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 ($K>0$) and pseudo-sphere ($K<0$), 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 ($K0$) 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 $Q^{2}/M$. 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