Debris disk size distributions: steady state collisional evolution with P-R drag and other loss processes

We present a new scheme for determining the shape of the size distribution, and its evolution, for collisional cascades of planetesimals undergoing destructive collisions and loss processes like Poynting-Robertson drag. The scheme treats the steady state portion of the cascade by equating mass loss and gain in each size bin; the smallest particles are expected to reach steady state on their collision timescale, while larger particles retain their primordial distribution. For collision-dominated disks, steady state means that mass loss rates in logarithmic size bins are independent of size. This prescription reproduces the expected two phase size distribution, with ripples above the blow-out size, and above the transition to gravity-dominated planetesimal strength. The scheme also reproduces the expected evolution of disk mass, and of dust mass, but is computationally much faster than evolving distributions forward in time. For low-mass disks, P-R drag causes a turnover at small sizes to a size distribution that is set by the redistribution function (the mass distribution of fragments produced in collisions). Thus information about the redistribution function may be recovered by measuring the size distribution of particles undergoing loss by P-R drag, such as that traced by particles accreted onto Earth. Although cross-sectional area drops with 1/age^2 in the PR-dominated regime, dust mass falls as 1/age^2.8, underlining the importance of understanding which particle sizes contribute to an observation when considering how disk detectability evolves. Other loss processes are readily incorporated; we also discuss generalised power law loss rates, dynamical depletion, realistic radiation forces and stellar wind drag.Comment: Accepted for publication by Celestial Mechanics and Dynamical Astronomy (special issue on EXOPLANETS

An Ultra-low Carbon, Thermomechanically Controlled Processed Microalloyed Steel: Microstructure and Mechanical Properties

In the current study, a novel ultra-low carbon, high-molybdenum-bearing microalloyed steel has been thermomechanically processed. Transformation of this steel during continuous cooling has been assessed. Variation in the microstructure and mechanical properties at different finish rolling temperatures has been studied. The average grain size, misorientation of grain boundary, and distribution of ferrite grains have been analyzed by using electron backscatter diffraction. The lower yield strength (251 to 377 MPa) with moderate tensile strength (406 to 506 MPa) along with high ductility (30 to 47 pct) has been achieved in the selected range of finish rolling temperatures. Superior impact toughness value in the range of 153 to 162 J is obtained in the subsize specimen even at subzero temperatures (233 K [−40 °C]), which is attributed to fine average ferrite grain size. The acicular ferrite dominated microstructure obtained at the 1023 K (750 °C) finish rolling temperature is the most attractive microstructure for pipeline applications due to its excellent combination of strength and toughness