Boltzmann statistics in a three-dimensional vibrofluidized granular bed: idealizing the experimental system

Platonic solids bouncing on a vibrating plate

The energy transfer between bouncing particles and rigid boundaries during impacts is crucially influenced not only by restitution coefficients of the material but also by particle shapes. This is particularly important when such particles are mechanically agitated with vibrating plates. Inertial measurement units are able to measure all acceleration and rotational velocity components of an object and store these data for subsequent analysis. We employ them to measure the dynamics of cubes and icosahedra on vibrating plates to study the efficiency of energy transfer into the individual degrees of freedom (DOFs) of the excited object. The rotational DOFs turn out to be much less excited than the vertical translational motion. Most remarkably, there is only little difference between the two Platonic solids in both the absolute energies and the energy partition ratios.

Using Gaussian process for velocity reconstruction after coronary stenosis applicable in positron emission particle tracking: An in-silico study

Accurate velocity reconstruction is essential for assessing coronary artery disease. We propose a Gaussian process method to reconstruct the velocity profile using the sparse data of the positron emission particle tracking (PEPT) in a biological environment, which allows the measurement of tracer particle velocity to infer fluid velocity fields. We investigated the influence of tracer particle quantity and detection time interval on flow reconstruction accuracy. Three models were used to represent different levels of stenosis and anatomical complexity: a narrowed straight tube, an idealized coronary bifurcation with stenosis, and patient-specific coronary arteries with a stenotic left circumflex artery. Computational fluid dynamics (CFD), particle tracking, and the Gaussian process of kriging were employed to simulate and reconstruct the pulsatile flow field. The study examined the error and uncertainty in velocity profile reconstruction after stenosis by comparing particle-derived flow velocity with the CFD solution. Using 600 particles (15 batches of 40 particles) released in the main coronary artery, the time-averaged error in velocity reconstruction ranged from 13.4% (no occlusion) to 161% (70% occlusion) in patient-specific anatomy. The error in maximum cross-sectional velocity at peak flow was consistently below 10% in all cases. PEPT and kriging tended to overestimate area-averaged velocity in higher occlusion cases but accurately predicted maximum cross-sectional velocity, particularly at peak flow. Kriging was shown to be useful to estimate the maximum velocity after the stenosis in the absence of negative near-wall velocity.

Recent advances in positron emission particle tracking: a comparative review

Positron emission particle tracking (PEPT) is a technique which allows the high-resolution, three-dimensional imaging of particulate and multiphase systems, including systems which are large, dense, and/or optically opaque, and thus difficult to study using other methodologies. In this work, we bring together researchers from the world's foremost PEPT facilities not only to give a balanced and detailed overview and review of the technique but, for the first time, provide a rigorous, direct, quantitative assessment of the relative strengths and weaknesses of all contemporary PEPT methodologies. We provide detailed explanations of the methodologies explored, including also interactive code examples allowing the reader to actively explore, edit and apply the algorithms discussed. The suite of benchmarking tests performed and described within the document is made available in an open-source repository for future researchers.

Mpemba effect in driven granular Maxwell gases

A Mpemba effect refers to the counterintuitive result that, when quenched to a low temperature, a system at higher temperature may equilibrate faster than one at intermediate temperatures. This effect has recently been demonstrated in driven granular gases, both for smooth as well as rough hard-sphere systems based on a perturbative analysis. In this paper, we consider the inelastic driven Maxwell gas, a simplified model for a granular gas, where the rate of collision is assumed to be independent of the relative velocity. Through an exact analysis, we determine the conditions under which the Mpemba effect is present in this model. For monodispersed gases, we show that the Mpemba effect is present only when the initial states are allowed to be nonstationary, while for bidispersed gases, it is present for some steady-state initial states. We also demonstrate the existence of the strong Mpemba effect for bidispersed Maxwell gas, wherein the system at higher temperature relaxes to a final steady state at an exponentially faster rate leading to smaller equilibration time.

