Toward determination of optimal plane curves with a fixed degree over a finite field

AbstractFor a plane curve over Fq of degree q+1, it is known by our previous work that the number of its Fq-rational points is at most q2+1. In this paper, we determine the curves that attain this maximum, up to projective equivalence

High-sensitivity imaging with multi-mode twin beams

Twin entangled beams produced by single-pass parametric down-conversion (PDC) offer the opportunity to detect weak amount of absorption with an improved sensitivity with respect to standard techniques which make use of classical light sources. We propose a differential measurement scheme which exploits the spatial quantum correlation of type II PDC to image a weak amplitude object with a sensitivity beyond the standard quantum limit imposed by shot-noise.Comment: 13 pages, 8 figure

Optimal Survey Strategies and Predicted Planet Yields for the Korean Microlensing Telescope Network

The Korean Microlensing Telescope Network (KMTNet) will consist of three 1.6m telescopes each with a 4 deg^{2} field of view (FoV) and will be dedicated to monitoring the Galactic Bulge to detect exoplanets via gravitational microlensing. KMTNet's combination of aperture size, FoV, cadence, and longitudinal coverage will provide a unique opportunity to probe exoplanet demographics in an unbiased way. Here we present simulations that optimize the observing strategy for, and predict the planetary yields of, KMTNet. We find preferences for four target fields located in the central Bulge and an exposure time of t_{exp} = 120s, leading to the detection of ~2,200 microlensing events per year. We estimate the planet detection rates for planets with mass and separation across the ranges 0.1 <= M_{p}/M_{Earth} <= 1000 and 0.4 <= a/AU <= 16, respectively. Normalizing these rates to the cool-planet mass function of Cassan (2012), we predict KMTNet will be approximately uniformly sensitive to planets with mass 5 <= M_{p}/M_{Earth} <= 1000 and will detect ~20 planets per year per dex in mass across that range. For lower-mass planets with mass 0.1 <= M_{p}/M_{Earth} < 5, we predict KMTNet will detect ~10 planets per year. We also compute the yields KMTNet will obtain for free-floating planets (FFPs) and predict KMTNet will detect ~1 Earth-mass FFP per year, assuming an underlying population of one such planet per star in the Galaxy. Lastly, we investigate the dependence of these detection rates on the number of observatories, the photometric precision limit, and optimistic assumptions regarding seeing, throughput, and flux measurement uncertainties.Comment: 29 pages, 31 figures, submitted to ApJ. For a brief video explaining the key results of this paper, please visit: https://www.youtube.com/watch?v=e5rWVjiO26

Switching dynamics of spatial solitary wave pixels

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching

Rheology effect determination of the heterogeneous rock massif on the stress-strain state of the breakage face geomechanical system

The purpose of this study is to determine the nature of influence of the rheological properties of the rocks on the results of computational experiments simulating the mine workings contour condition during the breakage face advance. To determine the deformations along the mine workings contour, the calculations have been made of the junction area between the preparatory and stope face mine workings by the finite element method for various parameters of the material models. These data provided the basis for analysis of the patterns development of the rheology modelling influence on the stress-strain state of the geomechanical system. The obtained patterns are described by a function of many variables, and this function determines the limit and degree of rheology effect on the results of calculations. For the first time this pattern takes into account the heterogeneity of the rheological characteristics of rocks and the specifics of the computational domain geometry. The use of the obtained patterns makes it possible to simplify significantly the process of modelling in time and space of the geomechanical systems, which have a complex structure describing the interaction of several objects

Microlensing Searches for Exoplanets

Gravitational microlensing finds planets through their gravitational influence on the light coming from a more distant background star. The presence of the planet is then inferred from the tell-tale brightness variations of the background star during the lensing event, even if no light is detectable from the planet or the host foreground star. This review covers fundamental theoretical concepts in microlensing, addresses how observations are performed in practice, the~challenges of obtaining accurate measurements, and explains how planets reveal themselves in the data. It~concludes with a presentation of the most important findings to-date, a description of the method's strengths and weaknesses, and a discussion of the future prospects of microlensing.Comment: 35 pages,9 figures, invited review for Geosciences Special Issue "Detection and Characterization of Extrasolar Planets