An itinerant oscillator model with cage inertia for mesorheological granular experiments

Microscopic self-dynamics in liquid Ne-D_{2} mixtures: Quantum features and itinerant oscillators reexamined

In this paper, we report the results of a centroid molecular dynamics (CMD) study of the canonical velocity autocorrelation functions (VACFs) in liquid Ne-D_{2} mixtures at a temperature of T=30K and in the full D_{2}-concentration range (0%≤x_{D_{2}}≤100%). This binary system was selected because of its moderate, although sizable, quantum effects which, as far as its equilibrium properties are concerned, are fully described by the path integral Monte Carlo (PIMC) simulations that have been also implemented. A comprehensive test of the VACF spectral moments carried out using three physical quantities (namely, mean kinetic energy, Einstein frequency, and mean-squared force) obtained from PIMC was performed revealing the potentialities, as well as the limitations, of the CMD approach to the single-particle dynamics in these low-T liquid mixtures. Additional physical information was extracted from the canonical VACFs by fitting their spectra via two distinct methods: the Levesque-Verlet model (LV, very flexible but highly heuristic) and the itinerant oscillator model (IO, based on the physical ground of a single particle rattling inside a short-lived diffusing pseudocage). Both provided good fits of the CMD outputs, with LV being always more adequate than IO in the case of the Ne VACFs, while, as for the D_{2} VACFs, the LV superiority is evident only at high x_{D_{2}} values. However, a peculiar and systematic effect was found after analyzing the IO-fitted parameters: the estimated pseudocage masses turned out to be at least one order of magnitude lower than the corresponding values inferred from the PIMC simulations. This outcome concerns both the Ne and the D_{2} rattling molecule and, as we also discovered, had already been observed (but promptly forgotten) in purely classical simulations of liquid Ar. The possible physical origins of this finding have been finally discussed in some detail, also in connection with the result of the more recent exponential expansion theory (EET), which manages to shed more light on the concept of single particles rattling inside short-lived pseudocages, ultimately demonstrating its untenability.

Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior

The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a one-dimensional time series, such a goal becomes challenging. A paradigmatic example is the angular diffusion of a rotator immersed in a vibro-fluidized granular gas. Here, we experimentally observe that the rotator's angular velocity exhibits significant differences with respect to an equilibrium process. Exploiting the presence of two relevant timescales and non-Gaussian velocity increments, we quantify the breakdown of time-reversal asymmetry, which would vanish in the case of a 1D Gaussian process. We deduce a new model for the massive probe, with two linearly coupled variables, incorporating both Gaussian and Poissonian noise, the latter motivated by the rarefied collisions with the granular bath particles. Our model reproduces the experiment in a range of densities, from dilute to moderately dense, with a meaningful dependence of the parameters on the density. We believe the framework proposed here opens the way to a more consistent and meaningful treatment of out-of-equilibrium and dissipative systems.

Thermodynamic bounds for diffusion in nonequilibrium systems with multiple timescales

We derive a thermodynamic uncertainty relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to previous results and also holds at finite time. We apply our findings to experimental and numerical data for a vibrofluidized granular medium, characterized by regimes of anomalous diffusion. In some cases our relation can distinguish between equilibrium and nonequilibrium behavior, a nontrivial inference task, particularly for Gaussian processes.

Slow time scales in a dense vibrofluidized granular material

Modeling collective motion in nonconservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, and not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed evidence of many time scales: Fast ballistic, intermediate caged, slow superdiffusive, and very slow diffusive. A numerical investigation has demonstrated that a tracer's superdiffusion is related to slow rotating drifts of the granular medium. Here we offer a deeper insight into the slow scales of the granular medium, and we propose a phenomenological model for such a "secular" dynamics. Based upon the model for the granular medium, we also introduce a model for the tracer (fast and slow) dynamics, which consists in a stochastic system of equations for three coupled variables, and is therefore more refined and successful than previous models.

Anomalous diffusion of a dipole interacting with its surroundings

A fractional Fokker-Planck equation based on the continuous time random walk Ansatz is written via the Langevin equations for the dynamics of a dipole interacting with its surroundings, as represented by a cage of dipolar molecules. This equation is solved in the frequency domain using matrix continued fractions, thus yielding the linear dielectric response for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio, and hence the complex susceptibility. The latter comprises a low frequency band with width depending on the anomalous parameter and a far infrared (THz) band with a comb-like structure of peaks. Several physical consequences of the model relevant to anomalous diffusion in the presence of interactions are discussed. The entire calculation may be regarded as an extension of the cage model interpretation of the dynamics of polar molecules to anomalous diffusion, taking into account inertial effects.

Dynamical Collective Memory in Fluidized Granular Materials

Recent experiments with rotational diffusion of a probe in a vibrated granular media revealed a rich scenario, ranging from a dilute gas to a dense liquid with cage effects and an unexpected superdiffusive behavior at large times. Here we set up a simulation that reproduces quantitatively the experimental observations and allows us to investigate the properties of the host granular medium, a task not feasible in the experiment. We discover a persistent collective rotational mode which emerges at a high density and a low granular temperature: a macroscopic fraction of the medium slowly rotates, randomly switching direction after very long times. Such a rotational mode of the host medium is the origin of the probe's superdiffusion. Collective motion is accompanied by a kind of dynamical heterogeneity at intermediate times (in the cage stage) followed by a strong reduction of fluctuations at late times, when superdiffusion sets in.

Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes

Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in vitro by single molecule approaches, but their in vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power stroke, and velocity) of the in vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration τ ∼ 300 μs resulting in an average force of F ∼ 0.4 pN on vesicles in in vivo oocytes, remarkably similar to the kinetics of in vitro myosin-V. Our results reveal that measuring in vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.

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

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.

The Role of Data in Model Building and Prediction: A Survey Through Examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play—and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components.

Cage model of polar fluids: Finite cage inertia generalization

The itinerant oscillator model describing rotation of a dipole about a fixed axis inside a cage formed by its surrounding polar molecules is revisited in the context of modeling the dielectric relaxation of a polar fluid via the Langevin equation. The dynamical properties of the model are studied by averaging the Langevin equations describing the complex orientational dynamics of two bodies (molecule-cage) over their realizations in phase space so that the problem reduces to solving a system of three index linear differential-recurrence relations for the statistical moments. These are then solved in the frequency domain using matrix continued fractions. The linear dielectric response is then evaluated for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio and along with the usual inertia corrected microwave Debye absorption gives rise to significant far-infrared absorption with a comb-like structure of harmonic peaks. The model may be also regarded as an extension of Budó's [J. Chem. Phys. 17, 686 (1949)] treatment of molecules containing rotating polar groups to include inertial effects.

Unified rheology of vibro-fluidized dry granular media: From slow dense flows to fast gas-like regimes

Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional μ(I)-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakening, shear thinning, a discontinuous thinning transition, and gaseous shear thickening. The employed setup gives access to dynamic fluctuations, which exhibit a broad range of timescales. In the slow dense regime the frequency of cage-opening increases with stress and enhances, with respect to μ(I)-rheology, the decrease of viscosity. Diffusivity is exponential in the shear stress in both thinning and thickening regimes, with a huge growth near the transition.

Active cage model of glassy dynamics

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.