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de Koster, P.B.J. (author), Wahls, S. (author)Lax-integrable partial differential equations (PDEs) can by definition be described through a compatibility condition between two linear operators. These operators are said to form a Lax pair for the PDE, which itself is usually nonlinear. Lax pairs are a very useful tool, but unfortunately finding them is a difficult problem in practice. In...journal article 2024
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Wang, Q. (author), Lechtenfeld, Oliver J. (author), Rietveld, L.C. (author), Schuster, Jonas (author), Ernst, Mathias (author), Hofman-Caris, Roberta (author), Kaesler, Jan (author), Wang, Chunmiao (author), Yang, Min (author), Yu, Jianwei (author), Zietzschmann, F.E. (author)Activated carbon is employed for the adsorption of organic micropollutants (OMPs) from water, typically present in concentrations ranging from ng L<sup>−1</sup> to μg L<sup>−1</sup>. However, the efficacy of OMP removal is considerably deteriorated due to competitive adsorption from background dissolved organic matter (DOM), present at...journal article 2024
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Despotopoulou, M. (author), Langejans, G.H.J. (author), Hendrikx, R.W.A. (author), Joosten, Ineke (author), Nijemeisland, M. (author), Poulis, J.A. (author), Kozowyk, P.R.B. (author)Archaeological findings prove the appearance and use of birch bark tar since the Middle Palaeolithic. The production and use of birch bark tar and pine wood tar has overlapped since at least the late Neolithic, but probably for much longer. The reliable chemical identification of such archaeological tar residues can offer valuable insights...journal article 2024
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Apostolidis, P. (author), Porot, Laurent (author)Bituminous binders are foreseen as colloidal dispersed systems characterised by high chemical complexity containing a plethora of molecules classified into maltenes and asphaltenes. The effect of these fractions on the overall response of bituminous binders remains elusive. This research selected two binders from the same refinery but with...journal article 2023
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de Koster, P.B.J. (author), Wahls, S. (author)We present a fast method to calculate the significantly large solitonic components of signals with large time-bandwidth products governed by the nonlinear Schrödinger equation, for which the computation typically becomes prohibitively expensive and/or numerically unstable. We partition the full signal in both frequency and time to obtain...journal article 2023
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de Koster, P.B.J. (author), Schulz, Olaf (author), Koch, Jonas (author), Pachnicke, Stephan (author), Wahls, S. (author)We experimentally investigate the problem of monitoring the Kerr-nonlinearity coefficient $\gamma$ from transmitted and received data for a single-mode fiber link of 1600 km length. We compare the accuracy and speed of three different approaches. First, a standard split-step Fourier method is used to predict the output at various $\gamma$...journal article 2023
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Chimmalgi, S. (author), Wahls, S. (author)Riemann theta functions play a crucial role in the field of nonlinear Fourier analysis, where they are used to realize inverse nonlinear Fourier transforms for periodic signals. The practical applicability of this approach has however been limited since Riemann theta functions are multi-dimensional Fourier series whose computation suffers...journal article 2023
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Zhao, Wenzhao (author), Fan, Yuling (author), Wang, Hongjian (author), Gemmeke, Hartmut (author), van Dongen, K.W.A. (author), Hopp, Torsten (author), Hesser, Jürgen (author)Objective. The image reconstruction of ultrasound computed tomography is computationally expensive with conventional iterative methods. The fully learned direct deep learning reconstruction is promising to speed up image reconstruction significantly. However, for direct reconstruction from measurement data, due to the lack of real labeled...journal article 2023
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Brühl, M. (author), Prins, Peter J. (author), Ujvary, Sebastian (author), Barranco, Ignacio (author), Wahls, S. (author), Liu, Philip L.-F. (author)In this paper, we study the propagation of bores over a long distance. We employ experimental data as input for numerical simulations using COULWAVE. The experimental flume is extended numerically to an effective relative length of x/h=3000, which allows all far-field solitons to emerge from the undular bore in the simulation data. We apply the...journal article 2022
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Prins, Peter J. (author), Wahls, S. (author)We propose a numerical algorithm that computes the eigenvalues of the Korteweg–de Vries equation (KdV) from sampled input data with vanishing boundary conditions. It can be used as part of the Non-linear Fourier Transform (NFT) for the KdV equation. The algorithm that we propose makes use of Sturm-Liouville (SL) oscillation theory to guaranty...journal article 2022
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Hajizad, O. (author), Kumar, A. (author), Petrov, R.H. (author), Sietsma, J. (author), Dollevoet, R.P.B.J. (author), Li, Z. (author)Microscopic stress and strain partitioning control the mechanical and damage behavior of multiphase steels. Using a combined numerical and experimental approach, local strain distributions and deformation localization are characterized in a carbide free bainitic steel produced by continuous cooling. The microstructure of the steel consists of...journal article 2022
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Prins, Peter J. (author), Wahls, S. (author)We present an algorithm to compute the N-fold Crum transform (also known as the dressing method) for the Korteweg–de Vries equation (KdV) accurately in floating point arithmetic. This transform can be used to generate solutions of the KdV equation, e.g. as a part of the inverse Non-linear Fourier Transform. Crum transform algorithms that...journal article 2021
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Dominguez, Oscar (author), Veraar, M.C. (author)In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff–Young, Hardy–Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include the Hausdorff–Young and Hardy–Littlewood inequalities and state that the Fourier transform is...journal article 2021
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Leus, G.J.T. (author), Segarra, Santiago (author), Ribeiro, Alejandro (author), Marques, Antonio G. (author)Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph shift operator (GSO), which is a sparse matrix accounting...journal article 2021
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Nguyen, Hieu Thao (author), Soloviev, O.A. (author), Verhaegen, M.H.G. (author)We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical...journal article 2021
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Chimmalgi, S. (author), Wahls, S. (author)The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear bandwidth, signal duration, and power are coupled when singularities in the nonlinear spectrum are...journal article 2020
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Wang, J. (author), Aubry, P.J. (author), Yarovoy, Alexander (author)3-D imaging with irregular planar multiple-input-multiple-output (MIMO) arrays is discussed. Due to signal acquisition on irregular spatial sampling grids by using these antenna arrays, the fast Fourier transform (FFT)-based imaging algorithms cannot readily be used for image formation. To avoid the application of computationally intensive...journal article 2020
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Liang, Jianbin (author), Jiang, James W. (author), Callegaro, Alan Dorneles (author), Bilgin, Berker (author), Dong, J. (author), Reeves, Debbie (author), Emadi, Ali (author)This study presents a numerical modelling approach for the prediction of vibration and acoustic noise for a 24/16 traction switched reluctance machine (SRM). The numerical modelling includes the simulation of electromagnetic force in JMAG, the calculation of natural frequencies and the simulation of vibration and acoustic noise in ACTRAN....journal article 2020
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Bajaj, V. (author), Chimmalgi, S. (author), Aref, Vahid (author), Wahls, S. (author)Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so-called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the...journal article 2020
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de Koster, P.B.J. (author), Wahls, S. (author)Efficient fiber-optic communication requires precise knowledge of the fiber coefficients, but these often change over time due to factors such as aging or bending. We propose a novel algorithm that identifies the average second-order dispersion and Kerr nonlinearity coefficient of a fiber, without employing any special training signals....journal article 2020