Nonequilibrium Brownian motion beyond the effective temperature

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.Comment: 10 pages, 5 figure

Non-equilibrium fluctuations in frictional granular motor: experiments and kinetic theory

We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe for the first time the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions (RC), with an average drift $\ \sim v_0^3$, and (ii) frequent collisions (FC), with $\ \sim v_0$. We also study the fluctuations of the angle spanned in a large time interval, $\Delta \theta$, which in the FC regime is proportional to the work done upon the motor. We observe that the Fluctuation Relation is satisfied with a slope which weakly depends on the relative collision frequency.Comment: 7 pages, 6 figure

Nutella: The Construction and Enactment of Simulated Macroworlds

In the last twenty years the development of new technologies has radically expanded the kind of activity structures that can be designed and built for the classroom. A subset among these technology-enhanced learning environments, that I call macroworlds, leverages the notions of ubiquitous computing, distributed interaction, and the increasing availability in classrooms of pervasive, non-desktop technologies (e.g. handhelds, large wall-mounted displays, tangibles and many others) to provide engaging ways for students to “experience” and interact with classroom-sized simulations of scientific phenomena. So far, a number of studies demonstrated how macroworlds can help students engage in authentic science practices, and build meaningful connections between physical activity and important principles in different science domains, making macroworlds an active area of research both in the field of Human-Computer Interaction and the Learning Sciences. Despite their promise, macroworlds have proven challenging to design, build, and enact, restricting this kind of learning environments to only few exemplars. In particular, one of the main challenges faced by developers while building and enacting macroworlds is the lack of a software framework supporting these processes, specifically designed to address the requirements of this learning technology. This work focuses on tackling this issue and presents a method, a set of guidelines and a software framework to support the construction and enactment of macroworlds

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

Structure factors in granular experiments with homogeneous fluidization

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions [10, 40]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the bath temperature T b, depending on shaking parameters, and the granular temperature T g T b, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with , after proper rescaling with the mean free path. © 2012 American Institute of Physics

Velocity distributions.

<p>PDF of the rotator’s angular velocity rescaled by for low (black circles, rad/s) and high (blue squares, rad/s) densities. The red dashed line shows a Gaussian fit for comparison.</p

Response and autocorrelation.

<p>Response function (black circles), rescaled velocity autocorrelation (red squares), and GFDT response with the factorization assumption, Eq. (6), (green diamonds) for (a), (b) and (c), that is packing fractions , and , respectively. In the inset the parametric plot <i>vs </i>, in the region where is positive and monotonously decreasing, is plotted in log-log scale. In the densest cases, and behave very differently and Einstein’s relation is significantly violated.</p

Experimental setup.

<p>A sketch of the setup illustrates the essential components. A wheel rotating around a fixed axis is suspended in a cylindrical cell containing steel spheres. The cell is shaken in order to fluidize the material and obtain a granular gas. The wheel performs a Brownian-like dynamics, randomly excited by collisions with the spheres. A small motor is coupled to the wheel axis, in order to apply an external impulsive perturbation. An angular encoder reads the angular velocity of the wheel. Statistical properties of the velocities of the spheres are collected through a fast camera, placed above the system. A detailed description is presented in Methods section.</p