arXiv subjects

Jean-Marc Luck

Publications and source records attributed to Jean-Marc Luck.

28 records · Page 2Linked to original sources

arXiv2020

On the coexistence of competing languages

We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we here revisit the question of language competition, with an emphasis on uncovering the ways in which coexistence might emerge. We find that this emergence is related to symmetry breaking, and explore two particular scenarios -- the first relating to an imbalance in the population dynamics of language speakers in a single geographical area, and the second to do with spatial heterogeneity, where language preferences are specific to different geographical regions. For each of these, the investigation of paradigmatic situations leads us to a quantitative understanding of the conditions leading to language coexistence. We also obtain predictions of the number of surviving languages as a function of various model parameters.

cond-mat.stat-mech↗

arXiv2019

Records for the moving average of a time series

We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general case, corroborated by exact results for three distributions (exponential, uniform, power-law with unit exponent), evidences a very robust dichotomy, irrespective of the window width, between superexponential and subexponential distributions. For superexponential distributions the statistics of records is asymptotically unchanged by taking the moving average, up to interesting distribution-dependent corrections to scaling. For subexponential distributions the probability of record breaking at late times is increased by a universal factor $R_p$, depending only on the window width.

cond-mat.stat-mech↗

arXiv2018

Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes

We characterise the nonequilibrium stationary state of a generic multivariate Ornstein-Uhlenbeck process involving $N$ degrees of freedom. The irreversibility of the process is encoded in the antisymmetric part of the Onsager matrix. The linearity of the Langevin equations allows us to derive closed-form expressions in terms of the latter matrix for many quantities of interest, including the entropy production rate and the fluctuation-dissipation ratio matrix. This general setting is then illustrated by two classes of systems. First, we consider the one-dimensional ferromagnetic Gaussian spin model endowed with a stochastic dynamics where spatial asymmetry results in irreversibility. The stationary state on a ring is independent of the asymmetry parameter, whereas it depends continuously on the latter on an open chain. Much attention is also paid to finite-size effects, especially near the critical point. Second, we consider arrays of resistively coupled electrical circuits. The entropy production rate is evaluated in the regime where the local temperatures of the resistors have small fluctuations. For $RL$ networks the entropy production rate grows linearly with the size of the array. For $RC$ networks a quadratic growth law violating extensivity is predicted.

cond-mat.stat-mech↗

arXiv2017

Generic phase coexistence in the totally asymmetric kinetic Ising model

The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question for a specific totally asymmetric kinetic Ising model on the square lattice. This nonequilibrium model possesses the remarkable property that its stationary-state measure in the absence of a magnetic field coincides with that of the usual ferromagnetic Ising model. We use both analytical arguments and numerical simulations in order to make progress in the quantitative understanding of the phenomenon of generic phase coexistence. At zero temperature a mapping onto the TASEP allows an exact determination of the time-dependent shape of the ballistic interface sweeping a large square minority droplet of up or down spins. At finite temperature, measuring the mean lifetime of such a droplet allows an accurate measurement of its shrinking velocity $v$, which depends on temperature $T$ and magnetic field $h$. In the absence of a magnetic field, $v$ vanishes with an exponent $Δ_v\approx2.5\pm0.2$ as the critical temperature $T_c$ is approached. At fixed temperature in the ordered phase, $v$ vanishes at the phase-boundary fields $\pm h_{\rm b}(T)$ which mark the limits of the coexistence region. The latter fields vanish with an exponent $Δ_h\approx3.2\pm0.3$ as $T_c$ is approached.

cond-mat.stat-mech↗

arXiv2017

Tracking random walks

In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured statistical properties of the walk, and we use here analytical and numerical methods of statistical physics to study the effects of sampling in movements alternating rests and moves of random durations. We evaluate how the statistical properties estimated are affected by the way trajectories are measured and we identify an optimal sampling frequency leading to the best possible measure. We solve analytically the simplest scenario of a constant sampling interval and short-tailed distributions of rest and move durations, which allows us to show that the measured displacement statistics can be significantly different from the original ones and also to determine the optimal sampling time. The corresponding optimal fraction of correctly sampled movements, analytically predicted for this short-tail scenario, is an upper bound for the quality of a trajectory's sampling. Indeed, we show with numerical simulations that this fraction is dramatically reduced in any real-world case where we observe long-tailed distributions of rest duration. We test our results with high resolution GPS human trajectories, where a constant sampling interval allows to recover at best $18\%$ of the movements, while over-evaluating the average trip length by a factor of $2$. If we use a sampling interval extracted from real communication data, we recover only $11\%$ of moves, a value that cannot be increased above $16\%$ even with ideal algorithms. These figures call for a more cautious use of data in all quantitative studies of individuals' trajectories, casting in particular serious doubts on the results of previous studies on human mobility based on mobile phone data.

physics.soc-ph↗

arXiv2016

Inverse participation ratios in the XXZ spin chain

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the "Ising" basis (i.e., eigenstates of $σ^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has $T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant value.

cond-mat.str-el↗

arXiv2013

Synaptic metaplasticity underlies tetanic potentiation in Lymnaea: a novel paradigm

We present a mathematical model which explains and interprets a novel form of short-term potentiation, which was found to be use-, but not time-dependent, in experiments done on Lymnaea neurons. The high degree of potentiation is explained using a model of synaptic metaplasticity, while the use-dependence (which is critically reliant on the presence of kinase in the experiment) is explained using a model of a stochastic and bistable biological switch.

physics.bio-ph↗

arXiv2010

Fluctuation effects in metapopulation models: percolation and pandemic threshold

Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are usually studied at the mean-field level by neglecting fluctuations. Here we include fluctuations in the models by adopting fully stochastic descriptions of the corresponding processes. This level of description allows to address analytically, in the SIS and SIR cases, problems such as the existence and the calculation of an effective threshold for the spread of a disease at a global level. We show that the possibility of the spread at the global level is described in terms of (bond) percolation on the network. This mapping enables us to give an estimate (lower bound) for the pandemic threshold in the SIR case for all values of the model parameters and for all possible networks.

cond-mat.dis-nn↗

arXiv2001

Aging, phase ordering and conformal invariance

In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the scaling function $f$. This quantitative prediction is confirmed in several spin systems, both for $T<T_c$ (phase ordering) and $T=T_c$ (non-equilibrium critical dynamics). The 2D and 3D Ising models with Glauber dynamics are studied numerically, while exact results are available for the spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.

hep-th↗

arXiv2001

Shaking a Box of Sand

We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by analysing the response of the packing fraction to steady, as well as cyclic, shaking, and indicators of the onset of a `glass transition' are analysed. In the `glassy' regime, our model is exactly solvable, and allows for the qualitative description of ageing phenomena in terms of two characteristic lengths; predictions are also made about the influence of grain shape anisotropy on ageing behaviour.

cond-mat↗