32,178 research outputs found
Reynolds Pressure and Relaxation in a Sheared Granular System
We describe experiments that probe the evolution of shear jammed states,
occurring for packing fractions , for frictional
granular disks, where above there are no stress-free static states. We
use a novel shear apparatus that avoids the formation of inhomogeneities known
as shear bands. This fixed system exhibits coupling between the shear
strain, , and the pressure, , which we characterize by the `Reynolds
pressure', and a `Reynolds coefficient', . depends only on , and diverges as , where , and . Under
cyclic shear, this system evolves logarithmically slowly towards limit cycle
dynamics, which we characterize in terms of pressure relaxation at cycle :
. depends only on the shear cycle
amplitude, suggesting an activated process where plays a
temperature-like role.Comment: 4 pages, 4 figure
The -log-convexity of Domb's polynomials
In this paper, we prove the -log-convexity of Domb's polynomials, which
was conjectured by Sun in the study of Ramanujan-Sato type series for powers of
. As a result, we obtain the log-convexity of Domb's numbers. Our proof is
based on the -log-convexity of Narayana polynomials of type and a
criterion for determining -log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273
Experiment and theoretical study of the propagation of high power microwave pulse in air breakdown environment
In the study of the propagation of high power microwave pulse, one of the main concerns is how to minimize the energy loss of the pulse before reaching the destination. In the very high power region, one has to prevent the cutoff reflection caused by the excessive ionization in the background air. A frequency auto-conversion process which can lead to reflectionless propagation of powerful EM pulses in self-generated plasmas is studied. The theory shows that under the proper conditions the carrier frequency, omega, of the pulse will indeed shift upward with the growth of plasma frequency, omega(sub pe). Thus, the plasma during breakdown will always remain transparent to the pulse (i.e., omega greater than omega(sub pe)). A chamber experiment to demonstrate the frequency auto-conversion during the pulse propagation through the self-generated plasma is then conducted in a chamber. The detected frequency shift is compared with the theoretical result calculated y using the measured electron density distribution along the propagation path of the pulse. Good agreement between the theory and the experiment results is obtained
On the -log-convexity conjecture of Sun
In his study of Ramanujan-Sato type series for , Sun introduced a
sequence of polynomials as given by
and he conjectured that the polynomials are -log-convex. By
imitating a result of Liu and Wang on generating new -log-convex sequences
of polynomials from old ones, we obtain a sufficient condition for determining
the -log-convexity of self-reciprocal polynomials. Based on this criterion,
we then give an affirmative answer to Sun's conjecture
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