Positron Emission Particle Tracking of Granular Flows

Positron emission particle tracking (PEPT) is a noninvasive technique capable of imaging the three-dimensional dynamics of a wide variety of powders, particles, grains, and/or fluids. The PEPT technique can track the motion of particles with high temporal and spatial resolution and can be used to study various phenomena in systems spanning a broad range of scales, geometries, and physical states. We provide an introduction to the PEPT technique, an overview of its fundamental principles and operation, and a brief review of its application to a diverse range of scientific and industrial systems.

Reversible Self-Assembly (fcc-bct) Crystallization of Confined Granular Spheres via a Shear Dimensionality Mechanism

By combining vibrational annealing and shear dimensionality, we experimentally show (1) a fast reversible crystallization fcc-bct (face-centered cubic-body-centered tetragonal) in a granular system that is composed of dissipative millimeter-sized dry spheres, (2) a two-dimensional (planar) shear promotes self-assembly into an fcc crystal, while one-dimensional shear produces a bct crystal, and (3) in analogy with heterogeneous nucleation, a granular temperature gradient leads to the formation of crystal domains showing competition of polymorphic phases in the cold regions. Our findings suggest that controlling the directionality of the interactions steers to reversible crystallization of hard spheres, adds clues for theoretical studies, and provides a novel mechanism for the technological development of the applications of self-assembling phononic crystals.

Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?

The decay of energy within particulate media subjected to an impulse is an issue of significant scientific interest, but also one with numerous important practical applications. In this paper, we study the dynamics of a granular system exposed to energetic impulses in the form of discrete taps from a solid surface. By considering a one-dimensional toy system, we develop a simple theory, which successfully describes the energy decay within the system following exposure to an impulse. We then extend this theory so as to make it applicable also to more realistic, three-dimensional granular systems, assessing the validity of the model through direct comparison with discrete particle method simulations. The theoretical form presented possesses several notable consequences; in particular, it is demonstrated that for suitably large systems, effects due to the bounding walls may be entirely neglected. We also establish the existence of a threshold system size above which a granular bed may be considered fully three dimensional.

Dynamic self-assembly of non-Brownian spheres studied by molecular dynamics simulations

Granular self-assembly of confined non-Brownian spheres under gravity is studied by molecular dynamics simulations. Starting from a disordered phase, dry or cohesive spheres organize, by vibrational annealing, into body-centered-tetragonal or face-centered-cubic structures, respectively. During the self-assembling process, isothermal and isodense points are observed. The existence of such points indicates that both granular temperature and packing fraction undergo an inversion process that may be in the core of crystal nucleation. Around the isothermal point, a sudden growth of granular clusters having the maximum coordination number takes place, indicating the outcome of a first-order phase transition. We propose a heuristic equation that successfully describes the dynamic evolution of the local packing fraction in terms of the local granular temperature, along the entire crystallization process.

Maximizing energy transfer in vibrofluidized granular systems

Using discrete particle simulations validated by experimental data acquired using the positron emission particle tracking technique, we study the efficiency of energy transfer from a vibrating wall to a system of discrete, macroscopic particles. We demonstrate that even for a fixed input energy from the wall, energy conveyed to the granular system under excitation may vary significantly dependent on the frequency and amplitude of the driving oscillations. We investigate the manner in which the efficiency with which energy is transferred to the system depends on the system variables and determine the key control parameters governing the optimization of this energy transfer. A mechanism capable of explaining our results is proposed, and the implications of our findings in the research field of granular dynamics as well as their possible utilization in industrial applications are discussed.

Translational and rotational temperatures of a 2D vibrated granular gas in microgravity

We present an experimental study performed on a vibrated granular gas enclosed into a 2D rectangular cell. Experiments are performed in microgravity conditions achieved during parabolic flights. High speed video recording and optical tracking allow to obtain the full kinematics (translation and rotation) of the particles. The inelastic parameters are retrieved from the experimental trajectories as well as the translational and rotational velocity distributions. We report that the experimental ratio of translational versus rotational temperature decreases with the density of the medium but increases with the driving velocity of the cell. These experimental results are compared with existing theories and we point out the differences observed. We also present a model which fairly predicts the equilibrium experimental temperatures along the direction of vibration.