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## A statistical mechanics framework for static granular matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/10/2008

Relevância na Pesquisa

65.57%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics

The physical properties of granular materials have been extensively studied
in recent years. So far, however, there exists no theoretical framework which
can explain the observations in a unified manner beyond the phenomenological
jamming diagram [1]. This work focuses on the case of static granular matter,
where we have constructed a statistical ensemble [2] which mirrors equilibrium
statistical mechanics. This ensemble, which is based on the conservation
properties of the stress tensor, is distinct from the original Edwards ensemble
and applies to packings of deformable grains. We combine it with a field
theoretical analysis of the packings, where the field is the Airy stress
function derived from the force and torque balance conditions. In this
framework, Point J characterized by a diverging stiffness of the pressure
fluctuations. Separately, we present a phenomenological mean-field theory of
the jamming transition, which incorporates the mean contact number as a
variable. We link both approaches in the context of the marginal rigidity
picture proposed by [3, 4].; Comment: 21 pages, 15 figures

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## The fraction of condensed counterions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We investigate the phenomenon of counterion condensation in a solution of
highly charged rigid polyelectrolytes within the cell model. A method is
proposed which -- based on the charge distribution function -- identifies both
the fraction of condensed ions and the radial extension of the condensed layer.
Within salt-free Poisson-Boltzmann (PB) theory it reproduces the well known
fraction 1-1/xi of condensed ions for a Manning parameter xi>1. Furthermore, it
predicts a weak salt dependence of this fraction and a breakdown of the concept
of counterion condensation in the high salt limit. We complement our
theoretical investigations with molecular dynamics simulations of a cell-like
model, which constantly yield a stronger condensation than predicted by PB
theory. While the agreement between theory and simulation is excellent in the
monovalent, weakly charged case, it deteriorates with increasing electrostatic
interaction strength and, in particular, increasing valence. For instance, at a
high concentration of divalent salt and large xi our computer simulations
predict charge oscillations, which mean-field theory is unable to reproduce.; Comment: 8 pages, 6 figures, using RevTeX style, revised version, 1 figure and
more pertinent remarks concerning the failure of the energy criterion

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## Tuned, driven, and active soft matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/01/2015

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65.57%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics

One characteristic feature of soft matter systems is their strong response to
external stimuli. As a consequence they are comparatively easily driven out of
their ground state and out of equilibrium, which leads to many of their
fascinating properties. Here, we review illustrative examples. This review is
structured by an increasing distance from the equilibrium ground state. On each
level, examples of increasing degree of complexity are considered. In detail,
we first consider systems that are quasi-statically tuned or switched to a new
state by applying external fields. These are common liquid crystals, liquid
crystalline elastomers, or ferrogels and magnetic elastomers. Next, we
concentrate on systems steadily driven from outside e.g. by an imposed flow
field. In our case, we review the reaction of nematic liquid crystals, of
bulk-filling periodically modulated structures such as block copolymers, and of
localized vesicular objects to an imposed shear flow. Finally, we focus on
systems that are "active" and "self-driven". Here our range spans from
idealized self-propelled point particles, via sterically interacting particles
like granular hoppers, via microswimmers such as self-phoretically driven
artificial Janus particles or biological microorganisms...

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## Stress transmission in granular matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/12/2001

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65.54%

The transmission of forces through a disordered granular system is studied by
means of a geometrical-topological approach that reduces the granular packing
into a set of layers. This layered structure constitutes the skeleton through
which the force chains set up. Given the granular packing, and the region where
the force is applied, such a skeleton is uniquely defined. Within this
framework, we write an equation for the transmission of the vertical forces
that can be solved recursively layer by layer. We find that a special class of
analytical solutions for this equation are L\'evi-stable distributions. We
discuss the link between criticality and fragility and we show how the
disordered packing naturally induces the formation of force-chains and arches.
We point out that critical regimes, with power law distributions, are
associated with the roughness of the topological layers. Whereas, fragility is
associated with local changes in the force network induced by local granular
rearrangements or by changes in the applied force. The results are compared
with recent experimental observations in particulate matter and with computer
simulations.; Comment: 14 pages, Latex, 5 EPS figures

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## Theory of Coherent Van der Waals Matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.59%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics#Condensed Matter - Strongly Correlated Electrons

We explain in depth the previously proposed theory of the coherent Van der
Waals(cVdW) interaction - the counterpart of Van der Waals (VdW) force -
emerging in spatially coherently fluctuating electromagnetic fields. We show
that cVdW driven matter is dominated by many body interactions, which are
significantly stronger than those found in standard Van der Waals (VdW)
systems. Remarkably, the leading 2- and 3-body interactions are of the same
order with respect to the distance $(\propto R^{-6})$, in contrast to the
usually weak VdW 3-body effects ($\propto R^{-9}$). From a microscopic theory
we show that the anisotropic cVdW many body interactions drive the formation of
low-dimensional structures such as chains, membranes and vesicles with very
unusual, non-local properties. In particular, cVdW chains display a
logarithmically growing stiffness with the chain length, while cVdW membranes
have a bending modulus growing linearly with their size. We argue that the cVdW
anisotropic many body forces cause local cohesion but also a negative effective
"surface tension". We conclude by deriving the equation of state for cVdW
materials and propose new experiments to test the theory, in particular the
unusual 3-body nature of cVdW.; Comment: 26 pages...

