Cartography for Martian Trojans

The last few months have seen the discovery of a second Martian Trojan (1998 VF31), as well as two further possible candidates (1998 QH56 and 1998 SD4). Together with the previously discovered Martian satellite 5261 Eureka, these are the only known possible solar system Trojan asteroids not associated with Jupiter. Here, maps of the locations of the stable Trojan trajectories of Mars are presented. These are constructed by integrating an ensemble of in-plane and inclined orbits in the vicinity of the Martian Lagrange points for between 25 million and 60 million years. The survivors occupy a band of inclinations between 15 degrees and 40 degrees and longitudes between 240 degrees and 330 degrees at the L5 Lagrange point. Around the L4 point, stable Trojans inhabit two bands of inclinations (15 degrees < i < 30 degrees and 32 degrees < i < 40 degrees) with longitudes restricted between 25 degrees and 120 degrees. Both 5261 Eureka and 1998 VF31 lie deep within one of the stable zones, which suggests they may be of primordial origin. Around Mars, the number of such undiscovered primordial objects with sizes greater than 1 km may be as high as 50. The two candidates 1998 QH56 and 1998 SD4 are not presently on Trojan orbits and will enter the sphere of influence of Mars within half a million years.Comment: 14 pages, 3 figures, in press at the Astrophysical Journal (Letters

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.Comment: 12 pages, 5 figure

Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic $Q$-factors at low temperature, with $Q\times f$ products of order $10^{18}$ Hz. In this work we couple such a resonator to a SQUID amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime

A new conjecture extends the GM law for percolation thresholds to dynamical situations

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q_2 of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.Comment: 8 pages, latex, 3 figures include

A comparison between academic success and responses on a sentence completion test

Thesis (Ed.M.)--Boston Universit

Discrete and continuum fundamental solutions describing heat conduction in 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling

In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176, 2021, 121442) ballistic heat propagation in 1D harmonic crystal is considered and the properties of the exact discrete solution and the solution of the ballistic heat equation introduced by Krivtsov are numerically compared. The aim of this note is to demonstrate that the latter continuum fundamental solution can be formally obtained as the slow time-varying component of the large-time asymptotics for the exact discrete solution on a moving point of observation.Comment: 11 pages, 1 figur