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.

Scientific posters

A collection of scientific posters I made over the years. Click on the images to get the PDF (all vector graphics).

Poster at DTC Mini-Symposium

While my 3 year research project is with the Mathematical Institute, I am also part of the Oxford Systems Biology Doctoral Training Centre (DTC). The DTC hosted an internal mini Symposium on February 3rd 2015, in which I presented the poster below aimed at a general scientific audience.

Acoustic Doppler Current Profiling

A poster prepared as part of my undergraduate labwork training at the University of Bremen.

Energy Transformation in Solar Cells

Another poster prepared as part of my undergraduate labwork training at the University of Bremen.

Black body radiation

Another poster prepared as part of my undergraduate labwork training at the University of Bremen.

Seashell morphogenesis and ornamentation

Quick summary: Preprint here, personal notes here and here.

This post serves as a collection of information and work related to seashell morphogenesis and ornamentation, which is collaborative work with Professor Derek Moulton and my PhD thesis supervisor Professor Alain Goriely at Oxford, as well as Professor Régis Chirat at Lyon.

Currently, we are in the finishing stages of a publication on ammonite ornamentation, extending this recent work by Moulton, Chirat and Goriely. I will add a preprint very soon.

In summer 2013, I wrote this work on antimarginal ornamentation as a ten week research project supervised by Professor Derek Moulton. Prior to that, I wrote some personal notes to get acquainted with the topic, which you can find here and here.

As the topic of seashells naturally generates beautiful images, I am showing a few 3D seashell renderings below.

Photos and 3D renderings of Lambis truncata seashell. Our model captures both the coiling of the shell surface and the finger-like antimarginal ornamentation.

Plots of parametric surfaces serving as foundation for ornamentation (such as ribbing).

Undergraduate thesis: Transition to Chaos

Quick summary: Thesis here, slides here, related notes here.

This post serves as a collection of information and work related to my undergraduate thesis, which I wrote in summer 2010 under the supervision of Professor Peter H. Richter at the Physics department of the University of Bremen, Germany. A brief summary aimed at a general audience can be found below in this post.

The title of my thesis is: Melnikov’s Method and the transition to chaotic behaviour in Cardan-mounted Euler tops. It is written in German. The thesis is available here and the presentation slides here. As a way of learning about Melnikov’s method, I wrote these notes prior to the thesis. The Cardan-mounted Euler top to which the method is applied is depicted in the picture below.

The Cardan-mounted Euler top to which Melnikov’s Method is applied in my thesis. The reference coordinate system is (x,y,z), the current system is (1,2,3).

Animations and source code

I wrote a little Matlab program which visualises the motion of the Cardan-mounted Euler top. It is hosted on Matlab File Exchange.  Below, you can see two videos, one showing regular (oscillating) motion and the other showing irregular (chaotic) motion.

A brief summary

Here is a brief summary aimed at a general audience:

Euler’s top is a rigid body (with arbitrary shape, say, a potato) suspended from its centre of gravity (CoG). Its motion is regular and well-known. In most cases, however, the CoG cannot be reached by a regular suspension method like a thread or rod (one would have to reach inside the potato, i.e. pierce a hole through it). But the problem can be solved using a more sophisticated suspension mechanism: a ‘Cardan mounting’ (e.g. helicopters or gyro compasses are similar to Cardan-mounted rigid bodies).

But as the dynamic properties of the Cardan-mounted Euler top are different from those of the normal Euler top, the resulting motion is much more complex: the spectrum of possible motion ranges from regular (i.e. harmonic, predictable) to chaotic (i.e. unpredictable) in a multitude of varying degrees. My thesis provides a description of the transition from regular to chaotic motion, using methods from nonlinear dynamics and Melnikov’s Method from perturbation theory.

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: