We will explore the formation of complex structure in soft matter systems, relevant to both synthetic and biological systems, in response to minimisation of relatively simple energy functionals that are often very geometric in their nature. The seminar will give an overview of the systems where such approaches apply, including biological membranes, liquid foams, cellular systems, minimal surfaces, biophotonic crystals, granular materials, etc. Each set of seminar talks (see format description below) will represent some background on the different disciplines, and some handson projects, e.g. computational projects using the 'Surface Evolver', 3D printing of complex structures or experiments on foams or granular matter.
The seminar is conducted in English, and takes place Mondays from 3:30pm to 5pm
The seminar will also include regular tutorials (Übungen) that we highly recommend you participate in. We will offer two timeslots for these tutorials, on Tuesdays from 46 pm and Thursdays from 24pm. The tutorials will be handson to make you familiar with numeric methods and experimental techniques and to help you in preparing your own seminar presentations. These tutorials will be held in one of the smaller front rooms of the CIP pool.
We will deviate slightly from the traditional format of a seminar, in order to spread the workload more evenly throughout the semester and to maintain livelyness of the programm throughout the semester. Each student will give two talks, each about 2030 minutes.
The first set of talks, to be given in November or December, shall provide an introduction into the different topics, emphasizing the key problems and aspects of the topic.
The second set of talks, to be given in January or February, shall describe the specific project carried out by the student.
Optimal shape of a trefoil knot : The trefoil knot is the simplest knotting of a string, readily occurring in structures throughout the natural science, from DNA with specific function to complex chemical frameworks. The geometry of the trefoil knot in an energy minimising form is shown in the figure. This project explores discretised and analytical forms of this shape, as well as the distribution of curvature over the knotted tube. (References: Pieranski & Przybyl ; Recommended reading: Pieranski's web page ; Contact person: Myfanwy Evans)
Exotic photonic effects of complex biomaterials : Ordered geometry and chirality of biomaterials often dictates exotic photonics properties. This project explores two biomaterials with related chiral geometry, butterfly wingscales and human skin, from the perspective of photonics. In the case of the butterfly wings, the photonic effects add to the brilliant green colour to the wing, yet the photonic effect of the translucent outer layer of human skin is still unknown. (Recommended reading: Hyde et al , Evans et al , Saba et al ; Recommended reading: ; Contact person: Myfanwy Evans)
Biophotonics: Strongly angulardependent reflections of the Blue Morpho butterfly caused by nanostructure : Many butterflies and beetles are known to generate their brilliant coloration through a microstructure rather than pigmentation. Among the most famous examples is the Morpho rhetenor, a butterfly that is found in South America and generates its iridescent blue color by an effectively twodimensional microstructure: Morpho's wing scales are covered with a lamella structure made of chitin that looks like a Christmas tree when cut and viewed from the side (see scanning electron micrographs in the picture). It has been shown by qualitative argumentation and simulation that this microstructure with feature size on the order of the wavelength of visible light is responsible for the blue coloration. In this project we calculate the reflection spectrum with a semianalytical method for a simplified structure model based on a transfer matrix treatment. The aim of this calculation is to obtain a fine grasp on the physics of the scattering process at the Christmas tree structure that induces frequency dependent reflection as a function of the angle of incidence. (this project involves analytical calculations) (References: Vukusic & Shambles , Whittaker & Culshaw , Vukusic et al, Yoshioka & Kinoshita , Siddique et al ; Preparation material: Tutorial Scattering Matrix ; Contact person: Matthias Saba )
Wrinkly skin from complex geometry : The complex 3dimensional weaving of filaments shown in the Figure describes the arrangement of keratin intermediate filaments in the dead outer layer of mammalian skin. The geometry of the filaments enables a simple but large expansion of the material, readily observed when the skin swells and wrinkles on prolonged exposure to water. This project examines the interaction of geometry and mechanics in the system. (References: Evans et al; Recommended reading: ; Contact person: Myfanwy Evans)
