Seminar on the Theory of Complex Systems  Winter Term 2013/14

We employ both experimental and theoretical methods to understand how species invade structured environments and how such range expansions affect their genetic diversity. We thereby focus on continuous environments with finite-sized regions of poor growth conditions. In particular, we study an experimental model system, in which a population of bacteriophage T7 spreads on a lawn of susceptible E. coli bacteria while a region of resistant bacteria, i.e., a region with poor growth conditions for the phage, poses an obstacle to growth of the plaque. We use a printing assay to create single regions of resistant bacteria around which the plaque grows and examine the plaque dynamics quantitatively. A simple coarse-grained description and reaction-diffusion modeling allow us to understand the dynamics in such simplified geometries. We predict that during the encounter of an obstacle, alleles present in the expanding population are driven to extinction, are unaffected, or even sweep through part of the population, depending on their spatial distribution relative to the region of poor growth and purely for geometric reasons. This effect of selection by geometry is confirmed using stochastic simulations and a range expansion of fluorescently labeled E. coli strains.

We compute the universal conductivity of the (2+1)-dimensional XY universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical (2+1)-dimensional $J$-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, $\sigma(\infty)=0.359(4)\sigma_Q$ with $\sigma_Q$ the conductivity quantum. The universal conductivity is the schoolbook example of where the AdS/CFT correspondence from string theory can be tested and made to use. The shape of our $\sigma(i\omega_n)- \sigma(\infty)$ function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particle-like nature of charge transport. We find that the holographic gauge/gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation.

Life relies heavily on pattern formation: during embryo- genesis, for example, the fertilized egg undergoes complicated transitions leading to the development of a fetus. Inside each cell, the organelles and the cytoskeleton remodel constantly and change their shape to adapt to evolving environmental stimuli. Symmetry breaking is supposed to be one of the key players to explain the resulting patterns.
In my talk I will focus on two examples where symmetry breaking induces global shape shanges: the formation of membrane invaginations in confinement [1] and the dynamics of microtubules [2]. For both cases a simplified elastic model will be used which might be too naive to explain all aspects of the complicated living systems under scrutiny, but offers an in-depth understanding of the basic building blocks of these systems.

1. O. Kahraman, N. Stoop and M. M. Müller, EPL 97, 68008 (2012); NJP 14, 095021 (2012).
2. O. Kahraman, H. Mohrbach, M. M. Müller and I. Kuli ́c, in preparation (2013).

We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a T-matrix approximation. We discuss the implications of our results for the attempted quantum simulation of the Froehlich Hamiltonian using ultra cold atoms.

Mechanics plays a major role in the determination of morphologies of biological objects such as organelles, cells, tissues and even whole organisms. Its understanding can shed light on important processes at all biologically relevant scales. A major challenge in modeling biomechanical processes is the complexity of the emerging shapes, the nonlinear mechanical responses of the biological material, and that the stress fields are generally unknown. The latter point forces us to couch the mechanical problem in terms of strains and then to solve the inverse problem to predict forces and resulting morphological configurations. However, this leads to excessive computational loads for complex shapes. Therefore we developed a three dimensional shape parameterization -- using the spherical harmonics basis functions -- that is able to capture shape outlines concisely, while maintaining high accuracy, thereby allowing efficient continuum shell mechanics simulations. The technique admits symmetry considerations, efficient shape transformations, shape-distance calculations and representation of any number of scalar fields. We demonstrate its power by showing two example applications that provide important biophysical insights. The first is a combined theoretical and experimental study of the morphology of the human red blood cell. We show the efficient traversal of minimum energy shape-phase-space without need for the traditional restrictions on symmetry. Importantly, we predict a stabilizing mechanical role for the cytoskeletal scaffold, that is associated with the red blood cell membrane. In a second application we focus on whole fruit fly embryo tissue mechanics modeling during the early developmental event of mesoderm invagination. We show excellent correlation between the predicted morphogenetic configuration and experimental data, and demonstrate that anterior-posterior morphological symmetry-breaking is responsible for determining the exact strain field pattern. The most striking result is the prediction that forces generated during this fold formation provide long-range mechanical support for the succeeding developmental event of germ-band extension.