921 research outputs found
Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling
This paper is devoted to the homogenization (or upscaling) of a system of
partial differential equations describing the non-ideal transport of a
N-component electrolyte in a dilute Newtonian solvent through a rigid porous
medium. Realistic non-ideal effects are taken into account by an approach based
on the mean spherical approximation (MSA) model which takes into account finite
size ions and screening effects. We first consider equilibrium solutions in the
absence of external forces. In such a case, the velocity and diffusive fluxes
vanish and the equilibrium electrostatic potential is the solution of a variant
of Poisson-Boltzmann equation coupled with algebraic equations. Contrary to the
ideal case, this nonlinear equation has no monotone structure. However, based
on invariant region estimates for Poisson-Boltzmann equation and for small
characteristic value of the solute packing fraction, we prove existence of at
least one solution. To our knowledge this existence result is new at this level
of generality. When the motion is governed by a small static electric field and
a small hydrodynamic force, we generalize O'Brien's argument to deduce a
linearized model. Our second main result is the rigorous homogenization of
these linearized equations and the proof that the effective tensor satisfies
Onsager properties, namely is symmetric positive definite. We eventually make
numerical comparisons with the ideal case. Our numerical results show that the
MSA model confirms qualitatively the conclusions obtained using the ideal model
but there are quantitative differences arising that can be important at high
charge or high concentrations.Comment: 46 page
Survey on nonlocal games and operator space theory
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states
- …