Random Close Packing and Dense Crystals in Granular Materials : Crystalline sphere packs can achieve packing fractions (fraction of space covered by the spheres) of 74%. Yet, when pouring beads in a jar, one observes a fairly strict upper limit for the packing fraction of 64%, first observed by Bernal. This limit is referred to as the random close packing limit. The corresponding configurations are disordered. It is nowadays well known that, somewhat against intuition, ellipsoids can reach higher packing fractions. We will explore the notion of random close packing, in various contexts from biology to the physics of amorphous materials. This topic will include packing experiments of ellipsoidal and spherical lollies and likely some handson tomography experiments. (References: van Hecke et al ; Recommended reading: Aste & Weaire ; Contact person: Fabian Schaller )
The role of friction in random packings : Friction is a major determinant of both the maximally achieved packing fractions and the speed of compactification, and is hence of huge relevance for understanding random close packing. We will discuss the role of friction, for example with respect to isostaticity (the number of neighbors required for completely constraining all degrees of freedom of a particle). This project will include some handson experiments on customfabricated plastic particles. (References: van Hecke et al ; Recommended reading: Aste & Weaire ; Contact person: Fabian Schaller )
Random packings on negativelycurved interfaces: Defects and scars : The densest packing of equal sized disks on an infinite plane is obtained by arranging the disks into a triangular tilling. Similarly, the lowest energy configuration of monodisperse (i.e. equal volume) two dimensional bubbles corresponds to a hexagonal bubble lattice. In both cases the disks and the bubbles occupy the same area on the plane and have the same local environment of six equallyspaced first neighbours which is reproduced all over the plane according to the laws of classical crystallography. However, this ideal organization is no longer possible when the disks are assembled onto curved surfaces. Several natural and manmade mechanical systems can be viewed as twodimensional curved crystals. Examples include architectural structures, viral shells and colloidosomes (crystals formed by beads selfassembled on water droplets in oil). In such systems most of the constituent particles have six nearest neighbours but in addition distinctive high angle grain boundaries are observed. These consist of disclinations (disks or bubbles with five or seven neighbours) and dislocations (a pair of adjacent fiveseven disclinations), which together form complex “scar” like arrangements. Dislocations have been observed in flat 2D foams but disclinations and scars have not. In this project you will conduct simple numerical simulations to the elucidate properties on familiar geometries, such as spheres, and end up with analysing packings of equalsized disks onto complex negatively curved surfaces, such as triplyperiodic minimal surfaces. (This project is best carried out together with the following project, and may involve some 3D printing) (References: Bausch et al , Irvine et al , Cox ; Recommended reading: Bowick & Giomi , Vitelli et al ; Contact person: Adil Mughal )
Random and ordered foams on negativelycurved interfaces: Why do bees build hexagons? : We will explore the shape and structure of random and ordered foams that 'live' in negatively curved manifolds, again addressing the question of where and how defects form in the polygonal structure, as a consequence of the Euler formula. The packings of disks in the previous project will be used as a starting point for simulations involving 2D foams which you will investigate using the Surface Evolver package. Furthermore, you may use 3D printing technology to produce a mould into which monodisperse foam will be injected, or onto which the bees could build their honeycombs... (References: Bausch et al , Irvine et al , Cox ; Recommended reading: Bowick & Giomi , Vitelli et al ; Contact person: Adil Mughal )
The shape and feel of random soap froth: geometry determines physical properties : Foams (such as beer foam, shaving foam, polymeric foams) are not only important for our daily life and wellbeing but are interesting because of their close correlation between geometry and physics. When modelling these structures in the socalled drylimit, the problem reduces essentially to areaminimisation of a spatial tessellation under the constraint of constant bubble volumes. We will review the Plateau's laws that govern the structure of liquid foams, discuss the relevance of topological transitions and the relationship between physical stress and geometric structure, particularly for sheared foams. (this project will involve quite a bit of surface evolver simulation and or participation in the coarsening experiments described below) (References: Evans et al , Kraynik et al ; Recommended reading: Weaire & Hutzler ; Contact person: Gerd SchröderTurk)
