144 research outputs found
Critical scaling in linear response of frictionless granular packings near jamming
We study the origin of the scaling behavior in frictionless granular media
above the jamming transition by analyzing their linear response. The response
to local forcing is non-self-averaging and fluctuates over a length scale that
diverges at the jamming transition. The response to global forcing becomes
increasingly non-affine near the jamming transition. This is due to the
proximity of floppy modes, the influence of which we characterize by the local
linear response. We show that the local response also governs the anomalous
scaling of elastic constants and contact number.Comment: 4 pages, 3 figures. v2: Added new results; removed part of
discussion; changed Fig.
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
Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses
We investigate correlations between low-frequency vibrational modes and
rearrangements in two-dimensional colloidal glasses composed of thermosensitive
microgel particles which readily permit variation of sample packing fraction.
At each packing fraction, the particle displacement covariance matrix is
measured and used to extract the vibrational spectrum of the "shadow" colloidal
glass (i.e., the particle network with the same geometry and interactions as
the sample colloid but absent damping). Rearrangements are induced by
successive, small reductions in packing fraction. The experimental results
suggest that low-frequency quasi-localized phonon modes in colloidal glasses,
i.e., modes that present low energy barriers for system rearrangements, are
spatially correlated with rearrangements in this thermal system
Exact mean field inference in asymmetric kinetic Ising systems
We develop an elementary mean field approach for fully asymmetric kinetic
Ising models, which can be applied to a single instance of the problem. In the
case of the asymmetric SK model this method gives the exact values of the local
magnetizations and the exact relation between equal-time and time-delayed
correlations. It can also be used to solve efficiently the inverse problem,
i.e. determine the couplings and local fields from a set of patterns, also in
cases where the fields and couplings are time-dependent. This approach
generalizes some recent attempts to solve this dynamical inference problem,
which were valid in the limit of weak coupling. It provides the exact solution
to the problem also in strongly coupled problems. This mean field inference can
also be used as an efficient approximate method to infer the couplings and
fields in problems which are not infinite range, for instance in diluted
asymmetric spin glasses.Comment: 10 pages, 7 figure
Scaling of phononic transport with connectivity in amorphous solids
The effect of coordination on transport is investigated theoretically using
random networks of springs as model systems. An effective medium approximation
is made to compute the density of states of the vibrational modes, their energy
diffusivity (a spectral measure of transport) and their spatial correlations as
the network coordination is varied. Critical behaviors are obtained as
where these networks lose rigidity. A sharp cross-over from a regime
where modes are plane-wave-like toward a regime of extended but
strongly-scattered modes occurs at some frequency , which
does not correspond to the Ioffe-Regel criterion. Above both the
density of states and the diffusivity are nearly constant. These results agree
remarkably with recent numerical observations of repulsive particles near the
jamming threshold \cite{ning}. The analysis further predicts that the length
scale characterizing the correlation of displacements of the scattered modes
decays as with frequency, whereas for
Rayleigh scattering is found with a scattering length . It is argued that this description applies to silica glass
where it compares well with thermal conductivity data, and to transverse
ultrasound propagation in granular matter
Bounds on the shear load of cohesionless granular matter
We characterize the force state of shear-loaded granular matter by relating
the macroscopic stress to statistical properties of the force network. The
purely repulsive nature of the interaction between grains naturally provides an
upper bound for the sustainable shear stress, which we analyze using an
optimization procedure inspired by the so-called force network ensemble. We
establish a relation between the maximum possible shear resistance and the
friction coefficient between individual grains, and find that anisotropies of
the contact network (or the fabric tensor) only have a subdominant effect.
These results can be considered the hyperstatic limit of the force network
ensemble and we discuss possible implications for real systems. Finally, we
argue how force anisotropies can be related quantitatively to experimental
measurements of the effective elastic constants.Comment: 17 pages, 6 figures. v2: slightly rearranged, introduction and
discussion rewritte
Ensemble Theory for Force Networks in Hyperstatic Granular Matter
An ensemble approach for force networks in static granular packings is
developed. The framework is based on the separation of packing and force
scales, together with an a-priori flat measure in the force phase space under
the constraints that the contact forces are repulsive and balance on every
particle. In this paper we will give a general formulation of this force
network ensemble, and derive the general expression for the force distribution
. For small regular packings these probability densities are obtained in
closed form, while for larger packings we present a systematic numerical
analysis. Since technically the problem can be written as a non-invertible
matrix problem (where the matrix is determined by the contact geometry), we
study what happens if we perturb the packing matrix or replace it by a random
matrix. The resulting 's differ significantly from those of normal
packings, which touches upon the deep question of how network statistics is
related to the underlying network structure. Overall, the ensemble formulation
opens up a new perspective on force networks that is analytically accessible,
and which may find applications beyond granular matter.Comment: 17 pages, 17 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
Identification of an alternative triglyceride biosynthesis pathway
Triacylglycerols (TAGs) are the main source of stored energy in the body, providing an important substrate pool for mitochondrial beta-oxidation. Imbalances in the amount of TAGs are associated with obesity, cardiac disease and various other pathologies 1,2. In humans, TAGs are synthesized from excess, coenzyme A-conjugated fatty acids by diacylglycerol O-acyltransferases (DGAT1 and DGAT2) 3. In other organisms, this activity is complemented by additional enzymes 4, but whether such alternative pathways exist in humans remains unknown. Here we disrupt the DGAT pathway in haploid human cells and use iterative genetics to reveal an unrelated TAG-synthesizing system composed of a protein we called DIESL (also known as TMEM68, an acyltransferase of previously unknown function) and its regulator TMX1. Mechanistically, TMX1 binds to and controls DIESL at the endoplasmic reticulum, and loss of TMX1 leads to the unconstrained formation of DIESL-dependent lipid droplets. DIESL is an autonomous TAG synthase, and expression of human DIESL in Escherichia coli endows this organism with the ability to synthesize TAG. Although both DIESL and the DGATs function as diacylglycerol acyltransferases, they contribute to the cellular TAG pool under specific conditions. Functionally, DIESL synthesizes TAG at the expense of membrane phospholipids and maintains mitochondrial function during periods of extracellular lipid starvation. In mice, DIESL deficiency impedes rapid postnatal growth and affects energy homeostasis during changes in nutrient availability. We have therefore identified an alternative TAG biosynthetic pathway driven by DIESL under potent control by TMX1. </p
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
- …