arXiv subjects

T. S. Grigera

Publications and source records attributed to T. S. Grigera.

18 recordsLinked to original sources

arXiv2020

Joint assessment of density correlations and fluctuations for analysing spatial tree patterns

Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g., in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kind of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well known empirical Taylor's power law. Density correlations and fluctuations, in conjunction, provide an unique opportunity to interpret the behaviors and possibly to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones.

cond-mat.stat-mech↗

arXiv2016

Dynamic scaling in natural swarms

Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to negotiate with scores of details whose relevance is often hard to assess. In an attempt to improve on this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z~1. We run simulations of a model of self-propelled particles in its swarming phase and find z~2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of non-exponential relaxation and paramagnetic spin-wave remnants, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely relaxational regime suggests that natural swarms are subject to a near-critical censorship of hydrodynamics.

cond-mat.stat-mech↗

arXiv2015

An intermediate state between the kagome-ice and the fully polarized state in Dy$_2$Ti$_2$O$_7$

Dy$_2$Ti$_2$O$_7$ is at present the cleanest example of a spin-ice material. Previous theoretical and experimental work on the first-order transition between the kagome-ice and the fully polarized state has been taken as a validation for the dipolar spin-ice model. Here we investigate in further depth this phase transition using ac-susceptibility and dc-magnetization, and compare this results with Monte-Carlo simulations and previous magnetization and specific heat measurements. We find signatures of an intermediate state between the kagome-ice and full polarization. This signatures are absent in current theoretical models used to describe spin-ice materials.

cond-mat.stat-mech↗

arXiv2012

Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry

The problem of measuring nontrivial static correlations in deeply supercooled liquids made recently some progress thanks to the introduction of amorphous boundary conditions, in which a set of free particles is subject to the effect of a different set of particles frozen into their (low temperature) equilibrium positions. In this way, one can study the crossover from nonergodic to ergodic phase, as the size of the free region grows and the effect of the confinement fades. Such crossover defines the so-called point-to-set correlation length, which has been measured in a spherical geometry, or cavity. Here, we make further progress in the study ofcorrelations under amorphous boundary conditions by analyzing the equilibrium properties of a glass-forming liquid, confined in a planar ("sandwich") geometry. The mobile particles are subject to amorphous boundary conditions with the particles in the surrounding walls frozen into their low temperature equilibrium configurations. Compared to the cavity, the sandwich geometry has three main advantages: i) the width of the sandwich is decoupled from its longitudinal size, making the thermodynamic limit possible; ii) for very large width, the behaviour off a single wall can be studied; iii) we can use "anti-parallel" boundary conditions to force a domain wall and measure its excess energy. Our results confirm that amorphous boundary conditions are indeed a very useful new tool inthe study of static properties of glass-forming liquids, but also raise some warning about the fact that not all correlation functions that can be calculated in this framework give the same qualitative results.

cond-mat.dis-nn↗

arXiv2010

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.

cond-mat.dis-nn↗

arXiv2010

Numerical simulations of liquids with amorphous boundary conditions

It has recently become clear that simulations under amorphpous boundary conditions (ABCs) can provide valuable information on the dynamics and thermodynamics of disordered systems with no obvious ordered parameter. In particular, they allow to detect a correlation length that is not measurable with standard correlation functions. Here we explain what exactly is meant by ABCs, discuss their relation with point-to-set correlations and briefly describe some recent results obtained with this technique.

cond-mat.dis-nn↗

arXiv2010

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension.

cond-mat.dis-nn↗

arXiv2009

Surface tension fluctuations and a new spinodal point in glass-forming liquids

The dramatic slowdown of glass-forming liquids has been variously linked to increasing dynamic and static correlation lengths. Yet, empirical evidence is insufficient to decide among competing theories. The random first order theory (RFOT) links the dynamic slowdown to the growth of amorphous static order, whose range depends on a balance between configurational entropy and surface tension. This last quantity is expected to vanish when the temperature surpasses a spinodal point beyond which there are no metastable states. Here we measure for the first time the surface tension in a model glass-former, and find that it vanishes at the energy separating minima from saddles, demonstrating the existence of a spinodal point for amorphous metastable order. Moreover, the fluctuations of surface tension become smaller for lower temperatures, in quantitative agreement with recent theoretical speculation that spatial correlations in glassy systems relax nonexponentially because of the narrowing of the surface tension distribution.