Coarsening (or ageing) of liquid foams : Geometry versus topology : Coarsening of liquid foams describes the process whereby cell volumes change due to gas diffusion through the liquid films. Since diffusion occurs as a consequence of pressure differences between neighboring cells, the equivalence of pressure differences across a film with the constant mean curvature of the film implies that coarsening is a geometric problem that can be numerically studied using the Surface Evolver. We will here address the coarsening (or lack thereof) of the Kelvin foam and the WeairePhelan foam by surface evolver, and that of a simple model cells called 'isotropic Plateau polyhedra'. This will clarify the significant differences between 2D and 3D, since in 2D coarsening reduces to a topological problem whereas it is a genuinely geometric problem in 3D. (this project will include experiments with real soap froth and, if possible, highspeed cameras to image equilibration and ageing. (References: Evans et al ; Recommended reading: Weaire & Hutzler ; Contact person: Gerd SchröderTurk)
Triplyperiodic minimal surfaces and the formation of the single Gyroid : Triplyperiodic minimal surfaces are fascinating ordered structures that divide space into two intergrown labyrinthine domains. Interestingly, these ordered phases have been observed in various soft matter systems, from lipid to copolymer selfassembly. We will review these structures, describe a very handable model for their description and will simulate a liquid confined to these structures, to provide some insight into the formation of the single Gyroid structure that is found e.g. in some butterfly wingscales where it acts as a photonic crystals. (this project will include a significant Monte Carlo simulation) (References: SchröderTurk et al , Almsherqui et al ; Recommended reading: ; Contact person: Gerd SchröderTurk )
You can use this module as (Material)Physikalisches Seminar im Bachelor und Master for modules PS, PSMAT, PSMMAT
14/Oct  Semester overview and project assignment  
21/Oct  GST  Introduction to the physics of liquid foams (slides) 
28/Oct  GST  Introduction to synthetic selfassembly of triplyperiodic bicontinuous forms 
04/Nov  GST  Introduction to complex negativelycurved nanostructures in biological systems 
11/Nov  Student presentations : introduction to field (20+10 minutes)  
DJ (MS/GST)  Exotic photonic effects of complex biomaterials  
SE (MS/GST)  Biophotonics: Reflections off Morpho butterflies  
18/Nov  No seminar: please use this time to discuss your talks with your supervisors  
25/Nov  Student presentations : introduction to field (20+10 minutes)  
SW (FS)  Disordered packings and the random close packing limit  
JH (FS)  The role of friction in jamming  
02/Dec  Student presentations : introduction to field (20+10 minutes)  
MO (AM)  Random packings on negativelycurved interfaces  
PM (AM)  Random and ordered foams on negativelycurved interfaces  
09/Dec  Student presentations : introduction to field (20+10 minutes)  
TS (GST)  Stresses in liquid foams  
TH (GST)  Diffusive coarsening of liquid foams  
JV (MEE)  Optimal shape of a trefoil knot  
Colloqium presentation at 5pm in Hörsaal E by eminent foam scientist Denis Weaire (Trinity College Dublin)  
16/Dec  Student presentations : introduction to field (20+10 minutes)  
FS (GST)  Simple fluids confined to complex pores  
MK (GST)  Diffusion of chiral molecules in chiral porous materials  
13/Jan  Student presentations : results of projects (30 minutes) 

SW (FS)  Granular matter  
JH (FS)  Granular matter  
PM (AM)  Foams on negatively curved surfaces  
14/Jan  Student presentations : results of projects (30 minutes) Note that this is a Tuesday 

TS (MEE/GST)  Liquid foams  
TH (MEE/GST)  Liquid foams  
JV (MEE)  Optimal shape of knots  
20/Jan  Student presentations : results of projects (30 minutes) 

SE (MS/GST)  Biophotonics  
DJ (GST)  Biophotonics  
FS(AM/GST)  Confined fluids  
21/Jan  Student presentations : results of projects (30 minutes) Note that this is a Tuesday 

MK (GST)  Chiral molecules in chiral pores  
WB (MEE)  Structure of skin 
The course for the winter term 2013/14 is now full. If you are interested in attending a similar seminar in a future term, please drop us an email (gerd.schroederturk@physik.unierlangen.de).