32 research outputs found
Non-affine response: jammed packings versus spring networks
We compare the elastic response of spring networks whose contact geometry is
derived from real packings of frictionless discs, to networks obtained by
randomly cutting bonds in a highly connected network derived from a
well-compressed packing. We find that the shear response of packing-derived
networks, and both the shear and compression response of randomly cut networks,
are all similar: the elastic moduli vanish linearly near jamming, and
distributions characterizing the local geometry of the response scale with
distance to jamming. Compression of packing-derived networks is exceptional:
the elastic modulus remains constant and the geometrical distributions do not
exhibit simple scaling. We conclude that the compression response of jammed
packings is anomalous, rather than the shear response.Comment: 6 pages, 6 figures, submitted to ep
Vibrations in materials with granularity
This thesis concerns the vibrational properties of different classical disordered condensed matter systems. In the first part we focus on materials that exhibit a rigidity transition as their density is increased. By introducing a new method into the field, we were able to look into the localization behavior of vibrational modes of jammed packings of soft spherical particles, both in the localized regime where the localization length is much less and in the regime where it is grater than the linear system size. We also analyze the nature of vibrational modes of jammed packings of soft elliptical particles, where we uncover the change of the structure of the spectrum, compared to the simplest model of sphere packings, due to the rotational degrees of freedom of the particles. In the second part of this thesis we explore the localization properties of collective modes and response to uniform driving of bubble clouds. We find that the response is often very different from that of a typical mode because the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by an ultrasound.UBL - phd migration 201
Excitations of Ellipsoid Packings near Jamming
We study the vibrational modes of three-dimensional jammed packings of soft
ellipsoids of revolution as a function of particle aspect ratio and
packing fraction. At the jamming transition for ellipsoids, as distinct from
the idealized case using spheres where , there are many
unconstrained and non-trivial rotational degrees of freedom. These constitute a
set of zero-frequency modes that are gradually mobilized into a new rotational
band as increases. Quite surprisingly, as this new band is
separated from zero frequency by a gap, and lies below the onset frequency for
translational vibrations, , the presence of these new degrees of
freedom leaves unaltered the basic scenario that the translational spectrum is
determined only by the average contact number. Indeed, depends
solely on coordination as it does for compressed packings of spheres. We also
discuss the regime of large , where the two bands merge.Comment: 6 pages, 4 figure
Critical jamming of frictional grains in the generalized isostaticity picture
While frictionless spheres at jamming are isostatic, frictional spheres at
jamming are not. As a result, frictional spheres near jamming do not
necessarily exhibit an excess of soft modes. However, a generalized form of
isostaticity can be introduced if fully mobilized contacts at the Coulomb
friction threshold are considered as slipping contacts. We show here that, in
this framework, the vibrational density of states (DOS) of frictional discs
exhibits a plateau when the generalized isostaticity line is approached. The
crossover frequency to elastic behavior scales linearly with the distance from
this line. Moreover, we show that the frictionless limit, which appears
singular when fully mobilized contacts are treated elastically, becomes smooth
when fully mobilized contacts are allowed to slip.Comment: 4 pages, 4 figures, submitted to PR
Universality in the jamming limit for elongated hard particles in one dimension
We study thermodynamics properties of a one dimensional gas of hard elongated
particles. The particle centers are restricted to a line, while they can rotate
in two-dimensional space. Correlations between orientations of the objects are
studied (by transfer matrix method) as a function of density and aspect ratio.
The behavior in the extreme high-density (jamming) limit is described by a few
universality classes depending on the object's shape. In particular, there is a
diverging correlation length when the contact point of adjacent objects is far
from the line along which their centers move, as for needles and rectangles.Comment: LaTeX, 6 pages, 4 figure
Localization behavior of vibrational modes in granular packings
We study the localization of vibrational modes of frictionless granular
media. We introduce a new method, motivated by earlier work on non-Hermitian
quantum problems, which works well both in the localized regime where the
localization length is much less than the linear size and in the
regime grater or of order when modes are extended throughout our
finite system. Our very lowest frequency modes show "quasi-localized"
resonances away from the jamming point; the spatial extent of these regions
increases as the jamming point is approached, as expected theoretically.
Throughout the remaining frequency range, our data show no signature of the
nearness of the jamming point and collapse well when properly rescaled with the
system size. Using Random Matrix Theory we derive the scaling relation ~
for the regime >> in dimensions.Comment: 6 pages, 7 figure
Origin of Corrections to Mean-field at the Onset of Unjamming
We present a detailed analysis of the unjamming transition in 2D frictionless
disk packings using a static correlation function that has been widely used to
study disordered systems. We show that this point-to-set (PTS) correlation
function exhibits a dominant length scale that diverges as the unjamming
transition is approached through decompression. In addition, we identify
deviations from meanfield predictions, and present detailed analysis of the
origin of non-meanfield behavior. A mean-field bulk-surface argument is
reviewed. Corrections to this argument are identified, which lead to a change
in the functional form of the critical PTS boundary size. An entropic
description of the origin of the correlations is presented, and simple rigidity
assumptions are shown to predict the functional form of the critical PTS
boundary size as a function of the pressure
Multi-step self-guided pathways for shape-changing metamaterials
Multi-step pathways, constituted of a sequence of reconfigurations, are
central to a wide variety of natural and man-made systems. Such pathways
autonomously execute in self-guided processes such as protein folding and
self-assembly, but require external control in macroscopic mechanical systems,
provided by, e.g., actuators in robotics or manual folding in origami. Here we
introduce shape-changing mechanical metamaterials, that exhibit self-guided
multi-step pathways in response to global uniform compression. Their design
combines strongly nonlinear mechanical elements with a multimodal architecture
that allows for a sequence of topological reconfigurations, i.e., modifications
of the topology caused by the formation of internal self-contacts. We realized
such metamaterials by digital manufacturing, and show that the pathway and
final configuration can be controlled by rational design of the nonlinear
mechanical elements. We furthermore demonstrate that self-contacts suppress
pathway errors. Finally, we demonstrate how hierarchical architectures allow to
extend the number of distinct reconfiguration steps. Our work establishes
general principles for designing mechanical pathways, opening new avenues for
self-folding media, pluripotent materials, and pliable devices in, e.g.,
stretchable electronics and soft robotics.Comment: 16 pages, 3 main figures, 10 extended data figures. See
https://youtu.be/8m1QfkMFL0I for an explanatory vide
Vibrations in materials with granularity
This thesis concerns the vibrational properties of different classical disordered condensed matter systems. In the first part we focus on materials that exhibit a rigidity transition as their density is increased. By introducing a new method into the field, we were able to look into the localization behavior of vibrational modes of jammed packings of soft spherical particles, both in the localized regime where the localization length is much less and in the regime where it is grater than the linear system size. We also analyze the nature of vibrational modes of jammed packings of soft elliptical particles, where we uncover the change of the structure of the spectrum, compared to the simplest model of sphere packings, due to the rotational degrees of freedom of the particles. In the second part of this thesis we explore the localization properties of collective modes and response to uniform driving of bubble clouds. We find that the response is often very different from that of a typical mode because the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by an ultrasound
Non-affine response: Jammed packings vs. spring networks
We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response