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## Self Assembly of Soft Matter Quasicrystals and Their Approximants

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.59%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Mesoscale and Nanoscale Physics#Condensed Matter - Materials Science

The surprising recent discoveries of quasicrystals and their approximants in
soft matter systems poses the intriguing possibility that these structures can
be realized in a broad range of nano- and micro-scale assemblies. It has been
theorized that soft matter quasicrystals and approximants are largely
entropically stabilized, but the thermodynamic mechanism underlying their
formation remains elusive. Here, we use computer simulation and free energy
calculations to demonstrate a simple design heuristic for assembling
quasicrystals and approximants in soft matter systems. Our study builds on
previous simulation studies of the self-assembly of dodecagonal quasicrystals
and approximants in minimal systems of spherical particles with complex,
highly-specific interaction potentials. We demonstrate an alternative
entropy-based approach for assembling dodecagonal quasicrystals and
approximants based solely on particle functionalization and shape, thereby
recasting the interaction-potential-based assembly strategy in terms of
simpler-to-achieve bonded and excluded-volume interactions. Here, spherical
building blocks are functionalized with mobile surface entities to encourage
the formation of structures with low surface contact area, including
non-close-packed and polytetrahedral structures. The building blocks also
possess shape polydispersity...

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## Jamming I: A volume function for jammed matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We introduce a "Hamiltonian"-like function, called the volume function,
indispensable to describe the ensemble of jammed matter such as granular
materials and emulsions from a geometrical point of view. The volume function
represents the available volume of each particle in the jammed systems. At the
microscopic level, we show that the volume function is the Voronoi volume
associated to each particle and in turn we provide an analytical formula for
the Voronoi volume in terms of the contact network, valid for any dimension. We
then develop a statistical theory for the probability distribution of the
volumes in 3d to calculate an average volume function coarse-grained at a
mesoscopic level. The salient result is the discovery of a mesoscopic volume
function inversely proportional to the coordination number. Our analysis is the
first step toward the calculation of macroscopic observables and equations of
state using the statistical mechanics of jammed matter, when supplemented by
the condition of mechanical equilibrium of jamming that properly defines jammed
matter at the ensemble level.; Comment: 23 pages, 8 figures

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## Entropy of jammed matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.55%

We investigate the nature of randomness in disordered packings of frictional
spheres. We calculate the entropy of 3D packings through the force and volume
ensemble of jammed matter, a mesoscopic ensemble and numerical simulations
using volume fluctuation analysis and graph theoretical methods. Equations of
state are obtained relating entropy, volume fraction and compactivity
characterizing the different states of jammed matter. At the mesoscopic level
the entropy vanishes at random close packing. The entropy of the jammed system
reveals that the random loose packings are more disordered than random close
packings, allowing for an unambiguous interpretation of both limits.; Comment: 5 pages, 1 figure

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## Random Loose Packing in Granular Matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/08/2008

Relevância na Pesquisa

65.55%

We introduce and simulate a two dimensional probabilistic model of granular
matter at vanishing pressure. The model exhibits a perfectly sharp random loose
packing density, a phenomenon that should be verifiable for real granular
matter.; Comment: 27 pages, 13 figures. Future versions may be found at:
http://www.ma.utexas.edu/users/radin/papers.html

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## Optical Microscopy of Soft Matter Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/08/2011

Relevância na Pesquisa

65.57%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Physics - Instrumentation and Detectors#Physics - Optics

The fast-growing field of soft matter research requires increasingly
sophisticated tools for experimental studies. One of the oldest and most widely
used tools to study soft matter systems is optical microscopy. Recent advances
in optical microscopy techniques have resulted in a vast body of new
experimental results and discoveries. New imaging modalities, such as nonlinear
optical microscopy techniques that were developed to achieve higher resolution,
enable soft matter research at length scales ranging from the molecular to the
macroscopic.
The aim of this chapter is to introduce a variety of optical microscopy
techniques available to soft matter researchers, starting from basic principles
and finishing with a discussion of the most advanced microscopy systems. We
describe traditional imaging techniques, such as bright field and polarizing
microscopy, along with state-of-the-art three-dimensional (3D) imaging
techniques, such as fluorescence confocal and nonlinear optical microscopies.
Different approaches are discussed along with their applications in the study
of soft matter systems by providing typical examples.; Comment: Total 41 pages (double spaced) including 18 figures, Soft Materials
book chapter

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## Active Matter Transport and Jamming on Disordered Landscapes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2014

Relevância na Pesquisa

65.55%

We numerically examine the transport of active run-and-tumble particles
driven with a drift force over random disordered landscapes comprised of fixed
obstacles. For increasing run lengths, the net particle transport initially
increases before reaching a maximum and decreasing at larger run lengths. The
transport reduction is associated with the formation of cluster or living
crystal states that become locally jammed or clogged by the obstacles. We also
find that the system dynamically jams at lower particle densities when the run
length is increased. Our results indicate that there is an optimal activity
level for active matter transport through quenched disorder, and could be
important for understanding biological transport in complex environments or for
applications of active matter particles in random media.; Comment: 7 pages, 6 postscript figures

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## Trapped Bose-Einstein Condensed Gas with Two and Three-Atom Interactions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/02/1999

Relevância na Pesquisa

65.55%

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms
is investigated under the assumption of an attractive two-body and a repulsive
three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear
Schr\"odinger equation is extended to include an effective potential dependent
on the square of the density and solved numerically for the $s-$wave. The
lowest frequency of the collective mode is determined through the Fourier
transform of the time dependent solution and its dependences on the number of
atoms and the strength of the three-body force are studied. We show that the
addition of three-body dynamics can allow the number of condensed atoms to
increase considerably, even when the strength of the three-body force is very
small compared with the strength of the two-body force.; Comment: Contribution to the "Internationl Workshop on Collective Excitations
in Fermi and Bose Systems", Serra Negra, Brazil, September 14-17, 1998. To be
published by World Scientific, Singapore

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## Thermodynamic approach to dense granular matter: a numerical realization of a decisive experiment

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.55%

Years ago Edwards proposed a thermodynamic description of dense granular
matter, in which the grains (the `atoms' of the system) interact with inelastic
forces. The approach is intriguing but is not justified from first principles,
and hence, in the absence of conclusive tests of its validity, it has not been
widely accepted. We perform a numerical experiment with a realistic granular
matter model specially conceived to be reproducible in the laboratory. The
results strongly support the thermodynamic picture.; Comment: 4 pages, 3 figures

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## Motility-induced phase separation and coarsening in active matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.56%

Active systems, or active matter, are self-driven systems which live, or
function, far from equilibrium - a paradigmatic example which we focus on here
is provided by a suspension of self-motile particles. Active systems are far
from equilibrium because their microscopic constituents constantly consume
energy from the environment in order to do work, for instance to propel
themselves. The nonequilibrium nature of active matter leads to a variety of
non-trivial intriguing phenomena. An important one which has recently been the
subject of intense interest among biological and soft matter physicists is that
of the so-called "motility-induced phase separation", whereby self-propelled
particles accumulate into clusters in the absence of any explicit attractive
interactions between them. Here we review the physics of motility-induced phase
separation, and discuss this phenomenon within the framework of the classic
physics of phase separation and coarsening. We also discuss theories for
bacterial colonies where coarsening may be arrested. Most of this work will
focus on the case of run-and-tumble and active Brownian particles in the
absence of solvent-mediated hydrodynamic interactions - we will briefly discuss
at the end their role, which is not currently fully understood in this context.; Comment: Contribution to the special issue "Coarsening dynamics"...

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## Jamming III: Characterizing Randomness via the Entropy of Jammed Matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/09/2009

Relevância na Pesquisa

65.56%

The nature of randomness in disordered packings of frictional and
frictionless spheres is investigated using theory and simulations of identical
spherical grains. The entropy of the packings is defined through the force and
volume ensemble of jammed matter and shown difficult to calculate analytically.
A mesoscopic ensemble of isostatic states is then utilized in an effort to
predict the entropy through the defnition of a volume function dependent on the
coordination number. Equations of state are obtained relating entropy, volume
fraction and compactivity characterizing the different states of jammed matter,
and elucidating the phase diagram for jammed granular matter. Analytical
calculations are compared to numerical simulations using volume fluctuation
analysis and graph theoretical methods, with reasonable agreement. The entropy
of the jammed system reveals that the random loose packings are more disordered
than random close packings, allowing for an unambiguous interpretation of both
limits. Ensemble calculations show that the entropy vanishes at random close
packing (RCP), while numerical simulations show that a finite entropy remains
in the microscopic states at RCP. The notion of a negative compactivity, that
explores states with volume fractions below those achievable by existing
simulation protocols...

