**Symmetry-Breaking bifurcations and reservoir computing in regular oscillator networks**

*Röhm, André* (2019)

The focus of this thesis is the investigation of regular oscillator networks with numerical and analytical tools. Such systems are ubiquitous in nature and can emerge in the shape of vastly different processes. Among others, they can be mathematically derived as discrete approximations of continuous wave equations or as a local approximation of coupled dynamical systems. In the most basic meani...

**Dynamics of collective attention**

*Lorenz-Spreen, Philipp Gert Josef* (2019)

This dissertation aims to capture and understand the macroscopic ebbs and flows of public interest and popular topics. Operationalized as e.g. usage volume of hashtags, movie ticket sales or the counts of comments on online forums, we measure the dynamics of `public attention' for various cultural items in large online data sets. These trajectories of public attention became accessible since th...

**Computational and analytical approaches towards epidemic spread containment of temporal animal trade networks**

*Bassett, George Jason* (2019)

In this thesis a threefold approach to assess the risk of epidemic spread on animal trade networks and pinpoint strategies to contain it is presented. Firstly, an exhaustive description of a stochastic, event-driven, hierarchical agent-based model designed to reproduce the infectious state of the cattle disease called Bovine Viral Diarrhea (BVD) on the German trade network is outlined. It takes...

**Heat flow due to time-delayed feedback**

*Loos, Sarah A. M. ; Klapp, Sabine H. L.* (2019-02-21)

Many stochastic systems in biology, physics and technology involve discrete time delays in the underlying equations of motion, stemming, e. g., from finite signal transmission times, or a time lag between signal detection and adaption of an apparatus. From a mathematical perspective, delayed systems represent a special class of non-Markovian processes with delta-peaked memory kernels. It is wel...

**Control of Chimera States in Multilayer Networks**

*Omelchenko, Iryna ; Hülser, Tobias ; Zakharova, Anna ; Schöll, Eckehard* (2019-01-30)

Chimera states are intriguing complex spatio-temporal patterns of coexisting coherent and incoherent domains. They can often be observed in networks with non-local coupling topology, where each element interacts with its neighbors within a fixed range. In small-size non-locally coupled networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the i...

**Out-of-equilibrium dynamics of open quantum many-body systems**

*Droenner, Leon Janek* (2019)

Many-body localization, which prevents a many-body quantum systems from reaching thermal equilibrium has opened the possibility to study out-of-equilibrium dynamics of isolated quantum systems, leading to new phases of matter such as the discrete time crystal. However, little is known about these effects when the quantum many-body system is coupled to an external environment. An intuitive assum...

**Is Spreading Depolarization Characterized by an Abrupt, Massive Release of Gibbs Free Energy from the Human Brain Cortex?**

*Dreier, Jens P. ; Isele, Thomas ; Reiffurth, Clemens ; Offenhauser, Nikolas ; Kirov, Sergei A. ; Dahlem, Markus A. ; Herreras, Oscar* (2013)

In the evolution of the cerebral cortex, the sophisticated organization in a steady state far away from thermodynamic equilibrium has produced the side effect of two fundamental pathological network events: ictal epileptic activity and spreading depolarization. Ictal epileptic activity describes the partial disruption, and spreading depolarization describes the near-complete disruption of the p...

**The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition**

*Koo, Hyearn-Maw ; Hess, Siegfried* (1987)

Solution of the Kirkwood-Smoluchowski equation for a hard sphere fluid yields an expression for the viscosity which shows a dramatic pretransitional increase and a divergence at a number density close to that one observed in computer simulations and in colloidal dispersions. The value for the transition density stems from a boundary condition at the surface of the hard sphere in the configurati...

**The Viscosity Coefficients of Oriented Nematic and Nematic Discotic Liquid Crystals; Affine Transformation Model**

*Baalss, D. ; Hess, Siegfried* (1988)

General expressions are derived for the anisotropy of the viscosity and for the Leslie coefficients governing the flow alignment subject to the assumption that the equipotential surfaces for the interaction of oriented nonspherical molecules in the nematic or nematic discotic phase of a liquid crystal are related to a spherical interaction potential by an affine transformation. In particular, f...

**Exciton-phonon coupling in monolayers of transition metal dichalcogenides**

*Selig, Malte* (2018)

Monolayers of transition metal dichalcogenides (TMDs) attracted much attention in recent research due to their promising optical and electronic properties for future technological applications. In this thesis, an excitonic description within the Heisenberg equation of motion formalism for the optical response of these semiconducting, ultra-thin materials is developed. Hereby the main focus lies...

