Matematiske modeller i nanovidenskab

Transkript

1 Matematiske modeller i nanovidenskab Torsdag, den 15. marts 2012 kl RUC, Bygning 27, Lokale I

2 Program Velkomst og introduktion Modelling structures of crystal X-ray diffraction data. v/ Henning Osholm Sørensen, Nano-Science Center, KU Deldiskussion Kaffe/te Particle and fluids confined in nanopores. v/ Jesper Schmidt Hansen, Dept. of Nature, Systems and Models, RUC Deldiskussion Frokost Green s function integral equation methods for modelling the optics of metal nanostructures v/ Thomas Sørensen, Dept. of Physics and Nanotechnology, AAU Deldiskussion Pause How geometrical structures can improve microsystems - a mathematical modeling v/ Fridolin Okkels, DTU Nanotech, DTU Deldiskussion Kaffe/te Opsamlende og afsluttende diskussion

3 Modeldag er navnet på en række heldagsseminarer, der afholdes løbende af forskergruppen ved. Forskergruppen er bygget op omkring tre tyngdepunkter, der relaterer sig til aktiviteter med, i og om matematik og fysik. Tyngdepunktet er matematisk modellering og matematiske modeller, deres rolle inden for andre fag- og praksisområder, samt de grundvidenskabelige forudsætninger herfor. Udvikling og undersøgelse af matematiske modeller og deres rolle i produktionen af ny viden og erkendelse, deres forskelligartede videnskabsteoretiske status og samfundsmæssige betydning udgør således en væsentlig del af s med, i og om aktiviteter på tværs af matematik og fysik. Matematiske modeller bruges i stigende udtrækning som et erkendelsesredskab inden for stort set alle vidensområder som f.eks. nanovidenskab, hvor modellerne giver mulighed for, at vi kan få adgang til viden, der af praktiske begrænsninger ellers ikke er adgang til eller som er meget omkostningstungt. Med den stærkt stigende brug af matematiske modeller er det relevant at undersøge hvorfor, hvornår og til hvad man kan stole på en matematisk model, samt hvilken form for indsigt en matematisk model kan give og hvorvidt denne indsigt kunne erhverves uden brug af modeller (eller hvorvidt det kun vanskeligt kunne gøres). På modeldagene undersøges og diskuteres forskellige fagligheder og deres brug af forskellige slags matematiske modeller efter tur ud fra eksempler. Ved mødet mellem de (som regel) eksterne oplægsholdere fra en given faglighed, modelfolk og studerende fra andre steder og håber vi at kunne indfri to formål. For det første, at folk udefra kan hente inspiration i s modelteoretiske overvejelser. For det andet, at kan få udbygget samlingen af konkrete eksempler med henblik på sammenligninger og udvikling af overvejelserne. Johnny Ottesen,, NSM Jesper Schmidt Hansen,, NSM

4 Tilmelding Der er åben adgang til seminaret, men tilmelding på tlf eller ville lette det praktiske. Frokost Vi byder foredragsholderne på frokost. Sted, Universitetsvej 1, 4000 Roskilde, Bygning 27, Lokale I Kontakt For spørgsmål om arrangementet kan sekretær Dorthe Vedel kontaktes på telefon eller vedel@ruc.dk

5 Abstracts Green s function integral equation methods for modelling the optics of metal nanostructures Thomas Søndergaard, Department of Physics and Nanotechnology, Aalborg University Metal nanostructures can support very strong electromagnetic resonances seen as strong resonant light scattering and large local resonant electric fields when illuminated with light. The resonance properties can to some extent be controlled via the geometry and environment of the metal nanostructures. Some recent examples of metal nanostructures will be presented with experimental measurements and corresponding theoretical modeling of their optical properties with Green s function integral equation methods. In these methods it is exploited that the electric or magnetic fields at any position in a scattering problem is given theoretically in terms of an overlap integral between a Green s function, representing the field generated by a point source, and the field inside or on the boundary of the scattering object. The properties of the Green s function automatically ensures e.g. that the calculated field satisfies appropriate boundary conditions. Particle and fluids confined in nanopores Jesper Schmidt Hansen,, Dept. of Nature, Systems and Models, Roskilde University This talk is divided into two parts. The first part shows a simple analysis of the dynamics of a single particle confined in a nanochannel. This toy model features interesting dynamics due to the realistic nature of the interactions with the confining wall particles. It is also shown that the ergodicity hypothesis is valid even for this single particle system. In the second part, the validity of continuum modelling of nanofludic devices are discussed. The discussion is based on comparison between molecular dynamics simulations and both classical and extended fluid dynamics.

6 Modelling structures of crystal X-ray diffraction data Henning Osholm Sørensen, Nano-Science Center, University of Copenhagen Since Laue and coworkers discovered that crystals diffracted electromagnetic radiation with wavelengths in the X-ray range 100 years ago, this phenomena has been employed to determine structures at the subatomic level of everything from the simplest minerals to complex biomolecules in their crystalline state. In this presentation the basics of structure determination will be explained and how spherical harmonic functions can be used to make detailed models of the electron density distribution in molecular crystals. How geometrical structures can improve microsystems - a mathematical modeling Fridolin Okkels, DTU Nanotech, Technical University of Denmark Many systems have traditionally been improved by focusing either on the overall system layout or the different materials involved, where the last can be viewed as an optimization on the smallest length-scale. The general activity of my research-group, "Theoretical Microsystems Optimization group" at DTU Nanotech, is to optimize system structures on the intermediate length-scale, and during the talk, I will illustrate the great potential that lies in this approach. First example of an ongoing research-area in our group is the micro-optimization of functionalized surface-structures. By introducing and optimizing special overhanging micro-structures on surfaces that are made of a hydrophilic (water-liking) materiel, the overall functionality can end up being hydrophobic (water-avoiding). Second example shows how the internal distribution of active material inside catalytic microfluidic reactors can dramatically improve the reaction performance. This approach is applicable to many research-areas, such as e.g. design of bio-reactors, and while it still remains to be verified experimentally, it has even aided the understanding of vascular capillary networks.