Salambô Dago, Jorge Pereda, Sergio Ciliberto
et al.
Abstract In this note, we correct the expression of the switching rate of the potential barrier for a system at temperature T expressed in equation (8) and derived in appendix B. We also update below all the equations using the switching rate expression. The error is nevertheless small enough to not change any of the other results or conclusions of the paper. The error came from the assumption that the total energy in the double well potential E was simply distributed according to the Boltzmann probability distribution P ( E ) = 1 k B T exp − E / ( k B T ) , which would be valid only in an harmonic potential. Indeed, in the double well potential, the motion period depends on the system energy. Therefore the probability distribution of the energy P ( E ) is obtained by integrating the Boltzmann canonical distribution on the time range (time range required to explore the full phase space). Contrary to the harmonic case where is constant, here the energy dependence modifies the expression of P ( E ).
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large collision velocities. To describe these effects of particle inertia, it is necessary to consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and non-dimensional parameters governing the particle dynamics, and have made qualitative, and in some cases quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and summarise their successes and failures. Annu. Rev. Fluid Mech. 56: In press. DOI: 10.1146/annurev-fluid-032822-014140.
Valtteri Haavisto, Marcin Mińkowski, Lasse Laurson
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media driven by a slowly increasing external force, a paradigmatic complex system exhibiting critical avalanche dynamics linked to a continuous non-equilibrium depinning phase transition. To this end, we train a variety of machine learning models to infer the mapping from features of the initial relaxed line shape and the random pinning landscape to predict the sample-dependent staircase-like force-displacement curve that emerges from the depinning process. Even if for a given realization of the quenched random medium the dynamics are in principle deterministic, we find that there is an exponential decay of the predictability with the displacement of the line as it nears the depinning transition from below. Our analysis on how the related displacement scale depends on the system size and the dimensionality of the input descriptor reveals that the onset of the depinning phase transition gives rise to fundamental limits to predictability.
The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles $N$ is exactly derived for both quenched and annealed realizations. It is proved that the results for both classes of systems tend in the thermodynamic limit ($N\to\infty$) to a common expression recently derived (Maestre M A G and Santos A 2020 J Stat Mech 063217). The theoretical finite-size results are particularized to the Kern--Frenkel model and confirmed by Monte Carlo simulations for quenched and (both biased and unbiased) annealed systems.
Lukas Schrack, Charlotte F. Petersen, Gerhard Jung
et al.
The complex behavior of confined fluids arising due to a competition between layering and local packing can be disentangled by considering quasi-confined liquids, where periodic boundary conditions along the confining direction restore translational invariance. This system provides a means to investigate the interplay of the relevant length scales of the confinement and the local order. We provide a mode-coupling theory of the glass transition (MCT) for quasi-confined liquids and elaborate an efficient method for the numerical implementation. The nonergodicity parameters in MCT are compared to computer-simulation results for a hard-sphere fluid. We evaluate the nonequilibrium-state diagram and investigate the collective intermediate scattering function. For both methods, nonmonotonic behavior depending on the confinement length is observed.
Abstract Numerous models in opinion dynamics focus on the temporal dynamics within a single electoral unit (e.g. country). The empirical observations, on the other hand, are often made across multiple electoral units (e.g. polling stations) at a single point in time (e.g. elections). Aggregates of these observations, while quite useful in many applications, neglect the underlying heterogeneity in opinions. To address this issue we build a simple agent–based model in which all agents have fixed opinions, but are able to change their electoral units. We demonstrate that this model is able to generate rank–size distributions consistent with the empirical data.
Abstract A new class of bootstrap percolation models in which particle culling occurs only for certain numbers of nearest neighbours is introduced and studied on a Bethe lattice. Upon increasing the density of initial configuration they undergo multiple hybrid (or mixed-order) phase transitions, showing that such intriguing phase behaviours may also appear in fully homogeneous environments, provided that culling is selective rather than cumulative . The idea immediately extends to facilitation dynamics, suggesting a simple way to construct one-component models of multiple glasses and glass-glass transitions as well as more general coarse-grained models of complex cooperative dynamics.
Vanda Inácio de Carvalho, Miguel de Carvalho, Adam Branscum
Accurate diagnosis of disease is of great importance in clinical practice and medical research. The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of continuous diagnostic test outcomes when there exist three‐ordered disease classes (e.g., no disease, mild disease, and advanced disease). We propose the Bayesian bootstrap, a fully nonparametric method, for conducting inference about the ROC surface and its functionals, such as the volume under the ROC surface (VUS). The proposed method is based on a simple, yet interesting, representation of the ROC surface in terms of placement variables and has the appealing feature of producing point and interval estimates for the ROC surface and its corresponding VUS in a single integrated framework. Results from a simulation study demonstrate the ability of our method to successfully recover the true ROC surface and to produce valid inferences in a variety of complex scenarios. An application to data from the Trail Making Test to assess cognitive impairment in Parkinson's disease patients is provided.
We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the interface heights at two times $t_1$ and $t_2>t_1$, with droplet initial conditions at $t=0$. In the limit of large times this JPDF is expected to become a universal function of the time ratio $t_2/t_1$, and of the (properly scaled) heights $h(x,t_1)$ and $h(x,t_2)$. Using the replica Bethe ansatz method for the KPZ equation, in [J. Stat. Mech. (2017) 053212] we obtained a formula for the JPDF in the (partial) tail regime where $h(x,t_1)$ is large and positive, subsequently found in excellent agreement with experimental and numerical data [Phys. Rev. Lett. 118, 125701 (2017)]. Here we show that our results are in perfect agreement with Johansson's recent rigorous expression of the full JPDF [arXiv:1802.00729 ], thereby confirming the validity of our methods.