1,423 research outputs found
Geometric interpretation of pre-vitrification in hard sphere liquids
We derive a microscopic criterion for the stability of hard sphere
configurations, and we show empirically that this criterion is marginally
satisfied in the glass. This observation supports a geometric interpretation
for the initial rapid rise of viscosity with packing fraction, or
pre-vitrification. It also implies that barely stable soft modes characterize
the glass structure, whose spatial extension is estimated. We show that both
the short-term dynamics and activation processes occur mostly along those soft
modes, and we study some implications of these observations. This article
synthesizes new and previous results [C. Brito and M. Wyart, Euro. Phys.
Letters, {\bf 76}, 149-155, (2006) and C. Brito and M. Wyart, J. Stat. Mech.,
L08003 (2007) ] in a unified view.Comment: accepted for publication in the Journal of Chemical Physics (added
discussion on RCP and ideal glass transition
Geometric and chemical non-uniformity may induce the stability of more than one wetting state in the same hydrophobic surface
It is established that roughness and chemistry play a crucial role in the
wetting properties of a substrate. Yet, few studies have analyzed
systematically the effect of the non-uniformity in the distribution of texture
and surface tension of substrates on its wetting properties. In this work we
investigate this issue theoretically and numerically. We propose a continuous
model that takes into account the total energy required to create interfaces of
a droplet in two possible wetting states: Cassie-Baxter(CB) with air pockets
trapped underneath the droplet; and the other characterized by the homogeneous
wetting of the surface, the Wenzel(W) state. To introduce geometrical
non-regularity we suppose that pillar heights and pillar distances are Gaussian
distributed instead of having a constant value. Similarly, we suppose a
heterogeneous distribution of Young's angle on the surface to take into account
the chemical non-uniformity. This allows to vary the "amount" of disorder by
changing the variance of the distribution. We first solve this model
analytically and then we also propose a numerical version of it, which can be
applied to study any type of disorder. In both versions, we employ the same
physical idea: the energies of both states are minimized to predict the
thermodynamic wetting state of the droplet for a given volume and surface
texture. We find that the main effect of disorder is to induce the stability of
both wetting states on the same substrate. In terms of the influence of the
disorder on the contact angle of the droplet, we find that it is negligible for
the chemical disorder and for pillar-distance disorder. However, in the case of
pillar-height disorder, it is observed that the average contact angle of the
droplet increases with the amount of disorder. We end the paper investigating
how the region of stability of both wetting states behaves when the droplet
volume changes
Theory for Swap Acceleration near the Glass and Jamming Transitions
Swap algorithms can shift the glass transition to lower temperatures, a
recent unexplained observation constraining the nature of this phenomenon. Here
we show that swap dynamic is governed by an effective potential describing both
particle interactions as well as their ability to change size. Requiring its
stability is more demanding than for the potential energy alone. This result
implies that stable configurations appear at lower energies with swap dynamics,
and thus at lower temperatures when the liquid is cooled. \maa{ The magnitude
of this effect is proportional to the width of the radii distribution, and
decreases with compression for finite-range purely repulsive interaction
potentials.} We test these predictions numerically and discuss the implications
of these findings for the glass transition.We extend these results to the case
of hard spheres where swap is argued to destroy meta-stable states of the free
energy coarse-grained on vibrational time scales. Our analysis unravels the
soft elastic modes responsible for the speed up swap induces, and allows us to
predict the structure and the vibrational properties of glass configurations
reachable with swap. In particular for continuously poly-disperse systems we
predict the jamming transition to be dramatically altered, as we confirm
numerically. A surprising practical outcome of our analysis is new algorithm
that generates ultra-stable glasses by simple descent in an appropriate
effective potential.Comment: 8 pages, 7 figures in the main text, 3 pages 4 figures in the
supplemental material. We improved the theoretical discussion in the v3. In
particular, we added a section with an extended discussion of the
implications of our findings for the glass transitio
Architecture and Co-Evolution of Allosteric Materials
We introduce a numerical scheme to evolve functional materials that can
accomplish a specified mechanical task. In this scheme, the number of
solutions, their spatial architectures and the correlations among them can be
computed. As an example, we consider an "allosteric" task, which requires the
material to respond specifically to a stimulus at a distant active site. We
find that functioning materials evolve a less-constrained trumpet-shaped region
connecting the stimulus and active sites and that the amplitude of the elastic
response varies non-monotonically along the trumpet. As previously shown for
some proteins, we find that correlations appearing during evolution alone are
sufficient to identify key aspects of this design. Finally, we show that the
success of this architecture stems from the emergence of soft edge modes
recently found to appear near the surface of marginally connected materials.
