Projects of the Collaborative Research Center 910

Coordinating Institution:
Technische Universität Berlin

Coordinator:
Prof. Dr. Sabine Klapp (since 02/2018)

Vice-Coordinator:
Prof. Dr. Andreas Knorr (since 02/2018)

Until 02/2018:
Coordinator Prof. Dr. Dr. h.c. Eckehard Schöll, PhD
Vice-Coordinator Prof. Dr. Sabine Klapp

Managing Director:
Henning Reinken (2019 - 2022)
Roland Aust (2011 - 2018)

Assistant:
Lise Germo (2022)
Norma Rettich (2011, 2021 - 2022)
Liza Oemler (2019 - 2021)
Ulrike Niederberger (2017 - 2018)
Yulia Jagodzinski (2011 - 2019)

Student assistants (third funding period):
Olga Lysenko
Moritz Gerster

The integrated research training group "Design and Control of Complex Systems" provides a structured PhD program for PhD students within and associated to the CRC 910 "Control of self-organizing nonlinear systems: Theoretical methods and concepts of application". Key elements of the qualification program include lecture courses taught by guest lecturers or project leaders, a tailored seminar program targeting scientific and non-scientific aspects, a workshop program, and the opportunity for long-term research visits abroad. By these measures, the integrated research training group supports the PhD students in developing into highly qualified researchers or professionals with positions in academia or industry worldwide.

Duration:
Third Funding Period (2019 - 2022)

Coordinator:
Prof. Dr. Holger Stark (TU Berlin)

Vice-Coordinators:
Prof. Dr. Alexander Mielke (WIAS Berlin)
Dr. Alexander Carmele (TU Berlin)

Managing Director:
Henning Reinken (TU Berlin)

Student assistants:
Olga Lysenko
Till Welker

The objective of the present project is to investigate emergent phenomena and their control in multilayer networks that offer better representation of the topology and dynamics of real-world systems in comparison with one-layer structures. We particularly aim to disclose the interconnections between multiplexing, communication delay, and stochasticity to develop efficient control strategies. For this purpose we study noise- and delay-induced dynamics as well as complex deterministic effects and synchronization patterns, and explore their underlying mechanisms in multilayer networks. We intend to develop control methods based on solely (i) multiplexing and on the (ii) interplay of multiplexing with time delay or/and noise.

Project leader:
Prof. Dr. Anna Mandel-Zakharova

Institution:
TU Berlin

Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems, and power networks. In many of the applications it is advantageous to formulate the DDAEs via a model hierarchy of port-Hamiltonian (pH) DDAE models. We will study existence, uniqueness and sensitivity for such pHDDAEs, in particular those where the interconnection of subsystems is delayed. We will derive variational formulations and study the resulting operator pH DDAEs with respect to space-time discretization and control. In particular we will derive model reduction techniques and methods for the estimation of stability regions for pHDDAEs.

Project leader:
Prof. Dr. Volker Mehrmann

Institution:
TU Berlin

Self-organized dynamical phenomena and collective behavior can be found in large coupled systems from various fields of science, e.g neural networks or laser systems. We will analyze and control complex and high dimensional dynamics induced by complex network structures, large coupling delays, and adaptive coupling. This includes spatial localization in coupled excitable systems, as well as temporal localization in delay systems, describing phase solitons, or in coupled oscillator systems for mode locking. The main methods for large coupled systems will be symmetric bifurcation theory and continuum limits, while for adaptive coupling and large delays we will use multi-scale methods and singular perturbations.

Project leader:
Dr. Matthias Wolfrum

Institution:
WIAS Berlin

Spatio-temporal patterns encompass a plethora of phenomena in Sciences and Engineering. Their mathematical understanding is comparably limited, mostly to patterns in partial differential equations of reaction-diffusion type, and to ordinary differential equations on very regular, symmetric, or small networks. In marked contrast to more traditional lines of research, our goal is a qualitative approach to open loop and feedback control, including networks and beneficial delays, and ultimately the rational design of spatial and temporal patterns of applied relevance. We therefore address three areas: delayed feedback control, qualitative analysis of networks, and design and control of global dynamics.

Project leaders:
Prof. Dr. Bernold Fiedler and Dr. Isabelle Schneider

Institution:
FU Berlin

This project studies pattern formation in reaction-diffusion systems and in models of fluid dynamics, such as Kolmogorov's two-equation model for turbulence. In addition to traveling waves, such as fronts and pulses, we also study self-similar structures that describe the asymptotic decay of localized profiles on unbounded domains. On the methodological side we use homogenization techniques for periodically structured materials and evolutionary Gamma-convergence for perturbed gradient flows, which will be combined with self-similar scaling techniques.

Project leader:
Prof. Dr. Alexander Mielke

Institution:
WIAS Berlin

Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. We focus on models enriched by, e.g., nonlocality in time or space as well as on non-standard assumptions as, e.g., non-monotone growth. We study existence of generalized solutions via convergence of suitable approximation schemes. Applications arise in soft matter and dynamics of complex fluids. We aim to study models for smectic phases as well as nonlocal models of liquid crystals and to apply the new concept of relative energy.

Project leader:
Prof. Dr. Etienne Emmrich

Institution:
TU Berlin

The main goal of this project is to develop the control theory of stochastic mean-field equations, and in parallel, stochastic reaction-diffusion systems, with a view towards potential applications to the control of brain states, described in terms of large systems of weakly coupled stochastic differential equations driving the internal dynamics of single neurons. Special emphasize will be laid on so called mean-field controls as mathematical models for non-invasive external stimulations of brain states. Such controls have been introduced in the mathematical literature only quite recently and studied mainly from the theoretical perspective. Their application to neural systems has not yet been investigated.

Project leader:
Prof. Dr. Wilhelm Stannat

Maintaining coherence in the face of interactions with the environment is essential for reliably manipulating quantum states and thus quantum information processing. One prominent strategy towards this goal relies on the measurement of error syndromes and subsequent active quantum error correction. Such error correcting codes typically rely on projective syndrome readout. In practice, such projective measurements may be too difficult or too time consuming. In this project, we explore feedback-based strategies towards this goal which use weak rather than projective measurements, with a focus on topological quantum computation and the underlying adiabatic quantum dynamics.

Project leader:
Prof. Dr. Felix von Oppen

Institution:
FU Berlin

We plan to theoretically study the use of quantum feedback control for engineering dissipative environments with tailored properties for systems of ultracold atoms in optical lattices. For this purpose continuous measurements of the system via the off-resonant scattering of photons from a tailored probe beam into a cavity mode shall be considered and a focus will lie on the combination of feedback control with Floquet engineering. Based on this approach, we will design and test strategies for cooling, dissipative state preparation, mimicking thermal baths, suppressing Floquet heating, studying heat transport and ordering in non-equilibrium steady states, and inducing non-trivial relaxation dynamics.

Project leaders:
Prof. Dr. André Eckardt und Dr. Ling-Na Wu

Institution:
TU Berlin

Funded since 2021

The superposition principle and the corresponding non-classical features introduced by quantum interference are essential to quantum mechanics. In this project, we will theoretically study the possibility to steer quantum interferences via a coherent self-feedback mechanism beyond classical Pyragas control. Our goal is to enhance the probability of specific quantum states and to reduce dissipation in networks consisting of coupled cavities and strongly-correlated emitters or spin-chains. Specifically, we will address phenomena in the few-excitation limit, such as feedback-controlled two-photon emission and reduction or enhancement of the spin-blockade effect in incoherently pumped Heisenberg spin chains.

Project leaders:
Prof. Dr. Andreas Knorr and Dr. Alexander Carmele

Institution:
TU Berlin

The present project aims at developing control strategies for dynamical phenomena in colloidal systems. In the upcoming funding period we will focus on a) open-loop and feedback control of oscillatory dynamics and local structure under shear, b) transport under a time-delayed feedback force, and c) feedback control of spatiotemporal dynamics on the mesoscale. New aspects concern the interplay of control and thermodynamics, as well as control in active systems. We employ a spectrum of methods including stochastic delay equations, Fokker-Planck equations, particle-based simulations, and continuum theory. The results will be relevant in the areas of rheology, nanotribology and single-particle manipulation.

Project leader:
Prof. Dr. Sabine Klapp

Institution:
TU Berlin

Soft materials or complex fluids show a rich and fascinating variety of flow phenomena in non-equilibrium. The project uses computer simulations to explore control strategies such as hysteretic and time-delayed feedback to manipulate complex fluids, engineer their self-assembly, and design novel motional flow patterns. In the first subproject we investigate timely aspects of inertial microfluidics, which is of high relevance for biomedical applications. In the second subproject we concentrate on viscoelastic, shear-thinning, and active fluids and use feedback control to design their flow. Our work treats model systems for complex flow occurring in nature and it is relevant for fluid mixing in microfluidics and for microrheology.

Project leader:
Prof. Dr. Holger Stark

Institution:
TU Berlin

We plan to analyze and control complex and typically chaotic spatiotemporal dynamics (1) in cardiac tissue and (2) in active fluids. In subproject 1, we will analyze and improve the mechanism of defibrillation by sequences of low-energy electrical-field stimuli (LEAP) that induce waves from internal heterogeneities. To achieve this, we plan to reduce a partial differential equations model to a stochastic mean-field like model and to identify suitable macrovariables for an effective control. Subproject 2 will on the one hand, deal with the control of mesoscale turbulence and stabilization of regular spatiotemporal states like unidirectional collective motion or vortex lattices in a simple model of an active suspension of swimmers through spatial modulation and feedback. On the other hand, the control of synchronization and chimera states in a model for phase oscillators with long-range coupling modelling arrays of cilia on the surface of biological cells shall be studied in part 2 of this project.

Project leader:
Prof. Dr. Markus Bär

Institution:
PTB Berlin

We will study models of inter-areal brain networks whose topology is constrained by data from human imaging studies. Delay-coupled network nodes will be equipped with (1) simplified dynamical systems (Hopf normal forms & FitzHugh-Nagumo models) and (2) biophysically calibrated neural mass models both including noise. Dynamics will be controlled through coupling terms describing the influence of external electric fields on the neuronal dynamics. We will characterize the dynamical states of the network and will design feedback control schemes for stabilizing or switching between states. Results will shed light on the controllability of high-dimensional states in heterogeneous networks and will lead to a better understanding of the impact of non-invasive brain stimulation on global brain activity.

Project leader:
Prof. Dr. Klaus Obermayer

Institution:
TU Berlin

We investigate complex laser networks for modern optical computing schemes. Having studied the bifurcation structure of simple laser networks and evaluated their reservoir computing performance, we will develop new concepts to both increase the realism of our numerical simulations with complex gain models and spontaneous emission noise, as well as develop novel analytical tools to study the information processing capabilities of generic oscillator networks with a tailored topology. Global phase space properties, photon distributions as well as entropy-based measures of the dynamics will be evaluated to link the performance to dynamical states and thus gain predictive results for optimization.

Project leader:
Prof. Dr. Kathy Lüdge

Institution:
TU Berlin / TU Ilmenau

The present project aims at analyzing spatiotemporal dynamics in complex ensembles of coupled chaotic oscillators for different coupling topologies and in the presence of regular and noisy excitations. We study complex networks with different types of inter- and intra-coupling, including time-dependent, time-delayed and random couplings, and analyze their sensitivity to variation of control parameters, initial conditions and noise influence. We mainly focus on the synchronization of different chimera states and their statistical features. The results will be relevant in the areas where the external influences play a crucial role in the functioning of complex interacting networks.

Project leaders:
Prof. Dr. Vadim S. Anishchenko, Prof. Dr. Tatiana E. Vadivasova and Dr. Galina Strelkova

Institution:
Saratov State University, Russia

The development and application of dissipative and nonreciprocal feedback protocols in engineered quantum systems lies at the center of the anticipated project. The aims of the project are summarized as (i) the design of feedback protocols via dissipation engineering, (ii) the realization of Hamiltonian filtering for selecting the desired coherent dynamics of a system while simultaneously suppressing undesired processes, (iii) and the development of nonreciprocal algorithms for the control and storage of information. Our findings will be of relevance for the processing and storage of quantum information, and enhance the unraveling of sensitive fundamental knowledge of systems in the quantum regime.

Project leader:
Prof. Dr. Anja Metelmann

Institution:
FU Berlin / Karlsruhe Institute of Technology

The interplay of time delay with network topology, nonlinearity, and noise leads to a plethora of complex phenomena with applications to physics, chemistry, biology, engineering, and even socio-economic systems. Time delay and stochasticity arise naturally in various systems and can be exploited for control purposes. Our objective is to establish the interconnections between the structure of complex networks, noise impact, and delay configurations in order to develop efficient control mechanisms. For this purpose we study noise-induced effects as well as complex deterministic symmetry-breaking phenomena and synchronization patterns.

Project leaders:
Prof. Dr. Eckehard Schöll and Prof. Dr. Anna Mandel-Zakharova

Institution:
TU Berlin

Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems and electronic networks. We will study existence and uniqueness as well as the development of numerical methods for general nonlinear DDAEs. For this, regularization techniques need to be performed that prepare the DDAE for numerical simulation and control. We will derive such techniques for DDAEs on the basis of a combination of time-differentiations and time-shifts, in particular for systems with multiple delays. We also plan to extend the spectral stability theory, i.e. the concepts of Lyapunov, Bohl and Sacker-Sell spectra, to DDAEs, and we will develop corresponding numerical methods.

Project leader:
Prof. Dr. Volker Mehrmann

Institution:
TU Berlin

Time delays appear commonly in mathematical models of natural systems, such as neural networks or coupled lasers. In this project, we investigate the emergence of new dynamical behaviors (activity patterns) in networks of delay-coupled systems as well as spatially distributed systems with delayed feedbacks. More specifically we address the following points: (i) description of dynamical patterns in networks of excitable systems with time-delayed coupling, (ii) derivations of amplitude equations for systems with multiple time delays, and (iii) control of localized solutions in PDEs with time-delayed feedback.

Project leaders:
PD Dr. Serhiy Yanchuk and Dr. Matthias Wolfrum

Institution:
HU Berlin and WIAS Berlin

Our goal is a new qualitatively oriented approach to the observation, the open-loop and feedback control, and ultimately the rational design of spatio-temporal patterns of applied relevance. Mathematical topics include differential equations on graphs, as well as partial and delayed differential equations. Applications include gene regulatory and metabolic networks. Specifically we plan to address three areas: (i) qualitative analysis of network sensitivity; (ii) observation and control of regulatory networks; (iii) rational design of spatio-temporal dynamics.

Project leader:
Prof. Dr. Bernold Fiedler

Institution:
FU Berlin

Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales and nonlinearities of the system as well as on the size and geometry of the underlying domain. The challenge is to understand how effects on the small scales generate effective pattern formation on the larger scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.

Project leader:
Prof. Dr. Alexander Mielke

Institution:
WIAS Berlin

We will develop a theoretical description of delayed feedback control for quantum transport processes, implement a microscopic analogon of coherent feedback control, and provide a thorough thermodynamic interpretation of feedback in presence of quantum coherence. We will furthermore introduce delayed feedback control for dissipative quantum phase transitions and study the phase diagram and the appearance of quantum chaos in Dicke-Hepp-Lieb superradiance and other models.

Project leaders:
Prof. Dr Tobias Brandes

Institution:
TU Berlin

Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. Relying upon the theory of monotone operators and compactness arguments, we study existence of solutions, convergence of discretization methods, and feedback control for equations of dissipative type. We focus on nonlocality in time (distributed delay, memory effects) and interpret time-delayed feedback control as a nonlocal-in-time coupling. Applications arise in soft matter and dynamics of complex fluids such as liquid crystals.

Project leader:
Prof. Dr. Etienne Emmrich

Institution:
TU Berlin

The project deals with reaction-diffusion systems involving hysteresis, or, more generally, bistability. The models under consideration have applications to a large number of biological, chemical, physical, and economic processes. Besides the nontrivial issue of well-posedness, we are interested in the qualitative description of solutions. The analysis will be in terms of emerging spatio-temporal patterns that are influenced primarily by the interplay between diffusion and spatially distributed hysteresis. We will also develop theoretical concepts for the stability analysis and control of these patterns by temporally and spatially nonlocal feedback.

Project leader:
PD Dr. Pavel Gurevich

Institution:
FU Berlin

The focus of this project is to study the collective properties of small solid state based networks (coupled photonic and acoustic cavities) in the extreme limit of only few quantum excitations. We develop strategies for a fully quantum coherent feedback control, i.e. the use of quantum controllers (such as external cavities or mirrors) for the selection, stabilization and synchronization of non-classical states in quantum networks.

Project leader:
Prof. Dr. Andreas Knorr

Institution:
TU Berlin

The present project aims at manipulating time-dependent phenomena in driven, correlated colloidal systems by closed-loop control. We focus on the control of a) oscillatory dynamics and excitations under shear and b) transport of low-dimensional colloidal systems subject to time-dependent fields. We advance control strategies with and without time delay based on particle computer simulations and Fokker-Planck equations, with the control targets being the particle's coordinates, density fields, or global material properties such as stress. The results will be relevant in the areas of (micro) rheology, nanotribology and single-particle manipulation.

Project leader:
Prof. Dr. Sabine Klapp

Institution:
TU Berlin

Soft materials or complex fluids strongly respond to external fields and thereby show prominent non-equilibrium structure formation. The project explores different control strategies such as optimal and (time-delayed) feedback control to manipulate complex fluids, engineer their self-assembly, and induce novel motional flow patterns. In the first subproject we investigate inertial microfluidics which has high relevance for biomedical applications. In the second subproject we look at specific complex fluid models for viscoelasticity and phase separation. Our work is relevant for fluid mixing in microfluidics and for microrheology.

Project leader:
Prof. Dr. Holger Stark

Institution:
TU Berlin

Multiscale pattern formation refers either to the simultaneous appearance of competing unstable modes with different critical wavelengths or to the interaction of pattern formation with spatial heterogeneities. This project will focus on control strategies in order to obtain desired or suppress unwanted patterns in multiscale reaction-diffusion systems. We plan (i) to study simple generic models to develop appropriate control methods like time delay and nonlocal coupling and (ii) to consider control of patterns on biomembranes as well as during pathological cardiac dynamics as applications for multiscale systems.

Project leader:
Prof. Dr. Markus Bär

Institution:
PTB Berlin

We aim at controlling self-organized spatio-temporal patterns in active media. In particular, we guide non-linear waves and moving localized spots according to a given protocol of movement within two- and three-dimensional domains. To reach our control goals we apply methods based on multiple scale perturbation theory for position and shape control and exploit the powerful methods of optimal control of partial differential equations including sparse control and pointwise state constraints. Additionally, we investigate the impact of spatial confinement on wave and spot dynamics and study reaction-diffusion processes in small compartments.

Project leaders:
Prof. Dr. Harald Engel and Prof. Dr. Fredi Tröltzsch

Institution:
TU Berlin

Cognitive processing in animals and humans is linked to neuronal activation within inter-areal brain networks. Here we apply methods from nonlinear dynamics and stochastic processes in order to understand the dynamical regimes supported by those networks in terms of the relationship between inter-areal connectivity, local node dynamics, and the emerging global “brain states”. We then explore how biologically plausible feedback loops and inputs from network external brain structures can contribute to the stabilization or switching of relevant dynamical regimes. Thus, potential brain internal control schemes will be examined.

Project leader:
Prof. Dr. Klaus Obermayer

Institution:
TU Berlin

The aim of the project is to study the nonlinear dynamics of delay-coupled lasers forming a complex network of nonidentical units, thereby exploring new frontiers in signal processing. Considering large optical laser networks, e.g. integrated on a chip, opens innovative paths for novel applications. The goal is to understand occurring bifurcation scenarios in an all-to-all coupled laser network and to predict stable patterns like synchronization, chimera states, or multi-cluster solutions. Furthermore, we will break new grounds in designing unconventional computational approaches such as machine learning based reservoir computing.

Project leader:
Prof. Dr. Kathy Lüdge

Institution:
TU Berlin

Many networks exhibit time-dependent topologies with edges existing for some time or weights subject to temporal fluctuations. This is particularly important, if the evolution of the network topology acts on a timescale similar to the local node dynamics. Thus, time-dependent topologies form profound challenges for the control of coupled elements. Our objective is to develop a framework for the investigation of the dynamics on temporal networks. We address (i) the controllability of networks, (ii) apply novel control designs to time-dependent network topologies, and (iii) test our findings on high-resolution datasets, e.g. animal trade, with important applications in epidemiology.

Project leader:
Dr. Philipp Hövel

Institution:
TU Berlin

Noise can significantly influence the dynamics of complex nonlinear systems. We study noise effects in distributed oscillatory systems, active media, and complex nonlinear networks with random connections and consider how external influences control their behavior. The diagnostics and characterization of the complex irregular behavior as well as dynamical changes related to control problems require advanced data processing tools. We address this problem with the statistics of Poincaré return times and wavelet-based techniques aiming to develop new methods for diagnosing the functioning regimes and characteristics of nonlinear systems.

Project leaders:
Prof. Dr. Vadim S. Anishchenko and Prof. Dr. Tatiana E. Vadivasova

Institution:
Saratov State University, Russia

A delay term added to a differential equation increases the dimension to infinity, and adds a wealth of complex dynamic behavior. Such delays arise naturally in coupled systems as delayed coupling or delayed feedback due to finite signal transmission and processing times, latencies, or external control loops. Our objective is to develop delayed feedback and coupling schemes in order to deliberately design and control the dynamics in composite systems and networks. For this purpose we study the deterministic and stochastic dynamics of (i) a few coupled nonlinear elements (network motifs), (ii) larger complex networks (e.g., regular, random, or small-world).

Project leader:
Prof. Dr. Eckehard Schöll

Institution:
TU Berlin

Delay differential equations arise in a variety of applications including biological systems and electronic networks. If the states of the physical system are constrained, e.g., by conservation laws or interface conditions, then algebraic equations have to be included and one has to analyze delay differential-algebraic equations. This topic is only in its infancy due to substantial mathematical difficulties in the analysis, numerical solution and control of such systems. We plan to study the stability properties and develop efficient numerical methods for the simulation, robust control and model reduction of delay differential-algebraic equations.

Project leaders:
Prof. Dr. Volker Mehrmann and Prof. Dr. Tatjana Stykel

Institution:
TU Berlin

Systems with time-delay can exhibit complicated spatio-temporal dynamics on multiple time scales. The main goal of this project is twofold: (i) Describing the appearance and properties of spatio-temporal patterns, in particular those arising due to the delay induced multiple-scale structures, e.g. long delay, multiple delays, etc; (ii) Designing new methods and analyzing the applicability of existing feedback control methods for the control of spatio-temporal dynamics in systems with delay. The obtained results will be applied to such fields as dynamics of semiconductor lasers and dynamics of neural networks.

Project leader:
PD Dr. Serhiy Yanchuk

Institution:
HU Berlin

The project aims at the design of self-organizing structures with prescribed spatio-temporal dynamics, via delayed feedback controls. Specific applied contexts arise in coupled neural or molecular networks, semiconductor nanostructures, and chemical reaction-diffusion systems. The project aims far beyond state-of-the-art modelling or compilations of the resulting spatial and temporal phenomena like static Turing patterns, recognition of static patterns by neural networks of spin-glass type, or spirals, meanders, and scrolls in reactive and diffusive media. It is the active design of prescribed spatio-temporally coherent behavior which is the principal focus here.

Project leader:
Prof. Dr. Bernold Fiedler

Institution:
FU Berlin

Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales of the system, the nonlinearities and the size and geometry of the underlying domain. The challenge is to understand how effects on the small spatial scales generate effective pattern formation on large spatial scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.

Project leader:
Prof. Dr. Alexander Mielke

Institution:
WIAS Berlin

Previous studies of dynamical networks have been largely focused on synchronization phenomena and spreading of infection fronts. Here, we plan to investigate more complex forms of self-organization phenomena. They will include network analogs of Turing and wave bifurcations and localized patterns in activator-inhibitor network models with longrange inhibition, as well as network turbulence. Introducing various feedbacks, we intend to show how self-organization processes in networks can be steered and particular kinds of patterns induced. In addition to considering large random and scale-free networks, we will also study control of adaptive dynamical networks which can change their architecture depending on the feedback signals.

Project leader:
Prof. Dr. Alexander S. Mikhailov

Institution:
FHI of the MPG Berlin

We will develop a theory of feedback control of quantum transport in the solid state, with a particular focus on single electron transport in nanostructures such as quantum dots. Systems of partial differential equations representing the feedback master equations will be analysed, and we will explore new methods for quantum transport and time-dependent full counting statistics beyond the standard Liouvillian perturbation theory. Applications are in high accuracy electron-pumping and the controlled suppression of noise and decoherence in quantum transport.

Project leaders:
Prof. Dr Tobias Brandes and Dr. Clive Emary

Institution:
TU Berlin

The mathematical modeling of time-dependent processes in science and engineering leads to, in general, nonlinear evolution equations of first or second order in time. The highest spatial derivatives appearing can often be described by a monotone and coercive operator; lower order terms are then treated as a strongly continuous perturbation of the principal part. Relying upon the variational approach and the theory of monotone operators, the approximate solution of such evolution problems is studied with focus on problems with nonlocality in time and on the convergence of appropriate discretization methods. Applications arise in the description of complex fluids as well as of neuron dynamics. A long term goal is the question of controllability of the systems above.

Project leader:
Prof. Dr. Etienne Emmrich

Institution:
TU Berlin

For externally pumped atomic or semiconductor based emitters in nano-cavities, the complex photon and phonon dynamics exhibits a wealth of bifurcations and instabilities. The central goal of this project is to systematically investigate exotic but intrinsically unstable quantum states and wavepackets, which can only be stabilized by additional feedback control mechanisms. Our vision is to extend concepts of time delayed feedback control and self-organization to few photon and phonon states, where quantum fluctuations contribute or even dominate over the usual classical dynamics.

Project leader:
Prof. Dr. Andreas Knorr

Institution:
TU Berlin

This project aims at analyzing and controling dynamic patterns in confined suspensions of magnetic nanoparticles driven out of equilibrium by planar shear. The dipolar colloidal interactions generate diverse film structures already in equilibrium. One focal point is to explore the resulting non-equilibrium behavior, including a) structural instabilities such as shear banding and b) phase separation under shear. Further, we will develop feedback control strategies to stabilize specific patterns, the vision being a deliberate design of soft magnetic films with tunable properties. We will employ computer simulations and dynamic density functional theory.

Project leader:
Prof. Dr. Sabine Klapp

Institution:
TU Berlin

Microfluidic Poiseuille flow in microchannels is an ideal means to create self-organized dynamic structures in complex fluids that only exist far from equilibrium. In this project, we aim at a thorough theoretical study how colloidal dispersions of micron-sized particles and more complex objects order in Poiseuille flow. One main emphasis will be to explore the influence of inertial forces on the structure formation at the transition from low to non-zero Reynolds numbers. At concrete examples, we will investigate how transient or unstable structures can be stabilized under appropriate feedback control.

Project leader:
Prof. Dr. Holger Stark

Institution:
TU Berlin

Multiscale pattern formation refers to the simultaneous appearance of competing unstable modes with largely different wavelengths typically reflecting competing mechanisms of self-organization. Examples for such phenomena include lipid domains in biomembranes, chemical patterns in microemulsions and surface reactions affected by promotors. We aim to construct models for multiscale pattern formation, analyse their behavior and develop strategies to control the spatiotemporal dynamics in such systems both for generic simple models and realistic descriptions of applications. Methods include numerical simulations, homogenization procedures and bifurcation analysis.

Project leader:
Prof. Dr. Markus Bär

Institution:
PTB Berlin

Our goal is the design of efficient and robust spatio-temporal control algorithms aimed at selecting and tracking desired travelling wave patterns in nonlinear macroscopic non-equilibrium systems. The focus is on three-dimensional wave solutions to reaction-diffusion equations such as scroll waves or travelling localized zones of wave activity. The results will open new possibilities for the control of three-dimensional wave phenomena in catalytic reactors, polymerisation fronts or solid fuel combustion and are motivated by the crucial role wave instabilities play in these systems as well as in the development of certain cardiac arrhythmia.

Project leaders:
Prof. Dr. Harald Engel and Prof. Dr. Fredi Tröltzsch

Institution:
TU Berlin

We aim to investigate theoretically how internal control mechanisms in the brain prevent the emergence of nonlinear excitation waves based on reaction-diffusion, i. e., spreading depression (SD), and how, if they fail, SD waves can be suppressed by external feedback control. SD is a pathological activity of the human cortex, and is related to migraine, stroke, and various kinds of brain injury. Control of SD by external neuromodulation is of clinical importance because SD causes transient neurological deficits and subsequently headache (migraine) or permanent brain damage (stroke and brain injury).

Project leaders:
Dr. Markus Dahlem and Prof. Dr. Eckehard Schöll

Institution:
TU Berlin

We will analyse the dynamics and “controllability” of recurrent networks of adaptive, pulse-coupled model neurons. We will first investigate the dynamical properties of network motifs and of biologically plausible, spatially structured models of cortical networks with noise and delays. We will then consider different kinds of cortical control strategies and ask how they affect rates, oscillations, and synchrony. We will determine parameter settings for which networks are particularly sensitive to feedback control. Results will be compared with data from primary visual cortex in order to provide evidence for self-organized control in cortical computation.

Project leader:
Prof. Dr. Klaus Obermayer

Institution:
TU Berlin