Langevin equations from experimental data: the case of rotational diffusion in granular media

Abstract

A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a Langevin-type stochastic equation from a time series of empirical data. Even if the protocol is based upon the introduction of drift and diffusion terms in stochastic differential equations, its implementation involves subtle conceptual problems and, most importantly, requires some prior theoretical knowledge about the system. Here we apply this approach to the data obtained in a rotational granular diffusion experiment, showing the power of this method and the theoretical issues behind its limits. A crucial point emerged in the dense liquid regime, where the data reveal a complex multiscale scenario with at least one fast and one slow variable. Identifying the latter is a major problem within the Langevin derivation procedure and led us to introduce innovative ideas for its solution.

References in corpus (21)

• Supercooled Liquids for Pedestrians
• Turbulent-like fluctuations in quasistatic flow of granular media
• Observing Brownian motion in vibration-fluidized granular matter
• Self-diffusion in dense granular shear flows
• Caging dynamics in a granular fluid
• Subdiffusion and cage effect in a sheared granular material
• Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass
• Irreversible dynamics of a massive intruder in dense granular fluids
• Simple stochastic models showing strong anomalous diffusion
• Long-time tails and cage effect in driven granular fluids
• Superdiffusive, heterogeneous, and collective particle motion near the jamming transition in athermal disordered materials
• Cages and anomalous diffusion in vibrated dense granular media
• Granular Brownian motion
• Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise
• Granular Brownian motion with dry friction
• Rheology of Weakly Vibrated Granular Media
• Mechanical fluctuations suppress the threshold of soft-glassy solids : the secular drift scenario
• Transport properties in chaotic and non-chaotic many particles systems
• The Role of Data in Model Building and Prediction: A Survey Through Examples
• Langevin equation in systems with also negative temperatures
• An Itinerant Oscillator model with cage inertia for mesorheological granular experiments

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• Effective equations for reaction coordinates in polymer transport
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
• Non-equilibrium attractor for non-linear stochastic dynamics
• Effective Equations in complex systems: from Langevin to machine learning