Filling a silo with a mixture of grains: Friction-induced segregation

We study the filling process of a two-dimensional silo with inelastic particles by simulation of a granular media lattice gas (GMLG) model. We calculate the surface shape and flow profiles for a monodisperse system and we introduce a novel generalization of the GMLG model for a binary mixture of particles of different friction properties where, for the first time, we measure the segregation process on the surface. The results are in good agreement with a recent theory, and we explain the observed small deviations by the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as wel

Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page

Microscopic Model for Granular Stratification and Segregation

We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured in two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the dissipation of energy in collisions between rolling and static grains and an energy barrier describing the geometrical asperities of the grains. We study the phase diagram of the different morphologies predicted by the model as a function of the two parameters. We find regions of segregation and stratification, in agreement with experimental finding, as well as a region of total mixing.Comment: 4 pages, 7 figures, http://polymer.bu.edu/~hmakse/Home.htm

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums

We study segregation of granular mixtures in the continuous avalanche regime (for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory for surface flows of grains. The theory predicts profiles in agreement with experiments only when we consider a flux dependent velocity of flowing grains. We find the segregation of species of different size and surface properties, with the smallest and roughest grains being found preferentially at the center of the drum. For a wide difference between the species we find a complete segregation in agreement with experiments. In addition, we predict a transition to a smooth segregation regime - with an power-law decay of the concentrations as a function of radial coordinate - as the size ratio between the grains is decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks

A Hedged Monte Carlo Approach to Real Option Pricing

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.Comment: 25 pages, 14 figure

On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed

Three-dimensional observation of the fracture process zone in anisotropic granitic rock by x-ray CT scan

see Abstract Volum

Aging in humid granular media

Aging behavior is an important effect in the friction properties of solid surfaces. In this paper we investigate the temporal evolution of the static properties of a granular medium by studying the aging over time of the maximum stability angle of submillimetric glass beads. We report the effect of several parameters on these aging properties, such as the wear on the beads, the stress during the resting period, and the humidity content of the atmosphere. Aging effects in an ethanol atmosphere are also studied. These experimental results are discussed at the end of the paper.Comment: 7 pages, 9 figure