Contraction Of Radius Research Articles

Effect of velocity and radius distribution on jet breakup

The focus of this paper is on the effect of velocity and radius distribution on jet breakup. A theoretical model is established to analyze and predict the velocity distribution along the jet, which is physically and mathematically continuous. The simplified forms of the breakup time, the disturbance growth rate, and the disturbance level considering the velocity and radius distribution are presented. A series of prediction methods for predicting the jet breakup length and droplet size are developed. A Newtonian laminar jet falling vertically was experimentally observed to validate the theoretical model and prediction methods. It is shown that the relaxation of the velocity profile leads to the rapid contraction of the jet radius near the outlet, which leads to the increase in the growth rate of the instability disturbance. The surface tension prevents the growth rate of disturbance from increasing by restraining the contraction of jet radius. The final amplification of jet velocity and contraction due to gravity acceleration depend on the Froude number and breakup length. When the influence of jet radius distribution on the growth rate of disturbance is considered, the breakup time is indirectly affected by the breakup length. The experimental and predicted results show that the accelerated falling of jet lengthens the breakup length traveled by the jet in a shortened breakup time due to the contraction of jet radius. The droplet volume is proportional to the predicted jet cross-sectional area at the breakup position and the Rayleigh wavelength determined by the nozzle radius.

Impact of the Diurnal Radiation Contrast on the Contraction of Radius of Maximum Wind during Intensification of Hurricane Edouard (2014)

Abstract This work examines the impacts of the diurnal radiation contrast on the contraction rate of the radius of maximum wind (RMW) during intensification of Hurricane Edouard (2014) through convection-permitting simulations. Rapid contraction of RMW occurs both in the low and midlevels for the control run and the sensitivity run without solar insolation, while the tropical cyclone contracts more slowly in the low levels and later in the midlevels and thereafter fails to intensify continuously in the absence of the night phase, under weak vertical wind shear (~4 m s−1). The clouds at the top of the boundary layer absorb solar shortwave heating during the daytime, which enhanced the temperature inversion there and increased the convective inhibition, while nighttime destabilization and moistening in low levels through radiative cooling decrease convective inhibition and favor more convection inside the RMW than in the daytime phase. The budget analysis of the tangential wind tendency reveals that the greater positive radial vorticity flux inside of the RMW is the key RMW contraction mechanism in the boundary layer at night because of the enhanced convection. However, the greater positive vertical advection of tangential wind inside of the RMW dominates the RMW contraction in the midlevels.

On Centered and Weakly Centered Operators

We show that if C is a contraction of spectral radius 1 then T is polynomially bounded if and only if the same is true of T ⊗ C. As a corollary, we obtain that every invertible, centered, polynomially bounded operator is similar to a contraction. We also prove a structure theorem for weakly centered operators that satisfy a hypothesis of a technical nature.

Bipolaron Formation in B12 and (B11C)+ Icosahedra

ABSTRACTBoron carbides, B1-xCx with 0.085 ≤ × ≤ 0.200, generally contain both B12 and B11C icosahedra. However, the electronic transport with 0.1 ≤ × ≤ 0.2 is believed to occur by means of bipolaron hopping between only B11 C icosahedra [i]. We have calculated the changes in energy, atomic positlions and charge distribution when a pair of electrons is added to the isoelectronic icosahedral clusters B12 and (B11C)+. We simulate an icosahedron in a neutral lattice by bonding the icosahedral atoms to hydrogenic atoms which we constrain to be neutral. The computations are performed with a self-consistent molecular-orbital method, PRDDO.We find a total energy reduction of -3.7 eV for two electrons added to a B12 icosahedron. Of this, -2.7 eV arises from the electrons filling the icosahedron's bonding orbitals. The remaining -1.0 eV comes from the contraction of the icosahedron's radius by -0.09 Å. For two electrons added to a (B11C)+ icosahedron we find a total energy reduction of -18.2 eV. Of this, -16.5 eV arises from filling the icosahedron's bonding orbitals. The remainder arises frop a -0.09 Å contraction of the icosahedron's radius. Thus, we find (B11C) icosahedra to be strongly energetically favored over B12 icosahedra as bipolaron sites.The positive charge associated with a (B11C)+ icosahedron is distributed over the eleven boron atoms. Concomitantly, we find the added two electrons of the bipolaron to be distributed over all twelve sites of the B11C icosahedron. We find the energy difference between an electron pair added to B12 and (B11C)+ icosahedra to arise principally from the increased Coulomic attraction provided by the extra positive charge of the (B11C) icosahedron.