arXiv subjects

Tomas S. Grigera

Publications and source records attributed to Tomas S. Grigera.

At least 37 records · Page 2Linked to original sources

arXiv2017

Propagating speed waves in flocks: a mathematical model

Efficient collective response to external perturbations is one of the most striking abilities of a biological system. Signal propagation through the group is an important condition for the imple- mentation of such a response. Information transfer has been experimentally observed in the turning mechanism of birds flocks. In this context it is well-known also the existence of density waves: birds under predation, attempting to escape, give rise to self-organized density waves that propagates linearly on the flock. Most aspects of this phenomenon are still not fully captured by theoretical models. In this work we present a new model for the propagation of the speed (the modulus of the velocity) fluctuations inside a flock, which is the simplest way to reproduce the observed density waves. We have studied the full solution of the model in d = 1 and we found that there is a line in the parameter space along which the system relaxes in the fastest way with no oscillation after a signal has passed. This is the critical damping condition. By analyzing the parameters plane we show that critical damping represents an attractor for a steepest descent dynamics of the return time of the system. Finally we propose a method to test the validity of the model through through future experiments.

cond-mat.stat-mech↗

arXiv2016

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws

Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect the propagation across the system of a signal triggered by some perturbation. However, for field experiments this method is inefficient, as the possibilities of the observer to perturb the group are limited and empirical observations must rely on rare natural perturbations. An alternative way is to use spatio-temporal correlations to assess the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. We test the approach on ground truth data provided by numerical simulations in three dimensions of two models of collective behaviour characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an un- derdamped inertial dynamics. By using dynamical finite size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.

cond-mat.stat-mech↗

arXiv2016

Structure and dynamics of the t154 lattice glass

We revisit the $t154$ variant of the Biroli-Mezard lattice glass, complementing previous studies by studying statics and dynamics under periodic boundary conditions as well as systems confined in cavities with amorphous boundaries. We compute the point-to-se correlation and relaxation times under the different boundary conditions. Results point to a scenario with dynamics ruled by structural correlations.

cond-mat.dis-nn↗

arXiv2016

Response to "Comment on Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry" [J. Chem. Phys. 144, 227101 (2016)]

The point-to-set correlation function has proved to be a very valuable tool to probe structural correlations in disordered systems, but more than that, its detailed behavior has been used to try to draw information on the mechanisms leading to glassy behavior in supercooled liquids. For this reason it is of primary importance to discern which of those details are peculiar to glassy systems, and which are general features of confinement. Within the present response we provide an answer to the concerns raised in [J. Chem. Phys. 144, 227101 (2016)].

cond-mat.dis-nn↗

arXiv2015

Specific heat anomaly in a supercooled liquid with amorphous boundary conditions

We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents α and ν, and random first-order theory, with two different length scales.

cond-mat.dis-nn↗

arXiv2014

Ageing and crystallization in a lattice glass model

We have studied a the 3-$d$ lattice glass of Pica Ciamarra, Tarzia, de Candia and Coniglio [Phys.\ Rev.\ E. 67, 057105 (2013)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times and ageing. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower that 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.

cond-mat.dis-nn↗

arXiv2014

Silent Flocks

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations and second sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap sharply separates first from second sound modes. This gap implies the existence of `silent' flocks, namely medium-sized systems across which neither first nor second sound can propagate.

