Survival and coexistence for a multitype contact process

We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the $d$-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.Comment: Published in at http://dx.doi.org/10.1214/08-AOP422 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Method for Determining Cloud-Droplet Impingement on Swept Wings

The general effect of wing sweep on cloud-droplet trajectories about swept wings of high aspect ratio moving at subsonic speeds is discussed. A method of computing droplet trajectories about yawed cylinders and swept wings is presented, and illustrative droplet trajectories are computed. A method of extending two-dimensional calculations of droplet impingement on nonswept wings to swept wings is presented. It is shown that the extent of impingement of cloud droplets on an airfoil surface, the total rate of collection of water, and the local rate of impingement per unit area of airfoil surface can be found for a swept wing from two-dimensional data for a nonswept wing. The impingement on a swept wing is obtained from impingement data for a nonswept airfoil section which is the same as the section in the normal plane of the swept wing by calculating all dimensionless parameters with respect to flow conditions in the normal plane of the swept wing

Variation of Local Liquid-Water Concentration About an Ellipsoid of Fineness Ratio 10 Moving in a Droplet Field

Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 10 (10 percent thick) in flight through a droplet field were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters that describe flight and atmospheric conditions. The data indicate that the expected local concentration factors should be considered when choosing the location of devices that protrude into the stream from aircraft fuselages or missiles, or when determining antiicing heat requirements for the protection of these devices

Impingement of Water Droplets on NACA 65A004 Airfoil at 0 Deg Angle of Attack

The trajectories of water droplets in the air flowing past an NACA 6511004 airfoil at a n angle of attack of 0 deg were determined. The amount of water in droplet form impinging on the airfoil , the area of droplet impingement, and the rate of droplet impingement per unit area on the airfoil surface were calculated from the trajectories and presented t o cover a large range of flight and atmospheric conditions. These impingement characteristics are compared briefly with those previously reported for the same airfoil at angles of attack of 4 deg and 8 deg

Impingement of Water Droplets on an NACA 65(sub 1) -212 Airfoil at an Angle of Attack of 4 Deg

The trajectories of droplets in the air flowing past an NACA 651-212 airfoil at an angle of attack of 40 were determined. The collection efficiency, the area of droplet impingement, and the rate of droplet impingement were calculated from the trajectories and are presented herein

An Instrument Employing a Coronal Discharge for the Determination of Droplet-Size Distribution in Clouds

A flight instrument that uses electric means for measuring the droplet-size distribution in above-freezing clouds has been devised and given preliminary evaluation in flight. An electric charge is placed on the droplets and they are separated aerodynamically according to their mass. Because the charge placed on the droplets is a. function of the droplet size, the size spectrum can 'be determined by measurement of the charge deposited on cylinders of several different sizes placed to intercept the charged droplets. An expression for the rate of charge acquisition by a water droplet in a field of coronal discharge is derived. The results obtained in flight with an instrument based on the method described indicate that continuous records of droplet-size spectrum variations in clouds can be obtained. The experimental instrument was used to evaluate the method and was not refined to the extent necessary for obtaining conclusive meteorological data. The desirable features of an instrument based on the method described are (i) The instrument can be used in clouds with temperatures above freezing; (2) the size and the shape of the cylinders do not change during the exposure time; (3) the readings are instantaneous and continuous; (4) the available sensitivity permits the study of variations in cloud structures of less than 200 feet in extent