Force distribution affects vibrational properties in hard-sphere glasses. DeGiuli, E.; Lerner, E.; Brito, C.; and Wyart, M. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 111(48):17054-17059, NATL ACAD SCIENCES, 12, 2014.
abstract   bibtex   
We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f) similar to f(theta e), the force distribution of such pairs and phi(c) the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale.*, rising up to it as D(omega)similar to omega(2+a), and decaying above omega* as D(omega)similar to omega(-a) where a=(1-theta(e))/(3+theta(e)) and omega is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with similar to 1/mu similar to(phi(c)-phi)(k), where kappa= 2-2=(3+theta(e)), and (iii) continuum elasticity breaks down on a scale l(c) similar to 1/root delta z similar to(phi(c)-phi)(-b), where b=(1+theta(e))/(6+2 theta(e)) and partial derivative z = z - 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that theta(e) approximate to 0.41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to kappa approximate to 1.41, a approximate to 0.17, and b approximate to 0.21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d =infinity, whereas some observations differ, as rationalized by the present approach.
@article{
 title = {Force distribution affects vibrational properties in hard-sphere glasses},
 type = {article},
 year = {2014},
 identifiers = {[object Object]},
 keywords = {colloids; glass transition; marginal stability; bo},
 pages = {17054-17059},
 volume = {111},
 month = {12},
 publisher = {NATL ACAD SCIENCES},
 city = {2101 CONSTITUTION AVE NW, WASHINGTON, DC 20418 USA},
 id = {e75e4697-e014-3814-b129-0514cbab382d},
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 last_modified = {2017-03-14T12:30:08.401Z},
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 abstract = {We theoretically and numerically study the elastic properties of
hard-sphere glasses and provide a real-space description of their
mechanical stability. In contrast to repulsive particles at zero
temperature, we argue that the presence of certain pairs of particles
interacting with a small force f soften elastic properties. This
softening affects the exponents characterizing elasticity at high
pressure, leading to experimentally testable predictions. Denoting P(f)
similar to f(theta e), the force distribution of such pairs and phi(c)
the packing fraction at which pressure diverges, we predict that (i) the
density of states has a low-frequency peak at a scale.*, rising up to
it as D(omega)similar to omega(2+a), and decaying above omega* as
D(omega)similar to omega(-a) where a=(1-theta(e))/(3+theta(e)) and omega
is the frequency, (ii) shear modulus and mean-squared displacement are
inversely proportional with <delta R-2>similar to 1/mu similar
to(phi(c)-phi)(k), where kappa= 2-2=(3+theta(e)), and (iii) continuum
elasticity breaks down on a scale l(c) similar to 1/root delta z similar
to(phi(c)-phi)(-b), where b=(1+theta(e))/(6+2 theta(e)) and partial
derivative z = z - 2d, where z is the coordination and d the spatial
dimension. We numerically test (i) and provide data supporting that
theta(e) approximate to 0.41 in our bidisperse system, independently of
system preparation in two and three dimensions, leading to kappa
approximate to 1.41, a approximate to 0.17, and b approximate to 0.21.
Our results for the mean-square displacement are consistent with a
recent exact replica computation for d =infinity, whereas some
observations differ, as rationalized by the present approach.},
 bibtype = {article},
 author = {DeGiuli, Eric and Lerner, Edan and Brito, Carolina and Wyart, Matthieu},
 journal = {PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA},
 number = {48}
}
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