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The paper deals with a mathematical model for the electric activity of the heart at macroscopic level. The membrane model used to describe the ionic currents is a generalization of the phase-I Luo-Rudy, a model widely used in 2-D and 3-D simulations of the action potential propagation. From the mathematical viewpoint the model is made up of a degenerate… (More)

- Antonio Segatti, Michael Snarski, Marco Veneroni
- Physical review. E, Statistical, nonlinear, and…
- 2014

The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our aim is to show how a different… (More)

- Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
- SIAM J. Math. Analysis
- 2010

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/ε. We choose H having two wells corresponding to two chemical states A… (More)

We study a singular-limit problem arising in the modelling of chemical reactions. At finite ε > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/ε, and in the limit ε→ 0, the solution concentrates onto the two wells, resulting into a limiting system that is a… (More)

We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves… (More)

- Ben Schweizer, Marco Veneroni
- NHM
- 2011

We introduce a new method to homogenization of non-periodic problems and illustrate the approach with the elliptic equation −∇·(a∇u) = f . On the coefficients a we assume that solutions u of homogeneous εproblems on simplices with average slope ξ ∈ R have the property that flux-averages − ∫ a∇u ∈ R converge, for ε → 0, to some limit a∗(ξ), independent of… (More)

- Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
- SIAM Review
- 2012

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/ε. We choose H having two wells corresponding to two chemical states A… (More)

This paper describes an exact algorithm for a variant of the vehicle routing problem in which customer demands are stochastic. Demands are revealed upon arrival at customer locations. As a result, a vehicle may reach a customer and not have sufficient capacity to collect the realized demand. Such a situation is referred to as a failure. In this paper the… (More)

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/ε. We choose H having two wells corresponding to two chemical states A… (More)

- Mark A. Peletier, Marco Veneroni
- Philosophical transactions. Series A…
- 2012

We describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P=e⊗e, where e is a unit vector field. We describe how this formulation is better adapted to the… (More)