## The 10 most recently published documents

Improved optimization models for potential-driven network flow problems via ASTS orientations
(2019)

The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the relaxations usu-
ally employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of bipolar orientations, as a combinatorial relaxation of feasible solutions of potential-driven flow problems, study their structure, and
show how they can be used to strengthen existing relaxations and thus provide improved optimization models. Our computational results indicate that ASTS orientations can be used to derive much stronger bounds on the flow variables than existing bound tightening methods. We also
show that our proposed model extensions yield significant performance improvements for an existing state-of-the-art MILP model for large-scale gas networks.

In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called “potential-driven” network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones (“looping”). The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models.
Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.

We discuss drift-diffusion models for charge-carrier transport in organic semiconductor de- vices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The for- mer leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlin- ear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder’s fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.

This paper deals with the analysis of an instationary drift-diffusion model for organic semicon- ductor devices including Gauss–Fermi statistics and application-specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent ener- getic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength.
To prove the existence of global weak solutions, we consider a problem with (for small den- sities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the time-continuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level en- sure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densi- ties. The estimates rely on Moser iteration techniques.

This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity) and its associated eigenvector, the so-called Fiedler vector. Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only non-zero entries. These structural genericity properties with the constraint of not adding edges in the underlying
graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems.

An optimal control problem is studied for a quasilinear Maxwell equation of nondegenerate parabolic
type. Well-posedness of the quasilinear state equation, existence of an optimal control, and weak G\^ateaux-differentiability of the control-to-state mapping are proved. Based on these results, first-order necessary optimality conditions and
an associated adjoint calculus are derived.

A mathematical model is set up that can be useful for controlled voltage excitation in time-dependent electromagnetism.
The well-posedness of the model is proved and an associated optimal control problem is investigated. Here, the control
function is a transient voltage and the aim of the control is the best approximation of desired electric and magnetic fields in
suitable $L^2$-norms.
Special emphasis is laid on an adjoint calculus for first-order necessary optimality conditions.
Moreover, a {peculiar attention is devoted to propose a formulation for which the computational complexity of the finite element solution method is substantially reduced}.

We report the cancellation of the soliton self-frequency shift in nonlinear optical fibers. A soliton which interacts with a group velocity matched low intensity dispersive pump pulse, experiences a continuous blue-shift in frequency, which counteracts the soliton self- frequency shift due to Raman scattering. The soliton self-frequency shift can be fully compensated by a suitably prepared dispersive wave. We quantify this kind of soliton-dispersive wave interaction by an adiabatic approach and demonstrate that the compensation is stable in agreement with numerical simulations.

We consider the phenomenon of an optical soliton controlled (e.g. amplified) by a much weaker second pulse which is efficiently scattered at the soliton. An important problem in this context is to quantify the small range of parameters at which the interaction takes place. This has been achieved by using adiabatic ODEs for the soliton characteristics, which is much faster than an empirical scan of the full propagation equations for all parameters in question.

We consider scattering of small-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analogue of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from Quantum Mechanics, we give a quantitative account for the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, for the first time we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.