On coupled systems of Kolmogorov equations with applications to stochastic differential games

We prove that a family of linear bounded evolution operators $({\bf G}(t,s))_{t\ge s\in I}$ can be associated, in the space of vector-valued bounded and continuous functions, to a class of systems of elliptic operators $\bm{\mathcal A}$ with unbounded coefficients defined in I\times \Rd (where $I$ is a right-halfline or $I=\R$) all having the same principal part. We establish some continuity and representation properties of $({\bf G}(t,s))_{t \ge s\in I}$ and a sufficient condition for the evolution operator to be compact in C_b(\Rd;\R^m). We prove also a uniform weighted gradient estimate and some of its more relevant consequence

An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations

The Spectrum of Pluto, 0.40 - 0.93 μ\mum I. Secular and longitudinal distribution of ices and complex organics

Context. During the last 30 years the surface of Pluto has been characterized, and its variability has been monitored, through continuous near-infrared spectroscopic observations. But in the visible range only few data are available. Aims. The aim of this work is to define the Pluto's relative reflectance in the visible range to characterize the different components of its surface, and to provide ground based observations in support of the New Horizons mission. Methods. We observed Pluto on six nights between May and July 2014, with the imager/spectrograph ACAM at the William Herschel Telescope (La Palma, Spain). The six spectra obtained cover a whole rotation of Pluto (Prot = 6.4 days). For all the spectra we computed the spectral slope and the depth of the absorption bands of methane ice between 0.62 and 0.90 $\mu$m. To search for shifts of the center of the methane bands, associated with dilution of CH4 in N2, we compared the bands with reflectances of pure methane ice. Results. All the new spectra show the methane ice absorption bands between 0.62 and 0.90 $\mu$m. The computation of the depth of the band at 0.62 $\mu$m in the new spectra of Pluto, and in the spectra of Makemake and Eris from the literature, allowed us to estimate the Lambert coefficient at this wavelength, at a temperature of 30 K and 40 K, never measured before. All the detected bands are blue shifted, with minimum shifts in correspondence with the regions where the abundance of methane is higher. This could be indicative of a dilution of CH4:N2 more saturated in CH4. The longitudinal and secular variations of the parameters measured in the spectra are in accordance with results previously reported in the literature and with the distribution of the dark and bright material that show the Pluto's albedo maps from New Horizons.Comment: This manuscript may change and improve during the reviewing process. The data reduction and calibration is reliable and has been checked independently using different reduction approaches. The data will be made publicily available when the paper is accepted. If you need them before, please, contact the autho

On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

Expected spectral characteristics of (101955) Bennu and (162173) Ryugu, targets of the OSIRIS-REx and Hayabusa2 missions

NASA's OSIRIS-REx and JAXA's Hayabusa2 sample-return missions are currently on their way to encounter primitive near-Earth asteroids (101955) Bennu and (162173) Ryugu, respectively. Spectral and dynamical evidence indicates that these near-Earth asteroids originated in the inner part of the main belt. There are several primitive collisional families in this region, and both these asteroids are most likely to have originated in the Polana-Eulalia family complex. We present the expected spectral characteristics of both targets based on our studies of our primitive collisional families in the inner belt: Polana-Eulalia, Erigone, Sulamitis, and Clarissa. Observations were obtained in the framework of our PRIMitive Asteroids Spectroscopic Survey (PRIMASS). Our results are especially relevant to the planning and interpretation of in-situ images and spectra to be obtained by the two spacecraft during the encounters with their targets.Comment: 22 pages, 11 figures. Accepted for publication in Icarus on May 11, 201