta from a cratering
event sometime in the past ~1 Gyr if the orbits are gradually dispersed by
gravitational diffusion and the Yarkovsky effect (Cuk et al, 2015). The
comparable sizes of the largest family members require either negligible target
strength or a particular impact geometry under this scenario (Durda et al,
2007; Benavidez et al, 2012). Alternatively, the family may have formed by a
series of YORP-induced fission events (Pravec.et.al, 2010). The shallow size
distribution of the family is similar to that of small MBAs (Gladman et al,
2009) interpreted as due to the dominance of this mechanism for
Eureka-family-sized asteroids (Jacobson et al, 2014). However, our population
index estimate is likely a lower limit due to the small available number of
family asteroids and observational incompleteness. Future searches for fainter
family members, further observational characterisation of the known Trojans'
physical properties as well as orbital and rotational evolution modelling will
help distinguish between different formation models.Comment: 3 Tables, 13 Figures, Accepted for publication in Icaru
The asymmetric sandwich theorem
We discuss the asymmetric sandwich theorem, a generalization of the
Hahn-Banach theorem. As applications, we derive various results on the
existence of linear functionals that include bivariate, trivariate and
quadrivariate generalizations of the Fenchel duality theorem. Most of the
results are about affine functions defined on convex subsets of vector spaces,
rather than linear functions defined on vector spaces. We consider both results
that use a simple boundedness hypothesis (as in Rockafellar's version of the
Fenchel duality theorem) and also results that use Baire's theorem (as in the
Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper
also contains some new results about metrizable topological vector spaces that
are not necessarily locally convex.Comment: 17 page
Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics
Finite-dimensional reductions of the 2D dispersionless Toda hierarchy,
constrained by the ``string equation'' are studied. These include solutions
determined by polynomial, rational or logarithmic functions, which are of
interest in relation to the ``Laplacian growth'' problem governing interface
dynamics. The consistency of such reductions is proved, and the Hamiltonian
structure of the reduced dynamics is derived. The Poisson structure of the
rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated
version of the previous submissio
Diffusion-Limited Aggregation on Curved Surfaces
We develop a general theory of transport-limited aggregation phenomena
occurring on curved surfaces, based on stochastic iterated conformal maps and
conformal projections to the complex plane. To illustrate the theory, we use
stereographic projections to simulate diffusion-limited-aggregation (DLA) on
surfaces of constant Gaussian curvature, including the sphere () and
pseudo-sphere (), which approximate "bumps" and "saddles" in smooth
surfaces, respectively. Although curvature affects the global morphology of the
aggregates, the fractal dimension (in the curved metric) is remarkably
insensitive to curvature, as long as the particle size is much smaller than the
radius of curvature. We conjecture that all aggregates grown by conformally
invariant transport on curved surfaces have the same fractal dimension as DLA
in the plane. Our simulations suggest, however, that the multifractal
dimensions increase from hyperbolic () geometry, which
we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig
The anomalous behavior of coefficient of normal restitution in the oblique impact
The coefficient of normal restitution in an oblique impact is theoretically
studied. Using a two-dimensional lattice models for an elastic disk and an
elastic wall, we demonstrate that the coefficient of normal restitution can
exceed one and has a peak against the incident angle in our simulation.
Finally, we explain these phenomena based upon the phenomenological theory of
elasticity.Comment: 4 pages, 4 figures, to be appeared in PR
Phytohormonal regulation of in vitro formation of wheat androgenic structures
This research is devoted to developing a method of phytohormonal regulation of in vitro formation of a certain type of wheat androgenic structures. Using the method of ELISA it was shown that the induction of certain sporophytic morphogenesis pathway in vitro of anther haploid cells - microspores depends on both the content of endogenous auxin IAA in anthers before inoculating them onto induction medium, and the concentration of exogenous auxin 2,4-D in this medium. The obtained data confirms the principle possibility of regulation of ways of getting androgenic regenerants in vitro by selecting the optimal balance of endogenous and exogenous auxin
Gravitational Lensing by Rotating Naked Singularities
We model massive compact objects in galactic nuclei as stationary,
axially-symmetric naked singularities in the Einstein-massless scalar field
theory and study the resulting gravitational lensing. In the weak deflection
limit we study analytically the position of the two weak field images, the
corresponding signed and absolute magnifications as well as the centroid up to
post-Newtonian order. We show that there are a static post-Newtonian
corrections to the signed magnification and their sum as well as to the
critical curves, which are function of the scalar charge. The shift of the
critical curves as a function of the lens angular momentum is found, and it is
shown that they decrease slightingly for the weakly naked and vastly for the
strongly naked singularities with the increase of the scalar charge. The
point-like caustics drift away from the optical axis and do not depend on the
scalar charge. In the strong deflection limit approximation we compute
numerically the position of the relativistic images and their separability for
weakly naked singularities. All of the lensing quantities are compared to
particular cases as Schwarzschild and Kerr black holes as well as
Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure
Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit
In the present work we study numerically quasi-equatorial lensing by the
charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the
strong deflection limit. In this approximation we compute the magnification and
the positions of the relativistic images. The most outstanding effect is that
the Kerr-Sen black hole caustics drift away from the optical axis and shift in
clockwise direction with respect to the Kerr caustics. The intersections of the
critical curves on the equatorial plane as a function of the black hole angular
momentum are found, and it is shown that they decrease with the increase of the
parameter . All of the lensing quantities are compared to particular
cases as Schwarzschild, Kerr and Gibbons-Maeda black holes.Comment: 31 pages, 17 figures; V2 references added, some typos corrected, V3
references added, language corrections, V4 table added, minor technical
correction
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