arXiv subjects

Alberto Rosso

Publications and source records attributed to Alberto Rosso.

At least 55 records · Page 3Linked to original sources

arXiv2022

Scaling description of creep flow in amorphous solids

Amorphous solids such as coffee foam, toothpaste or mayonnaise display a transient creep flow when a stress $Σ$ is suddenly imposed. The associated strain rate is commonly found to decay in time as $\dotγ \sim t^{-ν}$, followed either by arrest or by a sudden fluidisation. Various empirical laws have been suggested for the creep exponent $ν$ and fluidisation time $τ_f$ in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between $Σ$ and the transient yield stress $Σ_t(γ)$ that characterises the stability of configurations visited by the system at strain $γ$. Assuming the analyticity of $Σ_t(γ)$ allows us to predict $ν$ and asymptotic behaviours of $τ_f$ in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.

cond-mat.soft↗

arXiv2022

Bath induced phase transition in a Luttinger liquid

We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by an Kosterlitz-Thouless (KT) transition. At low coupling with the bath, the chain remains in a Luttinger liquid phase with a reduced but finite spin stiffness, while above a critical coupling the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: the Luttinger liquid is a perfect conductor while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder inducing signatures of localization.

cond-mat.dis-nn↗

arXiv2022

Clusters in an epidemic model with long-range dispersal

In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical regimes. We identify two diverging length scales, corresponding to the bulk and the outskirt of the epidemic. We reveal a nontrivial critical exponent that governs the cluster number, the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long range elasticity.

cond-mat.stat-mech↗

arXiv2022

Avalanches and deformation in glasses and disordered systems

In this chapter, we discuss avalanches in glasses and disordered systems, and the macroscopic dynamical behavior that they mediate. We briefly review three classes of systems where avalanches are observed: depinning transition of disordered interfaces, yielding of amorphous materials, and the jamming transition. Without extensive formalism, we discuss results gleaned from theoretical approaches -- mean-field theory, scaling and exponent relations, the renormalization group, and a few results from replica theory. We focus both on the remarkably sophisticated physics of avalanches and on relatively new approaches to the macroscopic flow behavior exhibited past the depinning/yielding transition.

cond-mat.dis-nn↗

arXiv2022

The Fate of Shear-Oscillated Amorphous Solids

The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subject to athermal and quasistatic oscillatory deformations at various fixed amplitudes. The steady-state reached after several oscillations is fully determined by the initial preparation and the oscillation amplitude, as seen from stroboscopic stress and energy measurements. Under small oscillations, poorly annealed materials display shear-annealing, while ultra-stabilized materials are insensitive to them. Yet, beyond a critical oscillation amplitude, both kind of materials display a discontinuous transition to the same mixed state composed by a fluid shear-band embedded in a marginal solid. Quantitative relations between uniform shear and the steady-state reached with this protocol are established. The transient regime characterizing the growth and the motion of the shear band is also studied.

cond-mat.soft↗

arXiv2021

Non-Newtonian rheology in a capillary tube with varying radius

The flow through a capillary tube with non-constant radius and where bubbles of yield stress fluid are injected is strongly non-linear. In particular below a finite yield pressure drop, $P_y$, flow is absent, while a singular behaviour is expected above it. In this paper we compute the yield pressure drop statistics and the mean flow rate in two cases: (i) when a single bubble is injected, (ii) when many bubbles are randomly injected in the fluid.

physics.flu-dyn↗

arXiv2021

Statistical properties of avalanches via the c-record process

We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one dimensional lattice where the pinning forces at each site are independent and identically distributed (I.I.D), each drawn from a continuous $f(x)$. The avalanches in this model correspond to the inter-record intervals in a modified record process of I.I.D variables, defined by a single parameter $c>0$. This parameter characterizes the record formation via the recursive process $R_k > R_{k-1}-c$, where $R_k$ denotes the value of the $k$-th record. We show that for $c>0$, if $f(x)$ decays slower than an exponential for large $x$, the record process is nonstationary as in the standard $c=0$ case. In contrast, if $f(x)$ has a faster than exponential tail, the record process becomes stationary and the avalanche size distribution $π(n)$ has a decay faster than $1/n^2$ for large $n$. The marginal case where $f(x)$ decays exponentially for large $x$ exhibits a phase transition from a non-stationary phase to a stationary phase as $c$ increases through a critical value $c_{\rm crit}$. Focusing on $f(x)=e^{-x}$ (with $x\ge 0$), we show that $c_{\rm crit}=1$ and for $c<1$, the record statistics is non-stationary. However, for $c>1$, the record statistics is stationary with avalanche size distribution $π(n)\sim n^{-1-λ(c)}$ for large $n$. Consequently, for $c>1$, the mean number of records up to $N$ steps grows algebraically $\sim N^{λ(c)}$ for large $N$. Remarkably, the exponent $λ(c)$ depends continously on $c$ for $c>1$ and is given by the unique positive root of $c=-\ln (1-λ)/λ$. We also unveil the presence of nontrivial correlations between avalanches in the stationary phase that resemble earthquake sequences.

