Abstract:
A recent segregation criterion [V. Garz\'o, Phys. Rev. E \textbf{78}, 020301(R) (2008)] based on the thermal diffusion factor $\Lambda$ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of $\Lambda$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to get the kinetic diffusion coefficient $D_0$. The comparison between theory and simulation shows that the second Sonine approximation to $D_0$ yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE/RBNE transition, the kinetic theory results for the factor $\Lambda$ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.

Abstract:
A solution of the inelastic Enskog equation that goes beyond the weak dissipation limit and applies for moderate densities is used to determine the thermal diffusion factor of an intruder immersed in a dense granular gas under gravity. This factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, density and coefficients of restitution). The form of the phase-diagrams for the BNE/RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the parameters of the system. Two specific limits are considered with detail: (i) absence of gravity, and (ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis extends previous theoretical results derived in the dilute limit case [V. Garz\'o, Europhys. Lett. {\bf 75}, 521 (2006)] and is consistent with the findings of some recent experimental results.

Abstract:
We present a hydrodynamic theoretical model for "Brazil nut" size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local "granular temperature". The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.

Abstract:
The difference of temperatures between an impurity and the surrounding gas in an open vibrated granular system is studied. It is shown that, in spite of the high inhomogeneity of the state, the temperature ratio remains constant in the bulk of the system. The lack of energy equipartition is associated to the change of sign of the pressure diffusion coefficient for the impurity at certain values of the parameters of the system, leading to a segregation criterium. The theoretical predictions are consistent with previous experimental results, and also in agreement with molecular dynamics simulation results reported in this paper.

Abstract:
A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is statistically upward continuous if it preserves statistically upward half quasi-Cauchy sequences, is statistically downward continuous if it preserves statistically downward half quasi-Cauchy sequences; and a subset $E$ of $\textbf{R}$, is statistically upward compact if any sequence of points in $E$ has a statistically upward half quasi-Cauchy subsequence, is statistically downward compact if any sequence of points in $E$ has a statistically downward half quasi-Cauchy subsequence where a sequence $(x_{n})$ of points in $\textbf{R}$ is called statistically upward half quasi-Cauchy if \[ \lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n: x_{k}-x_{k+1}\geq \varepsilon\}|=0 \] is statistically downward half quasi-Cauchy if \[ \lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n: x_{k+1}-x_{k}\geq \varepsilon\}|=0 \] for every $\varepsilon>0$. We investigate statistically upward continuity, statistically downward continuity, statistically upward half compactness, statistically downward half compactness and prove interesting theorems. It turns out that uniform limit of a sequence of statistically upward continuous functions is statistically upward continuous, and uniform limit of a sequence of statistically downward continuous functions is statistically downward continuous.

Abstract:
Segregation by thermal diffusion of an intruder immersed in a sheared granular gas is analyzed from the (inelastic) Boltzmann equation. Segregation is induced by the presence of a temperature gradient orthogonal to the shear flow plane and parallel to gravity. We show that, like in analogous systems without shear, the segregation criterion yields a transition between upwards segregation and downwards segregation. The form of the phase diagrams is illustrated in detail showing that they depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. We find that both mechanisms (upwards and downwards segregation) are stronger and more clearly separated when compared with segregation criteria in systems without shear.

Abstract:
A recent solution of the inelastic Boltzmann equation that applies for strong dissipation and takes into account non-equipartition of energy is used to derive an explicit expression for the thermal diffusion factor. This parameter provides a criterion for segregation that involves all the parameters of the granular binary mixture (composition, masses, sizes, and coefficients of restitution). The present work is consistent with recent experimental results and extends previous results obtained in the intruder limit case.

Abstract:
We investigate the dynamics of an intruder pulled by a constant force in a dense two-dimensional granular fluid by means of event-driven molecular dynamics simulations. In a first step, we show how a propagating momentum front develops and compactifies the system when reflected by the boundaries. To be closer to recent experiments \cite{candelier2010journey,candelier2009creep}, we then add a frictional force acting on each particle, proportional to the particle's velocity. We show how to implement frictional motion in an event-driven simulation. This allows us to carry out extensive numerical simulations aiming at the dependence of the intruder's velocity on packing fraction and pulling force. We identify a linear relation for small and a nonlinear regime for high pulling forces and investigate the dependence of these regimes on granular temperature.

Abstract:
The aim of this paper is to contribute, in the theoretical and empirical sense, to better understanding the challenges of the EU welfare regimes and how particular regimes react on them. Despite significant differences among the EU welfare regimes, it is real to expect that they will converge because of the common challenges confronting them. In this paper, using the model of sigma and beta convergence, we are trying to predict the possible direction of convergence in the sense that Europe will go toward to more or less generosity or in other words it will converge downward or upward. The downward convergence means the strengthen competition among existing welfare regimes, in order to maintain and/or attract capital, that could reduce the social spending generosity. On the other hand, the upward convergence above involves the strengthening of coordination among existing welfare regimes according to the values of solidarity and social justice, which characterise not only the most developed EU countries but also the supranational European social model. .

Abstract:
A simple model for intruder in vibrating granular bed is constructed by introducing a term that governs frequency dependent granular bed density. Varying the vibrating frequency will drive the buoyant force acting on the intruder by the granular bed. Swapped regions of rising and sinking intruder compared to other reported result have bee found.