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## Phase Separation in Soft Matter: Concept of Dynamic Asymmetry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/07/2013

Relevância na Pesquisa

65.58%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics#Physics - Chemical Physics

Phase separation is a fundamental phenomenon that produces spatially
heterogeneous patterns in soft matter. In this Lecture Note we show that phase
separation in these materials generally belongs to what we call "viscoelastic
phase separation", where the morphology is determined by the mechanical balance
of not only the thermodynamic force (interface tension) but also the
viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry
between the components of a mixture, which can be caused by either a size
disparity or a difference in the glass transition temperature between the
components. We stress that such dynamic asymmetry generally exists in soft
matter. The key is that dynamical asymmetry leads to a non-trivial coupling
between the concentration, velocity, and stress fields. Viscoelastic phase
separation can be explained by viscoelastic relaxation in pattern evolution and
the resulting switching of the relevant order parameter, which are induced by
the competition between the deformation rate of phase separation and the
slowest mechanical relaxation rate of a system. We also discuss an intimate
link of viscoelastic phase separation, where deformation fields are
spontaneously generated by phase separation itself...

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## Unzipping DNA from the condensed globule state--Effects of unraveling

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2006

Relevância na Pesquisa

65.55%

We study theoretically the unzipping of a double stranded DNA from a
condensed globule state by an external force. At constant force, we find that
the double stranded DNA unzips an at critical force Fc and the number of
unzipped monomers M goes as M~(Fc-F)^{-3}, for both the homogeneous and
heterogeneous double stranded DNA sequence. This is different from the case of
unzipping from an extended coil state in which the number of unzipped monomers
M goes as M~(Fc-F)^{-chi}, where the exponent chi is either 1 or 2 depending on
whether the double stranded DNA sequence is homogeneous or heterogeneous
respectively. In the case of unzipping at constant extension, we find that for
a double stranded DNA with a very large number N of base pairs, the force
remains almost constant as a function of the extension, before the unraveling
transition, at which the force drops abruptly to zero. Right at the unraveling
transition, the number of base pairs remaining in the condensed globule state
is still very large and goes as N^{3/4}, in agreement with theoretical
predictions of the unraveling transition of polymers stretched by an external
force.; Comment: 17 pages, 4 figures

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## Effective temperature and glassy dynamics of active matter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.55%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Statistical Mechanics#Quantitative Biology - Subcellular Processes

A systematic expansion of the many-body master equation for active matter, in
which motors power configurational changes as in the cytoskeleton, is shown to
yield a description of the steady state and responses in terms of an effective
temperature. The effective temperature depends on the susceptibility of the
motors and a Peclet number which measures their strength relative to thermal
Brownian diffusion. The analytic prediction is shown to agree with previous
numerical simulations and experiments. The mapping also establishes a
description of aging in active matter that is also kinetically jammed.; Comment: 2 figures

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## Effect of interaction shape on the condensed DNA toroid

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/01/2007

Relevância na Pesquisa

65.55%

#Condensed Matter - Soft Condensed Matter#Condensed Matter - Statistical Mechanics#Quantitative Biology - Biomolecules

We investigate how different microscopic interactions between semiflexible
chain segments can qualitatively alter the physical properties of the condensed
toroid. We propose a general form of the Hamiltonian of the toroid and discuss
its analytic properties. For different interactions, the theory predicts
different scaling behaviours of the mean toroidal and cross sectional radii,
$r_c$ and $r_{cross}$, as functions of the contour length L: $(r_c, r_{cross})
\sim L^{\nu(N_c)}$ with $\nu=(1/5, 2/5)$ for the van der Waals type,
$\nu=(-1/3, 2/3)$ for the Coulomb type, $\nu=(-1, 1)$ for the delta function
type attractions in the asymptotic limit. For the toroids with finite winding
number $N_c=100 \sim 400$, we find $\nu \simeq 0$ for the Yukawa interaction
with screening parameter $\kappa=0.5 \sim 1.0$, and $\nu=0.1 \sim 0.13$ for the
van der Waals type interactions. These findings could provide possible
explanation for the experimentally well known observation $\nu \simeq 0$ of the
condensed DNA toroids. Conformational transitions are also discussed.; Comment: 5 pages (double column), 1 table and 3 figures (colour)

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## Soft matter and fractional mathematics: insights into mesoscopic quantum and time-space structures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/05/2004

Relevância na Pesquisa

65.56%

Recent years have witnessed a great research boom in soft matter physics. by
now, most advances, however, are of either empirical results or purely
mathematical extensions. The major obstacle is lacking of insights into
fundamental phsysical laws underlying fractal mesostructures of soft matter.
This study will use fractional mathematics, which consists of fractal,
fractional calculus, fractional Brownian motion, and Levy stable distribution,
to examine mesoscopic quantum mechanics and time-space structures governing
"anomalous" behaviors of soft matter. Our major results include fractional
Planck quantum energy relationship, fractional phonon, and time-space scaling
transform.; Comment: Welcome comments to chen_wen@iapcm.ac.cn

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