title: Evidence for Marginal Stability in Emulsions.
abstract: We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(ω) exhibits a low-frequency cutoff ω^{*}, which scales linearly with the number of extra contacts per particle δz. Moreover, for ω<ω^{*}, our results are consistent with D(ω)∼ω^{2}/ω^{*2}, a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings [E. DeGiuli, A. Laversanne-Finot, G. A. Düring, E. Lerner, and M. Wyart, Soft Matter 10, 5628 (2014); S. Franz, G. Parisi, P. Urbani, and F. Zamponi, Proc. Natl. Acad. Sci. U.S.A. 112, 14539 (2015)]. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.
authors.affiliation: Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA.|School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Lin
authors.affiliation: Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA.
authors.forename: Ivane
authors.initials: I
authors.lastname: Jorjadze
authors.affiliation: Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA.|Institut des Nanosciences de Paris, UMR 7588-CNRS/Universite Pierre et Marie Curie, 75005 Paris, France.
authors.forename: Lea-Laetitia
authors.initials: LL
authors.lastname: Pontani
authors.affiliation: Physics Institute, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland.
authors.forename: Matthieu
authors.initials: M
authors.lastname: Wyart
authors.affiliation: Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA.
authors.forename: Jasna
authors.initials: J
authors.lastname: Brujic