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A Survey on Mathematical Modelling of Deposition in Waxy Crude Oils

A. Fasano, L. Fusi, S. Correra, M. Margarone (2011)

Mathematical Modelling of Natural Phenomena

Waxy Crude Oils (WCO’s) are characterized by the presence of heavy paraffins in sufficiently large concentrations. They exhibit quite complex thermodynamical and rheological behaviour and present the peculiar property of giving rise to the formation of segregated wax deposits, when temperature falls down the so called WAT, or Wax Appearance Temperature. In extreme cases, segregated waxes may lead to pipeline occlusion due to deposition on cold walls....

A symmetrization result for nonlinear elliptic equations.

Vincenzo Ferone, Basilio Messano (2004)

Revista Matemática Complutense

We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

A symmetry problem

A. G. Ramm (2007)

Annales Polonici Mathematici

Consider the Newtonian potential of a homogeneous bounded body D ⊂ ℝ³ with known constant density and connected complement. If this potential equals c/|x| in a neighborhood of infinity, where c>0 is a constant, then the body is a ball. This known result is now proved by a different simple method. The method can be applied to other problems.

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

M. Billaud-Friess, A. Nouy, O. Zahm (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal residual method with a measure of the residual corresponding to the error in a specified solution norm. The residual norm can be designed such that the resulting low-rank approximations are optimal with respect to particular norms of interest, thus allowing to take...

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