Pore radii (space between soil particles) can range from millimetre-scale between sand grains to micrometre-scale between clay grains.
In the inertial regime of frequency-radius space, irregularity and aggregation of particles can result in values of acoustic attenuation that are significantly different from those predicted by assuming separated smooth spherical particles.
So, in being created, the universe must leap from no size at all -- zero radius, "no space and no time" -- to a radius large enough for inflation to take over without passing through the in-between sizes, a quantum-mechanical process called "tunneling".
Also, for the Kuramoto Sivashinsky equation, we give a partial answer to a conjecture that the radius of space analyticity on the attractor is independent of the spatial period.
I left for a minute to go make out with someone in a cellar and when I came back Twodeadsluts Onegoodfuck were playing, and there was a ten-foot radius of space around them.
For so-called small masses, the solution does not differ appreciably from that afforded by Newton's gravitational law; but for "large" masses the radius of space-time curvature may approach or exceed that of the physical object, and the Schwarzschild solution predicts unusual properties.
Numerical solutions for the crack tip field and the stress in the fiber are obtained for various values such as crack radius, crack spacing and fiber volume fraction.
Specifically, the optimum particle radius and spacing that can strengthen the interface exist; and (4) the toughening effect is also dependent on the relative orientation and the twinning orientation.
The first gray-shaded area corresponds to the 1979 solar maximum, and the second gray-shaded area relates to the 1986 solar minimum Fig. 8 Short-term (periods ranging from ~0.50 to ~13.00 years) phase space radius, R st, for: the sunspot area (upper panel), the neutron monitor count rate (middle panel), and the potential gradient (lower panel).
The defining formula for the i-th time step is: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0018678.e001.PNG" class= inline-graphic"/> where the transinformation I is a function of the relative shift and relative phase space radius r, given for every sample point i.
