Málstofa í stærðfræði við Háskóla Íslands

[Íslenska stærðfræðafélagið]

Stærðfræðimálstofa við HÍ verður haldin næstkomandi föstudag, 4. júlí.

Fyrirlesari: Ana Carpio, Universidad Complutense de Madrid, Spain

Titill: The shape of biofilms

Staðsetning: V-158, VRII

Tími: Föstudaginn 4. júlí , frá 14:00 til 15:00.

Ágrip:

Biofilms are bacterial aggregates attached to moist surfaces that are  

able to survive in extreme conditions and are uncommonly resistant to  

antibiotics and disinfectants. They play an important role in many  

medical, ecological and industrial problems. Depending on the  

bacterial strain and the environmental conditions, biofilms may adopt  

different structures and expand in different ways. A rich variety of  

patterns is observed: streamers, ripples, fingers, wrinkled films... The  

evolution of these multicellular systems is governed by coupled  

cellular, chemical and mechanical processes acting on multiple scales.  

We propose a hybrid stochastic-continuum description of biofilm  

evolution. Cells perform different tasks according to probability laws  

informed by the status of continuum concentration and mechanical  

fields, governed by Navier-Stokes and elasticity equations. We apply  

this strategy to two model systems: Biofilms in flows and Biofilms on  

air/solid interfaces. Numerical simulations show qualitative agreement  

with experimental observations and provide insight on the factors  

controlling the dynamics of these bacterial aggregates.

http://math.hi.is/malstofa/ana-carpio-040714/

[Íslenska stærðfræðafélagið]

Málstofa í stærðfræði við Háskóla Íslands á morgun þriðjudag.

Fyrirlesari: Björn Birnir, University of California, Santa Barbara og Háskóli Íslands
Titill: Stochastic Closure in Turbulence

Staðsetning: V-158, VRII
Tími: Þriðjudagur 8. júlí, frá 14:00 til 15:00.

Ágrip:

We will discuss the closure problem in turbulence and how it can be solved using basic theorems in probability and stochastic partial differential equations. The existence of stochastic processes describing turbulent> solutions of the full Navier-Stokes equation, will be discussed. These turbulent solutions can then be used to proof the existence of an invariant measure in dimensions one, two and three. The invariant measure characterizes the statistically stationary state of turbulence. It determines all the deterministic properties of turbulence and everything that can be computed and measured. In particular, the invariant measure determines the probability density of the turbulent velocity and velocity differences. It gives a proof of the celebrated Kolmogorov-Obukhov scaling with the She-Leveque intermittency corrections. This can then be used to develop accurate sub-grid models in computations of turbulence, by-passing the problem that three-dimensional turbulence cannot be fully resolved with currently existing computer technology. We will also discuss applications of the theory to homogeneous turbulence, boundary value problems and Lagrangian.