cond-mat.stat-mech↗

arXiv2013

Superfluid transport of information in turning flocks of starlings

Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition, the efficiency of information transport is a key factor to prevent cohesion loss and preserve robustness. The precise mechanism by which natural groups achieve such efficiency, though, is currently not fully understood. Here, we present an experimental study of starling flocks performing collective turns in the field. We find that the information to change direction propagates across the flock linearly in time with negligible attenuation, hence keeping group decoherence to a minimum. This result contrasts with current theories of collective motion, which predict a slower and dissipative transport of directional information. We propose a novel theory whose cornerstone is the existence of a conserved spin current generated by the gauge symmetry of the system. The theory turns out to be mathematically identical to that of superfluid transport in liquid helium and it explains the dissipationless propagating mode observed in turning flocks. Superfluidity also provides a quantitative expression for the speed of propagation of the information, according to which transport must be swifter the stronger the group's orientational order. This prediction is verified by the data. We argue that the link between strong order and efficient decision-making required by superfluidity may be the adaptive drive for the high degree of behavioural polarization observed in many living groups. The mathematical equivalence between superfluid liquids and turning flocks is a compelling demonstration of the far-reaching consequences of symmetry and conservation laws across different natural systems.

cond-mat.stat-mech↗

arXiv2011

Dynamic relaxation of a liquid cavity under amorphous boundary conditions

The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between MCT and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.

cond-mat.dis-nn↗

arXiv2011

glsim: A general library for numerical simulation

We describe glsim, a C++ library designed to provide routines to perform basic housekeeping tasks common to a very wide range of simulation programs, such as reading simulation parameters or reading and writing self-describing binary files with simulation data. The design also provides a framework to add features to the library while preserving its structure and interfaces.

physics.comp-ph↗

arXiv2009

Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids

There is a certain consensus that the very fast growth of the relaxation time $τ$ occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length $ξ$ in glass-formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power $ψ$ of the size of the correlated regions, we obtain a relationship between time and length, $T\logτ\sim ξ^ψ$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $ξ\sim (T-T_k)^{-1/(d-θ)}$, even though the two theories disagree on the value of $θ$. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents $ψ$ and $θ$ through the relationship $T\logτ\sim (T-T_k)^{-ψ/(d-θ)}$. Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass-former, finding $ψ=1$ and $θ=2$. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, $T\logτ\sim (T-T_k)^{-1}$.

cond-mat.dis-nn↗

arXiv2009

Non-equilibrium Characterization of Spinodal Points using Short Time Dynamics

Though intuitively appealing, the concept of spinodal is rigourously defined only in systems with infinite range interactions (mean field systems). In short-range systems, a pseudo-spinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase, by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean field systems and with the pseudo-spinodal point obtained by extrapolation of meta-equilibrium behavior in short range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.

cond-mat.stat-mech↗

arXiv2007

Mosaic multi-state scenario vs. one-state description of supercooled liquids

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.

cond-mat.dis-nn↗

arXiv2005

Geometrical properties of the potential energy of the soft-sphere binary mixture

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K vs. temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K vs. energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.

cond-mat.dis-nn↗

arXiv2004

A single saddle model for the beta-relaxation in supercooled liquids

We study the Langevin equation for a single harmonic saddle as an elementary model for the beta-relaxation in supercooled liquids close to Tc. The input of the theory is the spectrum of the eigenvalues of the dominant stationary points at a given temperature. We prove in general the existence of a time-scale t_eps, which is uniquely determined by the spectrum, but is not simply related to the fraction of negative eigenvalues. The mean square displacement develops a plateau of length t_eps, such that a two-step relaxation is obtained if t_eps diverges at Tc. We analyze the specific case of a spectrum with bounded left tail, and show that in this case the mean square displacement has a scaling dependence on time identical to the beta-relaxation regime of Mode Coupling Theory, with power law approach to the plateau and power law divergence of t_eps at Tc.

cond-mat.stat-mech↗

arXiv2004

Localization threshold of Instantaneous Normal Modes from level-spacing statistics

We study the statistics of level-spacing of Instantaneous Normal Modes in a supercooled liquid. A detailed analysis allows to determine the mobility edge separating extended and localized modes in the negative tail of the density of states. We find that at temperature below the mode coupling temperature only a very small fraction of negative eigenmodes are localized.

cond-mat.stat-mech↗

arXiv2002

Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.

cond-mat.stat-mech↗

arXiv2002

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles.

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