70 research outputs found
Elasticity Theory of a Twisted Stack of Plates
We present an elastic model of B-form DNA as a stack of thin, rigid plates or
base pairs that are not permitted to deform. The symmetry of DNA and the
constraint of plate rigidity limit the number of bulk elastic constants
contributing to a macroscopic elasticity theory of DNA to four. We derive an
effective twist-stretch energy in terms of the macroscopic stretch epsilon
along and relative excess twist sigma about the DNA molecular axis. In addition
to the bulk stretch and twist moduli found previously, we obtain a
twist-stretch modulus with the following remarkable properties: 1) it vanishes
when the radius of the helical curve following the geometric center of each
plate is zero, 2) it vanishes with the elastic constant K_{23} that couples
compression normal to the plates to a shear strain, if the plates are
perpendicular to the molecular axis, and 3) it is nonzero if the plates are
tilted relative to the molecular axis. This implies that a laminated helical
structure carved out of an isotropic elastic medium will not twist in response
to a stretching force, but an isotropic material will twist if it is bent into
the shape of a helix.Comment: 19 pages, plain LaTeX, 1 included eps figur
Elastic Energy, Fluctuations and Temperature for Granular Materials
We probe, using a model system, elastic and kinetic energies for sheared
granular materials. For large enough (pressure/Young's modulus) and
(kinetic energy density) elastic dominates kinetic energy, and
energy fluctuations become primarily elastic in nature. This regime has likely
been reached in recent experiments. We consider a generalization of the
granular temperature, , with both kinetic and elastic terms and that
changes smoothly from one regime to the other. This is roughly consistent
with a temperature adapted from equilibrium statistical mechanics.Comment: 4 pages, 4 figure
Enumeration of distinct mechanically stable disk packings in small systems
We create mechanically stable (MS) packings of bidisperse disks using an
algorithm in which we successively grow or shrink soft repulsive disks followed
by energy minimization until the overlaps are vanishingly small. We focus on
small systems because this enables us to enumerate nearly all distinct MS
packings. We measure the probability to obtain a MS packing at packing fraction
and find several notable results. First, the probability is highly
nonuniform. When averaged over narrow packing fraction intervals, the most
probable MS packing occurs at the highest and the probability decays
exponentially with decreasing . Even more striking, within each
packing-fraction interval, the probability can vary by many orders of
magnitude. By using two different packing-generation protocols, we show that
these results are robust and the packing frequencies do not change
qualitatively with different protocols.Comment: 4 pages, 3 figures, Conference Proceedings for X International
Workshop on Disordered System
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