Overall, our in silico evolution experiment offers a new window to study the
relationship between structure, function, and correlations emerging during
evolution.Comment: 6 pages, 5 figures, SI: 2 pages, 4 figure
Percolation and cooperation with mobile agents: Geometric and strategy clusters
We study the conditions for persistent cooperation in an off-lattice model of
mobile agents playing the Prisoner's Dilemma game with pure, unconditional
strategies. Each agent has an exclusion radius rP, which accounts for the
population viscosity, and an interaction radius rint, which defines the
instantaneous contact network for the game dynamics. We show that, differently
from the rP=0 case, the model with finite-sized agents presents a coexistence
phase with both cooperators and defectors, besides the two absorbing phases, in
which either cooperators or defectors dominate. We provide, in addition, a
geometric interpretation of the transitions between phases. In analogy with
lattice models, the geometric percolation of the contact network (i.e.,
irrespective of the strategy) enhances cooperation. More importantly, we show
that the percolation of defectors is an essential condition for their survival.
Differently from compact clusters of cooperators, isolated groups of defectors
will eventually become extinct if not percolating, independently of their size
Principles for optimal cooperativity in allosteric materials
Allosteric proteins transmit a mechanical signal induced by binding a ligand.
However, understanding the nature of the information transmitted and the
architectures optimizing such transmission remains a challenge. Here we show
using an {\it in-silico} evolution scheme and theoretical arguments that
architectures optimized to be cooperative, which propagate efficiently energy,
{qualitatively} differ from previously investigated materials optimized to
propagate strain. Although we observe a large diversity of functioning
cooperative architectures (including shear, hinge and twist designs), they all
obey the same principle {of displaying a {\it mechanism}, i.e. an extended
{soft} mode}. We show that its optimal frequency decreases with the spatial
extension of the system as , where is the spatial dimension.
For these optimal designs, cooperativity decays logarithmically with for
and does not decay for . Overall our approach leads to a natural
explanation for several observations in allosteric proteins, and { indicates an
experimental path to test if allosteric proteins lie close to optimality}.Comment: 11 pages, 9 figures in the main text, 9 pages 9 figures in the
supplemental materia
On the Modeling of Droplet Evaporation on Superhydrophobic Surfaces
When a drop of water is placed on a rough surface, there are two possible
extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets
trapped underneath the droplet and the one characterized by the homogeneous
wetting of the surface, called the Wenzel (W) state. A way to investigate the
transition between these two states is by means of evaporation experiments, in
which the droplet starts in a CB state and, as its volume decreases, penetrates
the surface's grooves, reaching a W state. Here we present a theoretical model
based on the global interfacial energies for CB and W states that allows us to
predict the thermodynamic wetting state of the droplet for a given volume and
surface texture. We first analyze the influence of the surface geometric
parameters on the droplet's final wetting state with constant volume, and show
that it depends strongly on the surface texture. We then vary the volume of the
droplet keeping fixed the geometric surface parameters to mimic evaporation and
show that the drop experiences a transition from the CB to the W state when its
volume reduces, as observed in experiments. To investigate the dependency of
the wetting state on the initial state of the droplet, we implement a cellular
Potts model in three dimensions. Simulations show a very good agreement with
theory when the initial state is W, but it disagrees when the droplet is
initialized in a CB state, in accordance with previous observations which show
that the CB state is metastable in many cases. Both simulations and theoretical
model can be modified to study other types of surface.Comment: 23 pages, 7 figure
Fast generation of ultrastable computer glasses by minimization of an augmented potential energy
We present a model and protocol that enable the generation of extremely
stable computer glasses at minimal computational cost. The protocol consists of
an instantaneous quench in an augmented potential energy landscape, with
particle radii as additional degrees of freedom. We demonstrate how our
glasses' mechanical stability, which is readily tunable in our approach, is
reflected both in microscopic and macroscopic observables. Our observations
indicate that the stability of our computer glasses is at least comparable to
that of computer glasses generated by the celebrated Swap Monte Carlo
algorithm. Strikingly, some key properties support even qualitatively enhanced
stability in our scheme: the density of quasilocalized excitations displays a
gap in our most stable computer glasses, whose magnitude scales with the
polydispersity of the particles. We explain this observation, which is
consistent with the lack of plasticity we observe at small stress. It also
suggests that these glasses are depleted from two-level systems, similarly to
experimental vapor-deposited ultrastable glasses.Comment: 11 pages, 10 figure
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