808 research outputs found
Granular Rheology in Zero Gravity
We present an experimental investigation on the rheological behavior of model
granular media made of nearly elastic spherical particles. The experiments are
performed in a cylindrical Couette geometry and the experimental device is
placed inside an airplane undergoing parabolic flights to cancel the effect of
gravity. The corresponding curves, shear stress versus shear rate, are
presented and a comparison with existing theories is proposed. The quadratic
dependence on the shear rate is clearly shown and the behavior as a function of
the solid volume fraction of particles exhibits a power law function. It is
shown that theoretical predictions overestimate the experiments. We observe, at
intermediate volume fractions, the formation of rings of particles regularly
spaced along the height of the cell. The differences observed between
experimental results and theoretical predictions are discussed and related to
the structures formed in the granular medium submitted to the external shear.Comment: 10 pages, 6 figures to be published in Journal of Physics : Condensed
Matte
Past production constrains current energy demands: persistent scaling in global energy consumption and implications for climate change mitigation
Climate change has become intertwined with the global economy. Here, we
describe the importance of inertia to continued growth in energy consumption.
Drawing from thermodynamic arguments, and using 38 years of available
statistics between 1980 to 2017, we find a persistent time-independent scaling
between the historical time integral of world inflation-adjusted economic
production , or , and
current rates of world primary energy consumption , such that
Gigawatts per trillion 2010 US dollars.
This empirical result implies that population expansion is a symptom rather
than a cause of the current exponential rise in and carbon dioxide
emissions , and that it is past innovation of economic production efficiency
that has been the primary driver of growth, at predicted rates
that agree well with data. Options for stabilizing are then limited to
rapid decarbonization of through sustained implementation of over
one Gigawatt of renewable or nuclear power capacity per day. Alternatively,
assuming continued reliance on fossil fuels, civilization could shift to a
steady-state economy that devotes economic production exclusively to
maintenance rather than expansion. If this were instituted immediately,
continual energy consumption would still be required, so atmospheric carbon
dioxide concentrations would not balance natural sinks until concentrations
exceeded 500 ppmv, and double pre-industrial levels if the steady-state was
attained by 2030
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
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
Granular Elasticity without the Coulomb Condition
An self-contained elastic theory is derived which accounts both for
mechanical yield and shear-induced volume dilatancy. Its two essential
ingredients are thermodynamic instability and the dependence of the elastic
moduli on compression.Comment: 4pages, 2 figure
Pricing currency derivatives under the benchmark approach
© 2014 Elsevier B.V. This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic volatility model that recovers not only the typically observed implied volatility smiles and skews for short dated vanilla foreign exchange options but allows one also to price payoffs in foreign currencies, lower than possible under classical risk neutral pricing, in particular, for long dated derivatives. The main reason for this important feature is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. Using a real dataset on vanilla option quotes, we calibrate our model on a triangle of currencies and find that the risk neutral approach fails for the calibrated model, while the benchmark approach still works
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
- …