A "Modellalkotás és természettudományos alkalmazások" tárgy honlapja,
Alkalmazott matematikus MSc, Alkalmazott analí­zis szakirány, 2011


Az előadáson elhangzott anyag részletes vázlata (első verzió; lehetnek benn hibák, pontatlanságok).
vázlat1
Külön a kémiai reakciók matematikai modellezéséről szóló rész.
vázlat2

A tantárgy számonkéréséhez kapcsolódó cikkek letölthetők az egyes absztraktok utáni linkre kattintva.
Minden cikkhez 4-5 oldalas összefoglalót kell í­rni (nem fontos elektronikusan, de legyen jól tagolt, áttekinthető), amelyben a modell bemutatásán és a szimulációkból kapott eredmények ismertetésén legyen a hangsúly. Ezt 20-30 percben (akár a kis összefoglalót használva) világosan elő kell adni. Fontos az időkeret betartása: a cikket össze kell foglalni, ismertetni kell, nem pedig az egészet szó szerint elmondani. Az utolsó két cikk esetében mind az összefoglaló, mind az ismertetés lehet hosszabb; ezt ketten együtt is fel lehet dolgozni. Ekkor az összefoglaló lehet hosszabb, de a munkának egységesnek kell lennie, ne látszódjon, hogy ketten állí­tották össze. Az utolsó előtti cikk első 4 szakaszát is lehet választani egyéni beszámolóhoz.
Mindez a lehetőség azokra vonatkozik, akik figyelemmel követték az előadást. Akik az órák nagy részén nem voltak benn, azoknak az ott elhangzott anyagból kell beszámolniuk.




We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, landmarks) in a region using local counts performed by a network of sensors, each of which measures the number of targets nearby but neither their identities nor any positional information. We formulate and solve several such problems based on the types of sensors and mobility of the targets. The main contribution of this paper is the adaptation of a topological sheaf integration theoryí´integration with respect to Euler characteristicí´to yield complete solutions to these problems.
baryshnikov10.pdf

We introduce some free boundary problems which describe the evolution of calcium carbonate stones under the attack of atmospheric SO2 , taking into account both swelling of the external gypsum layer and the influence of humidity. Different behaviors are described according to the relative humidity of the environment, and in all cases reliable explicit quasi-steady approximations are introduced under reasonable assumptions on the data. Some numerical simulations are also performed to describe gypsum formation using experimental data, which show a good agreement with the quasi-steady solutions. The influence of the cleaning the crust and of the change in concentration of pollution is evaluated and discussed.
clarelli08.pdf

Structure and fluid models need to be combined, or coupled, when problems of fluid- structure interaction (FSI) are addressed. We first present the basic knowledge required for building and then evaluating a simple coupling. The approach proposed is to con- sider a dedicated solver for each of the two physical systems involved. We illustrate this approach by examining the interaction between a gas contained in a one-dimensional cham- ber closed by a moving piston attached to an external and fixed point with a spring. A single model is introduced for the structure, while three models of increasing complexity are proposed for the fluid flow solver. The most complex fluid flow model leads us to the arbitrary Lagrangian Eulerian (ALE) approach. The pros and cons of each model are discussed. The computer implementations of the structure model, the fluid model, and the coupling use MATLAB scripts, downloadable from either http://www.utc.fr/elefra02/ifs or http://www.hds.utc.fr/boufflet/ifs.
lefrancois10.pdf

A linear stability of freely propagating, adiabatic premixed flames is investigated in the context of a thermal-diffusive or constant density model, together with a simple two-step chain- branching model of the chemistry. This study considers the case of realistic, finite activation energy of the chain-branching step, and emphasis is on comparing with previous high activation energy asymptotic results. It is found that for realistic activation energies, a pulsating instability is absent in regimes predicted to be unstable by the asymptotic analysis. For the cellular instability, however, the finite activation energy results are in qualitative agreement with the asymptotic results, in that the flame is unstable only below a critical Lewis number of the fuel and becomes more unstable as the Lewis number is decreased. However, it is shown that very high activation energies would be required for the asymptotic analysis to be quantitatively predictive. The flame is less unstable for finite activation energies than predicted by the asymptotic analysis, in that a lower fuel Lewis number is required for instability. It is also shown that the flame structure and stability can have nonmonotonic dependencies on the activation energy.
sharpe09.pdf

There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly knead a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the material itself (for dough or taffy) as rapidly as possible. The growth rate of material lines is conveniently given by the topological entropy of the rod motion. We discuss the problem of optimizing such rod devices from a topological viewpoint. We express rod motions in terms of generators of the braid group and assign a cost based on the minimum number of generators needed to write the braid. We show that for one cost function—the topological entropy per generator—the optimal growth rate is the logarithm of the golden ratio. For a more realistic cost function, involving the topological entropy per operation where rods are allowed to move together, the optimal growth rate is the logarithm of the silver ratio, 1 +\sqrt 2. We show how to construct devices that realize this optimal growth, which we call silver mixers.
finn11.pdf

The critical domain size problem determines the size of the region of habitat needed to ensure population persistence. In this paper we address the critical domain size problem for seasonally fluctuating stream environments and determine how large a reach of suitable stream habitat is needed to ensure population persistence of a stream-dwelling species. Two key factors, not typically found in critical domain size problems, are fundamental in determining whether population can persist. These are the unidirectional nature of stream flow and seasonal fluctuations in the stream environment. We characterize the fluctuating environments in terms of seasonal correlations among the flow, transfer rates, diffusion, and settling rates, and we investigate the effect of such correlations on the critical domain size problem. We show how results for the seasonally fluctuating stream can formally be connected to those for autonomous integro-differential equations, through the appropriate weighted averaging methods.
jin11.pdf

The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an inverse problem in which emission source rates are determined from a given set of groundlevel contaminant measurements. This source identification problem can be formulated as an overdetermined linear system of equations that is most easily solved using the method of least squares. Various generalizations of this problem are discussed, and we illustrate our results with an application to the study of zinc emissions from a smelting operation.
stockie11.pdf

This paper presents a review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena. The survey of models deals with the representation scales and the mathematical frameworks that are used for the modeling approach. The paper also considers the challenging objective of modeling complex systems consisting of large systems of individuals interacting in a nonlinear manner, where one of the modeling difficulties is the fact that these systems are difficult to model at a global level when based only on the description of the dynamics of individual elements. The review is concluded with a critical analysis focused on research perspectives that consider the development of a unified modeling strategy.
bellomo11.pdf