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Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics

M. Aguiar, B.W. Kooi, J. Martins, N. Stollenwerk (2012)

Mathematical Modelling of Natural Phenomena

In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton...

Segmentation of MRI data by means of nonlinear diffusion

Radomír Chabiniok, Radek Máca, Michal Beneš, Jaroslav Tintěra (2013)

Kybernetika

The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...

Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

Journées équations aux dérivées partielles

We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit Λ ( h ) of the ground state energy of this operator. For Kac’s spin model, Λ ( h ) is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...

Shape transition under excess self-intersections for transient random walk

Amine Asselah (2010)

Annales de l'I.H.P. Probabilités et statistiques

We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.

Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill, K. M. Shaw, B. L. Rountree, C. E. Kehl, H. J. Chiel (2011)

Mathematical Modelling of Natural Phenomena

We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...

SLE and triangles.

Dubédat, Julien (2003)

Electronic Communications in Probability [electronic only]

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

In this paper we establish a decoupling feature of the random interlacement process ℐ u ⊂ ℤ d at level u , d ≥ 3 . Roughly speaking, we show that observations of ℐ u restricted to two disjoint subsets A 1 and A 2 of ℤ d are approximately independent, once we add a sprinkling to the process ℐ u by slightly increasing the parameter u . Our results differ from previous ones in that we allow the mutual distance between the sets A 1 and A 2 to be much smaller than their diameters. We then provide an important application of this...

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

Luise Blank, Martin Butz, Harald Garcke (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...

Currently displaying 381 – 400 of 498