cond-mat.dis-nn↗

arXiv2008

Thermodynamic signature of growing amorphous order in glass-forming liquids

Although several theories relate the steep slowdown of glass formers to increasing spatial correlations of some sort, standard static correlation functions show no evidence for this. We present results that reveal for the first time a qualitative thermodynamic difference between the high temperature and deeply supercooled equilibrium glass-forming liquid: the influence of boundary conditions propagates into the bulk over larger and larger lengthscales upon cooling, and, as this static correlation length grows, the influence decays nonexponentially. Increasingly long-range susceptibility to boundary conditions is expected within the random firt-order theory (RFOT) of the glass transition, but a quantitative account of our numerical results requires a generalization of RFOT where the surface tension between states fluctuates.

cond-mat.dis-nn↗

arXiv2004

Asymptotic aging in structural glasses

Using a non-local Monte Carlo algorithm, we study the aging of a fragile glass, being able to follow it up to equilibibrium down to 0.89 Tmc (Tmc is the Mode-Coupling temperature) and up to unprecedentedly large waiting times at lower temperatures. We show that the fluctuation-dissipation ratio is independent of the dynamics chosen and is compatible with a phase transition, and that the scaling behaviour of the aging part of the correlation supports the full-aging scenario.

cond-mat.dis-nn↗

arXiv2004

Anderson Localization in Euclidean Random Matrices

We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the localization threshold. We solve numerically an exact equation for the probability distribution function of the diagonal element of the the resolvent matrix, with a population dynamics algorithm, and we show how this can be used to find the localization threshold. An application of the method in the context of the Instantaneous Normal Modes of a liquid system is given.

cond-mat.stat-mech↗

arXiv2003

The Boson peak and the phonons in glasses

Despite the presence of topological disorder, phonons seem to exist also in glasses at very high frequencies (THz) and they remarkably persist into the supercooled liquid. A universal feature of such a systems is the Boson peak, an excess of states over the standard Debye contribution at the vibrational density of states. Exploiting the euclidean random matrix theory of vibrations in amorphous systems we show that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). The theoretical predictions are checked by means of numeric simulations.

cond-mat↗

arXiv2003

Brillouin and Boson peaks in Glasses from vector Euclidean Random Matrix Theory

A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean Random Matrix Theory to include vector vibrations. Rather generally, it is found that i) the dynamic structure factor shows sound-like Brillouin peaks whose longitudinal/transverse character can only be distinguished for small transferred momentum, p, ii) the model presents a mechanical instability transition at small densities, for which scaling laws are analytically predicted and confirmed numerically, iii) the Brillouin peaks persist deep into the unstable phase, the phase transition being noticeable mostly in their linewidth, iv) the Brillouin linewidth scales like p square in the stable phase, and like p in the unstable one. The analytical results are checked numerically for a simple potential. The main features of glassy vibrations previously deduced from scalar ERMT are not substantially altered by these new results.

cond-mat.dis-nn↗

arXiv2003

Phonons in supercooled liquids: a possible explanation for the Boson Peak

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystals, elasticity is associated with phonons, quantized sound-wave excitations. Phonon-like excitations exist also in glasses at very high frequencies (THz), and they remarkably persist into the supercooled liquid. A universal feature of these amorphous systems is the Boson peak: the vibrational density of states $g(ω)$ has an excess over the Debye (squared frequency) law, seen as a peak in $g(ω)/ω^2$. We claim that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). Here, by studying the spectra of inherent structures (local minima of the potential energy), we show that this is the case in a realistic glass model: the Boson peak moves to lower frequencies on approaching the phonon-saddle transition and its height diverges at the critical point. The numerical results agree with Euclidean Random Matrix Theory predictions on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.

cond-mat↗

arXiv2001

Vibrations in glasses and Euclidean Random Matrix theory

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), the Euclidean random matrix theory provide a single and fairly simple theoretical framework to their explanation.

cond-mat↗

arXiv2001

Boson peak in an harmonic scalar model

We study, analytically and numerically, an off-lattice model of scalar harmonic vibrations for structural glasses. The model has a Boson-Peak which we argue can be considered as a prototype for materials with a Boson Peak frequency that decreases with lowering temperature. The density evolution of the Boson Peak in silica is qualitatively reproduced. The dispersion relation is linear at the Boson Peak frequency, in agreement with experiments. In our model the Boson Peak is a precursor of a nearby mechanical instability. The Boson Peak is built up by the hybridization of the sound waves with extended, but non propagating (in the sense of a flat dispersion relation), modes.

cond-mat↗

arXiv2001

Vibrational spectrum of topologically disordered systems

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.

cond-mat.dis-nn↗

arXiv2001

Vibrational spectra in glasses

The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key ingredient which strongly affects the vibrational spectra of those systems. We present a resummation scheme for a perturbative expansion in the inverse particle density, allowing an accurate analytical computation of the dynamical structure factor within the range of densities encountered in real systems.

cond-mat.dis-nn↗