Flow rate of polygonal grains through a bottleneck: Interplay between shape and size

We report two-dimensional simulations of circular and polygonal grains passing through an aperture at the bottom of a silo. The mass flow rate for regular polygons is lower than for disks as observed by other authors. We show that both the exit velocity of the grains and the packing fraction are lower for polygons, which leads to the reduced flow rate. We point out the importance of the criteria used to define when two objects of different shape are considered to be of the same size. Depending on this criteria, the mass flow rate may vary significantly for some polygons. Moreover, the particle flow rate is non-trivially related to a combination of mass flow rate, particle shape and particle size. For some polygons, the particle flow rate may be lower or higher than that of the corresponding disks depending on the size comparison criteria.Comment: 9 pages, 8 figure

On the Role of Viscosity in Early Cosmology

We present a discussion of the effects induced by bulk viscosity on the very early Universe stability. The viscosity coefficient is assumed to be related to the energy density $\rho$ via a power-law of the form $\zeta=\zeta_0 \rho^s$ (where $\zeta_0, s=const.$) and the behavior of the density contrast in analyzed. In particular, we study both Einstein and hydrodynamic equations up to first and second order in time in the so-called quasi-isotropic collapsing picture near the cosmological singularity. As a result, we get a power-law solution existing only in correspondence to a restricted domain of $\zeta_0$. The particular case of pure isotropic FRW dynamics is then analyzed and we show how the asymptotic approach to the initial singularity admits an unstable collapsing picture.Comment: 4 pages, no figur

Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns

We simulate via a Discrete Element Method the tapping of a narrow column of disk under gravity. For frictionless disks, this system has a simple analytic expression for the density of states in the Edwards volume ensemble. We compare the predictions of the ensemble at constant compactivity against the results for the steady states obtained in the simulations. We show that the steady states cannot be properly described since the microstates sampled are not in correspondence with the predicted distributions, suggesting that the postulates of flat measure and ergodicity are, either or both, invalid for this simple realization of a static granular system. However, we show that certain qualitative features of the volume fluctuations difficult to predict from simple arguments are captured by the theory.Comment: 11 pages, 6 figure

Counterfactual Building and Evaluation via eXplainable Support Vector Data Description

Increasingly in recent times, the mere prediction of a machine learning algorithm is considered insufficient to gain complete control over the event being predicted. A machine learning algorithm should be considered reliable in the way it allows to extract more knowledge and information than just having a prediction at hand. In this perspective, the counterfactual theory plays a central role. By definition, a counterfactual is the smallest variation of the input such that it changes the predicted behaviour. The paper addresses counterfactuals through Support Vector Data Description (SVDD), empowered by explainability and metric for assessing the counterfactual quality. After showing the specific case in which an analytical solution may be found (under Euclidean distance and linear kernel), an optimisation problem is posed for any type of distances and kernels. The vehicle platooning application is the use case considered to demonstrate how the outlined methodology may offer support to safety-critical applications as well as how explanation may shed new light into the control of the system at hand

Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics. The BPS is studied with a 1D code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an n-body hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distint regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad-hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided

The Jeans Instability in Presence of Viscous Effects

An analysis of the gravitational instability in presence of dissipative effects is addressed. In particular, the standard Jeans Mechanism and the generalization in treating the Universe expansion are both analyzed when bulk viscosity affects the first-order Newtonian dynamics. As results, the perturbation evolution is founded to be damped by dissipative processes and the top-down mechanism of structure fragmentation is suppressed. In such a scheme, the value of the Jeans Mass remains unchanged also in presence of viscosity.Comment: 13 pages, 2 figure

Nonmonotonic reversible branch in four model granular beds subjected to vertical vibration

We present results from four independent models of a granular assembly subjected to tapping. We find that the steady-state packing fraction as a function of the tapping intensity is nonmonotonic. In particular, for high tapping intensities, we observe an increase of the packing fraction with tapping strength. This finding challenges the current understanding of compaction of granular media since the steady-state packing fraction is believed to decrease monotonically with increasing tapping intensity. We propose an explanation of our results based on the properties of the arches formed by the particles.Comment: 8 pages, 7 figure

On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influence the fragmentation process. To this end we study the dynamics of a uniform and spherically symmetric cloud with corrections due to the negative pressure contribution associated to the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian, either the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0 \rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how, in the adiabatic-like behavior of the gas (i.e. when the politropic index takes values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. We can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. $1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur

Bulk Viscosity Effects on the Early Universe Stability

We present a discussion of the effects induced by the bulk viscosity on the very early Universe stability. The matter filling the cosmological (isotropic and homogeneous) background is described by a viscous fluid having an ultrarelativistic equation of state and whose viscosity coefficient is related to the energy density via a power-law of the form $\zeta=\zeta_0 \rho^\nu$. The analytic expression of the density contrast (obtained for $\nu=1/2$) shows that, for small values of the constant $\zeta_0$, its behavior is not significantly different from the non-viscous one derived by E.M. Lifshitz. But as soon as $\zeta_0$ overcomes a critical value, the growth of the density contrast is suppressed forward in time by the viscosity and the stability of the Universe is favored in the expanding picture. On the other hand, in such a regime, the asymptotic approach to the initial singularity (taken at $t=0$) is deeply modified by the apparency of significant viscosity in the primordial thermal bath i.e. the isotropic and homogeneous Universe admits an unstable collapsing picture. In our model this feature regards also scalar perturbations while in the non-viscous case it appears only for tensor modes.Comment: 8 pages, no figur