Presentation at Manchester Biomechanics Seminar

I have recently started as a new post-doc at the School of Mathematics at the University of Manchester (working with Dr Igor Chernyavsky, Prof Oliver Jensen,  and Dr Paul Brownbill on mathematical modelling of the fluid flow and oxygen uptake in the placenta). I have been kindly invited to speak at the internal Biomechanics Seminar at the School of Mathematics about my D.Phil. work from Oxford. Below you can find the abstract and slides of my presentationfrom Monday 23rd January 2017.

Growth Laws in Morphoelasticity

A. Erlich1, D.E. Moulton1, A. Goriely1 & R. Chirat2
1 Mathematical Institute, University of Oxford
2 Université Lyon 1

Many living biological tissues are known to grow in response to their mechanical environment, such as changes in the surrounding pressure. This growth response can be seen, for instance, in the adaptation of heart chamber size and arterial wall thickness to changes in blood pressure. Moreover, many living elastic tissues actively maintain a preferred level of mechanical internal (residual) stress, called the homeostasis. The tissue-level feedback mechanism by which changes of the local mechanical stresses affect growth is called a growth law within the theory of morphoelasticity, a theory for understanding the coupling between mechanics and geometry in growing and evolving biological material.

In this presentation we will discuss techniques to analyse growth laws that are biologically plausible, and explore issues of heterogeneity and growth stability. We present two models based on homeostasis-driven growth laws.

Firstly, we discuss the growth dynamics of tubular structures, which are very common in biology (e.g. arteries, plant stems, airways). We model the homeostasis-driven growth dynamics of tubes which produces spatially inhomogeneous residual stress. We show that the stability of the homeostatic state non-trivially depends on the anisotropy of the growth response. The key role of anisotropy may provide a foundation for experimental testing of homeostasis-driven growth laws.

Secondly, we apply our theoretical framework to the growth of Ammonites’ seashells. We demonstrate how homeostasis-driven growth produces seashell morphology that is consistent with observation and that cannot readily be captured with previous models.

Seashell presentation at BAMC 2016

I gave this talk at the British Applied Mathematics Colloquium which took place at Oxford 5th – 8th April 2016. Below you can find the abstract of my talk (see also the conference book of abstracts) as well as the slides.

Ammonites’ shells as mechanical oscillators

A. Erlich1, D.E. Moulton1, A. Goriely1 & R. Chirat2
1 Mathematical Institute, University of Oxford
2 Université Lyon 1

Compared to the intricate patterns observed in seashells, modern 3D printers seem almost primitive. To better understand the emergence of sophisticated patterns in the morphogenesis of seashells, we develop a morpho-elastic model for the growth of ammonites’s shells. Based on fundamental principles of growth and mechanics, we establish a mechanical basis for the relationships between the spiral-shaped coiling pattern, the oscillatory ribbing pattern and elliptic cross-section shape of the shells. Specifically, this is achieved by modeling the stretching, bending and active growth of the soft shell-generating organ. We demonstrate that our model is consistent with Buckman’s Law, which is a gold standard collection of rules about the relationship of geometry and ribbing in ammonite’s shells.

Seminar undergraduate talks in Bremen

In my undergraduate physics course in Bremen, we had the opportunity to present papers of our choice during group seminars of our choice. I gave two such presentations in January 2011, on a paper on theoretical neuroscience and another on random boolean networks. Here are the slides and some details:

Theoretical Neuroscience Seminar

My slides are here, the original paper by Gavornik, Shuler, Loewenstein, Bear, Shouval is here. The talk is about a simple network model for synaptic plasticity.

Complex Networks Seminar

I gave an introductory talk on Random Boolean Networks (RBNs). After a brief definition of RBNs I discuss some properties of RBNs and discuss them based on an example of a 5 node RBN (see image below). I created most of the visualisations with the Matlab RBN Toolbox.

Summer school presentations

I took part in several summer schools organised by the German National Academic Foundation. These usually take two weeks, comprising an academic programme and some fun social get together. In the academic part, students usually give talks that they prepared and the material is discussed with expert course organisers. Here are the talks that I gave during these summer schools:

Vortrag: Supraleitung

Dies ist ein Vortrag von mir im Rahmen der Veranstaltung “Mündliche Präsentationstechniken”. Der Vortrag stellt eine  Einführung in die Supraleitung dar und gibt einn Einblick in einige theoretische und experimentelle Grundlagender Supraleitung (Meißner-Ochsenfeld-Effekt, BCS-Theorie, Josephson-Effekt) und zeigt einige bereits realisierte und kommende Anwendungen der Supraleitung.

Supraleitung_Vortrag

Praktikum beim ZARM

Ich habe Juli/August ein dreiwöchiges Praktikum in der AG Fundamental Physics am ZARM (Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation) gemacht. Dabei beschäftigte ich mich mit der sog. Pioneer-Anomalie, einer nicht erklärten und etwa konstanten Beschleunigung, die die Pioneer-Sonden 10 und 11 seit dem Verlassen des Sonnensystems erfahren haben. Dazu arbeitete ich mit Fortran und Matlab und eignete mir Wissen zu Binärdaten und Datenanalyse, -manipulation und -auswertung an (siehe erstes Bild). 

Im März 2009 habe ich noch eine weitere Praktikumswoche beim ZARM gemacht. Dabei ging es vor allem um C-Programmierung. Aufgabe war es, die sehr schnelle Bibliothek FFTW (“Fastest Fourier Transform in the West”) in C einzubinden und damit einige numerische Fourier-Transformationen durchzuführen. z.B. war dies die Transformation von Stufenfunktionen, über die ich Interferenzmuster vom Doppelspalt oder Gittern berechnen konnte. Außerdem ist mit FFTW leicht die numerische Differenziation im Fourier-Raum möglich. Beim Vergleich von gewöhnlichen numerischen Methoden zum Differenzieren (über Steigungsdreiecke) konnte ich zeigen, dass die Differenziation im Fourier-Raum effizienter arbeitet. Genauere Informationen sind im Artikel Fast Fourier Transformation.

Ich habe meine Ergebnisse im Praktikumsbericht zusammengeschrieben.

Interferenz

Präsentation: das ptolemäische Weltbild

In dieser Präsentation geht es um das geozentrische (oder ptolemäische) Weltbild, das vor dem heliozentrischen (kopernikanischen) gegolten hat. Es wird auch auf das Werk (Almagest, Tierkreis) des unglaublich einflussreichen Universalgelehrten Ptolemäus eingegangen, dessen Astronomie 2000 Jahre lang allgemein akzeptierter Standard war.

Ich habe in Cabri Geometrie 2 die Ideen der Epizykeltheorie in Animationsfilmchen (*.avis) visualisiert: