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- ItemWPM package manager version 1.0 : software documentation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Streckenbach, TimoWPM is a command-line tool designed to support build and installation facilities. It is implemented as a collection of script files, written in Bourne shell syntax. For the sake of portability the code takes care of the common pitfalls of shell programming.
- ItemPredicting the data structure prior to extreme events from passive observables using echo state network(Lausanne : Frontiers Media, 2022) Banerjee, Abhirup; Mishra, Arindam; Dana, Syamal K.; Hens, Chittaranjan; Kapitaniak, Tomasz; Kurths, Jürgen; Marwan, NorbertExtreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.
- ItemTetGen: A quality tetrahedral mesh generator and a 3D Delaunay triangulator (Version 1.5 — User’s Manual)(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Si, HangTetGen is a software for tetrahedral mesh generation. Its goal is to generate good quality tetrahedral meshes suitable for numerical methods and scientific computing. It can be used as either a standalone program or a library component integrated in other software. The purpose of this document is to give a brief explanation of the kind of tetrahedralizations and meshing problems handled by TetGen and to give a fairly detailed documentation about the usage of the program. Readers will learn how to create tetrahedral meshes using input files from the command line. Furthermore, the programming interface for calling TetGen from other programs is explained.
- ItemLongitudinal dynamics of semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2001) Philip, JanWe investigate the longitudinal dynamics of semiconductor lasers using a model which couples a hyperbolic linear system of partial differential equations nonlinearly with ordinary differential equations. We prove the global existence and uniqueness of solutions using the theory of strongly continuous semigroups. Subsequently, we analyse the long-time behavior of the solutions in two steps. First, we find attracting invariant manifolds of low dimension benefitting from the fact that the system is singularly perturbed, i. e., the optical and the electronic variables operate on differente time-scales. The flow on these manifolds can be approximated by the so-called mode approximations. The dimension of these mode approximations depends on the number of critical eigenvalues of the linear hyperbolic operator. Next, we perform a detailed numerical and analytic bifurcation analysis for the two most common constellations. Starting from known results for the single-mode approximation, we investigate the two-mode approximation in the special case of a rapidly rotating phase difference between the two optical components. In this case, the first-order averaged model unveils the mechanisms for various phenomena observed in simulations of the complete system. Moreover, it predicts the existence of a more complex spatio-temporal behavior. In the scope of the averaged model, this is a bursting regime.
- ItemSynchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans(Lausanne : Frontiers Media, 2019) Pournaki, Armin; Merfort, Leon; Ruiz, Jorge; Kouvaris, Nikos E.; Hövel, Philipp; Hizanidis, JohanneWe investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities. © Copyright © 2019 Pournaki, Merfort, Ruiz, Kouvaris, Hövel and Hizanidis.
- ItemMaximally dissipative solutions for incompressible fluid dynamics(Cham (ZG) : Springer International Publishing AG, 2021) Lasarzik, RobertWe introduce the new concept of maximally dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumptions, we show that maximally dissipative solutions are well-posed as long as the bigger class of dissipative solutions is non-empty. Applying this result to the Navier–Stokes and Euler equations, we infer global well-posedness of maximally dissipative solutions for these systems. The concept of maximally dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique.
- ItemCan One Series of Self-Organized Nanoripples Guide Another Series of Self-Organized Nanoripples during Ion Bombardment: From the Perspective of Power Spectral Density Entropy?(Basel : MDPI, 2023) Li, Hengbo; Li, Jinyu; Yang, Gaoyuan; Liu, Ying; Frost, Frank; Hong, YilinIon bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of nanoripples is an outstanding issue to be overcome, similar to other self-organization methods. In this study, the IB-induced nanoripples on bilayer systems with enhanced quality are revisited from the perspective of guided self-organization. First, power spectral density (PSD) entropy is introduced to evaluate the degree of ordering of the irradiated nanoripples, which is calculated based on the PSD curve of an atomic force microscopy image (i.e., the Fourier transform of the surface height. The PSD entropy can characterize the degree of ordering of nanoripples). The lower the PSD entropy of the nanoripples is, the higher the degree of ordering of the nanoripples. Second, to deepen the understanding of the enhanced quality of nanoripples on bilayer systems, the temporal evolution of the nanoripples on the photoresist (PR)/antireflection coating (ARC) and Au/ARC bilayer systems are compared with those of single PR and ARC layers. Finally, we demonstrate that a series of intrinsic IB-induced nanoripples on the top layer may act as a kind of self-organized template to guide the development of another series of latent IB-induced nanoripples on the underlying layer, aiming at improving the ripple ordering. The template with a self-organized nanostructure may alleviate the critical requirement for periodic templates with a small period of ~100 nm. The work may also provide inspiration for guided self-organization in other fields.
- ItemNewton and Bouligand derivatives of the scalar play and stop operator(Les Ulis : EDP Sciences, 2020) Brokate, MartinWe prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strengthened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable. © The authors. Published by EDP Sciences, 2020.
- ItemScattering matrices and Dirichlet-to-Neumann maps(Amsterdam [u.a.] : Elsevier, 2017) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, HagenA general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh–Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps.
- ItemSpecial issue on conceptual structures(Dordrecht [u.a.] : Springer Science + Business Media B.V, 2022) Alam, Mehwish; Braun, Tanya; Endres, Dominik; Yun, Bruno[no abstract available]