cond-mat.dis-nn↗

arXiv2020

Spatial clustering of depinning avalanches in presence of long-range interactions

Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{é}-Galton-Watson process describing the statistics of the cluster number. Our work has a concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

cond-mat.stat-mech↗

arXiv2020

Topological effects and conformal invariance in long-range correlated random surfaces

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq-\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-\frac{3}{4}<H< 0$ instead, there is a line of critical points with continously varying exponents. The universality class of these points, in particular concerning the conformal invariance of the level clusters, is poorly understood. By combining the Conformal Field Theory and the numerical approach, we provide new insights on these phases. We focus on the connectivity function, defined as the probability that two sites belong to the same level cluster. In our simulations, the surfaces are defined on a lattice torus of size $M\times N$. We show that the topological effects on the connectivity function make manifest the conformal invariance for all the critical line $H<0$. In particular, exploiting the anisotropy of the rectangular torus ($M\neq N$), we directly test the presence of the two components of the traceless stress-energy tensor. Moreover, we probe the spectrum and the structure constants of the underlying Conformal Field Theory. Finally, we observed that the corrections to the scaling clearly point out a breaking of integrability moving from the pure percolation point to the long-range correlated one.

cond-mat.stat-mech↗

arXiv2020

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

physics.geo-ph↗

arXiv2020

Current fluctuations in non-interacting run-and-tumble particles in one-dimension

We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $ρ$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $μ(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[-ρ\, v_0\, γ\, t^2 ψ_{\rm RTP}\left(\frac{Q}{ρv_0\,t} \right) \right]$, where $γ$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $ψ_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(-c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte-Carlo method.

cond-mat.stat-mech↗

arXiv2020

Active Brownian Motion in Two Dimensions

We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion constant $D_R$. We show that, at short-times $t \ll D_R^{-1}$, the presence of `activness' results in a strongly anisotropic and non-diffusive dynamics in the $(xy)$ plane. We compute exactly the marginal distributions of the $x$ and $y$ position coordinates along with the radial distribution, which are all shown to be non-Brownian. In addition, we show that, at early times, the ABP has anomalous first-passage properties, characterized by non-Brownian exponents.

cond-mat.stat-mech↗

arXiv2020

Universal scaling of the velocity field in crack front propagation

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

cond-mat.stat-mech↗

arXiv2020

Stochastic growth in time dependent environments

We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-α}$ there is a transition at $α=1/2$. When $α>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $α<1/2$ the fluctuation field is governed by scaling exponents depending on $α$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

cond-mat.stat-mech↗

arXiv2020

Creep motion of elastic interfaces driven in a disordered landscape

The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful interplay between elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling the collective nature of such ultra-slow motion in terms of elementary activated events. We show that these events control the mean velocity of the interface and cluster into "creep avalanches" statistically similar to the deterministic avalanches observed at the depinning critical threshold. The associated spatio-temporal patterns of activated events have been recently observed in experiments with magnetic domain walls. The emergent physical picture is expected to be relevant for a large family of disordered systems presenting thermally activated dynamics.

cond-mat.dis-nn↗

arXiv2019

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_σ$ presents a pseudo-gap $P(x_σ) \sim (x_σ)^θ$, where $θ$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $θ$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

cond-mat.dis-nn↗

arXiv2019

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness $μ.$ The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate $γ$. We compute the stationary position distribution exactly for arbitrary values of $μ$ and $γ$ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as $β=γ/μ$ is changed. For $β<1,$ the distribution has a double-concave shape and shows algebraic divergences with an exponent $(β-1)$ both at the origin and at the boundaries. For $β>1,$ the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case $β=1,$ the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

cond-mat.stat-mech↗

arXiv2019

Long time position distribution of an active Brownian particle in two dimensions

We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution $P(x,y,t)$ in the $x$-$y$ plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_0 t$. In this regime, the distribution admits a large deviation form, $P(x,y,t) \sim \exp\left[-t\, D_R\, Φ\left(\sqrt{x^2+y^2}/(v_0 t)\right)\right]$, where we compute the rate function $Φ(z)$ analytically and also numerically using an importance sampling method. We show that the rate function $Φ(z)$, encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution $P_\text{stat}(x,y)$ depends explicitly on the activity parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring shape in the strongly active limit ($D_R\to 0$) to a Gaussian shape in the strongly passive limit $(D_R\to \infty)$.

cond-mat.stat-mech↗