**Derivation and Application of an Algorithm for the Numerical Calculation of the Local Orientation of Nematic Liquid Crystals**

*Kilian, A. ; Hess, Siegfried* (1989)

Starting from a relaxation equation for the alignment tensor, an algorithm is derived which allows the numerical calculation of the dynamic and static behavior of the director field n with the correct nematic symmetry property, where n and - n are equivalent. As a first application, a two-dimensional problem is treated where the typical nematic defects with half-integer winding numbers only occ...

**Dissipative systems with nonlocal delayed feedback control**

*Grawitter, Josua ; van Buel, Reinier ; Schaaf, Christian ; Stark, Holger* (2018-11-07)

We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a nonzero system delay acts to destabili...

**The Viscosity Coefficients of Biaxial-Nematic Liquid Crystals. Phenomenology and Affine Transformation Model**

*Baalss, Dieter* (1990)

The viscosity tensor of biaxial-nematic liquid crystals contains 16 independent elements. A complete set of these viscosity coefficients is introduced and related to experimentally accessible quantities. Furthermore, the flow alignment and its stability against an arbitrary infinitesimal disturbance are discussed. By the affine transformation model, formerly established for the uniaxial symmetr...

**Static and Dynamic Properties of Ferroelectric Liquid Crystals in the Vicinity of a First-Order SmA-SmC* Phase Transition**

*Netz, Roland R. ; Hess, Siegfried* (1992)

A unified theoretical description of static and dynamic properties of ferroelectric liquid crystals in terms of a Landau free energy is presented. The shear deformation tensor is used as principal order parameter. Results for the stationary case for tilt angle variation and dielectric properties are compared with experiments on a compound with a pronounced first-order SmA-SmC* phase transition ...

**Tunable Real Space Transfer Oscillator by Delayed Feedback Control of Chaos**

*Cooper, D. P. ; Schöll, E.* (1995)

It is demonstrated numerically that by using Pyragas' method of chaos self-control a stable semiconductor oscillator can be designed based on driven real-space transfer oscillations in a modulation-doped heterostructure. By application of a small time-continuous delayed feedback voltage control signal, different unstable periodic orbits embedded in the chaotic attractor can be stabilized. Thus ...

**A Simplified Thermodynamic Theory for Biaxial Nematics**

*Papenfuß, Christina ; Verhás, Jozsef ; Muschik, Wolfgang* (1995)

A continuum theory of a biaxial nematic phase in liquid crystals is presented. The liquid crystalline ordering is described by a field of three unit vectors. Because these are macroscopic directors, the present approach is a generalization of the Ericksen-Leslie theory to biaxial nematics. The applied tools from nonequilibrium thermodynamics are classical Linear Irreversible Thermodynamics and ...

**Monte Carlo Simulation of the Director Field of a Nematic Liquid Crystal with Three Elastic Coefficients**

*Gruhn, Thomas ; Hess, Siegfried* (1996)

In this article, a Monte Carlo simulation is presented, which generates the equilibrium director field of a nematic liquid crystal under the influence of an external field and fixed boundary conditions. The liquid crystal is characterized by a set of directors on a spatially fixed lattice. The simulation is based on an expression for the Frank free energy with three elastic coefficients. The ch...

**On the Shock Front Thickness in Water and other Molecular Liquids**

*Hess, Siegfried* (1997)

Theoretical explanations are presented for the deviation of the shock front thickness from linear hydrodynamics, as observed by W. Eisenmenger (1964) in water and several molecular liquids for large driving pressure differences. Two mechanisms are proposed, which are based on generalizations of the Maxwell relaxation equation for the friction pressure tensor. One is due to the spatial inhomogen...

**Pressure and Isotropic-Nematic Transition Temperature of Model Liquid Crystals**

*Hess, Siegfried ; Su, Bin* (1999)

The pressure in the gaseous, the isotropic liquid and nematic liquid crystalline states, as well as the isotropic-nematic transition temperature are calculated for a model system composed of non-spherical particles. The potential is a generalization of the Lennard-Jones interaction where the attractive part depends on the relative orientations of the particles and the vector joining their cente...

**Irreversibility and Second Law**

*Muschik, Wolfgang* (1998)

According to M. Eigen there are two reasons for irreversibility: weak and strict temporality. Measures for irreversibility are defined by different formulations of the 2nd law which can be divided into two classes: the more general in time integrated formulations as Clausius' inequality and the more special in time local formulations as the non-negativity of the entropy production density. The ...