arXiv subjects

Andreas Otto

Publications and source records attributed to Andreas Otto.

At least 19 recordsLinked to original sources

arXiv2025

Universal Numerical Simulation Model for Laser Material Processing

High power lasers are used for a variety of manufacturing processes on time and length scales that cover many orders of magnitude and on different materials. The variety of processes achievable through laser-material interaction results from numerous coupled, nonlinear physical phenomena. Simulation models can be used to gain process understanding, explain experimentally observed phenomena, and optimize or design processes. However, the inherent complexity and diversity of the phenomena make modeling a challenging task. Within this chapter, a universal model is presented that accurately simulates a broad spectrum of processes, including welding, additive manufacturing, cutting, ablation, drilling, and surface structuring, encompassing both continuous wave and ultrashort pulsed lasers and their interaction with various materials. Starting from the fundamental principles of conservation of mass, momentum, and energy, a continuum mechanical framework is introduced that captures the main multiphysical effects. A numerical solution using the Finite Volume Method is presented and validated against benchmark problems where detailed experimental data are available. Macroscopic examples with continuous wave lasers include keyhole drilling and collapse under stationary illumination as well as melt pool dynamics and pore formation in copper welding. At the microscopic level, copper ablation with femtosecond pulses is simulated. Finally, a set of real-world applications is shown, where the model helps to explain and optimize industrial phenomena and defects. Examples include deep penetration welding of steel with dynamic beam shaping, multilayer additive manufacturing via powder bed fusion, and ultrashort pulsed drilling of micro vias in dielectric materials.

physics.optics↗

arXiv2025

Rate-independent hysteretic energy dissipation in collagen fibrils

Nanoindentation cycles measured with an atomic force microscope on hydrated collagen fibrils exhibit a rate-independent hysteresis with return point memory. This previously unknown energy dissipation mechanism describes in unified form elastoplastic indentation, capillary adhesion, and surface leveling at indentation velocities smaller than 1 $\mu$m s$^{-1}$, where viscous friction is negligible. A generic hysteresis model, based on force-distance data measured during one large approach-retract cycle, predicts the force (output) and the dissipated energy for arbitrary indentation trajectories (input). While both quantities are rate independent, they do depend nonlinearly on indentation history and on indentation amplitude.

cond-mat.soft↗

arXiv2025

A particle-based approach for the prediction of grain microstructures in solidification processes

Grain microstructures are crucial to the mechanical properties, performance, and often lifetime of metallic components. Hence, the prediction of grain microstructures emerging from solidification processes at relevant macroscopic scale is essential to the design or optimization of new alloys and processing conditions. Yet, despite the broad range of multi-scale models proposed so far, all of them suffer from computational limitations, such that advances from computational and algorithm perspectives remain needed. Here, we present a novel approach for tracking crystallographic solidification grain envelopes capable of predicting competitive growth scenarios and columnar-to-equiaxed transitions for stationary grains. The model relies on classical assumptions and equations in use in several broadly used and thoroughly validated approaches (e.g. cellular automata). Yet, our approach defines the grain envelope using Lagrangian particles and tracks their evolution using an algorithm and an implementation relying on scalable libraries and using modern CPU/GPU architectures. The model is used to simulate several benchmarks of increasing complexity, and the results are compared to analytical, experimental, and numerical results from literature for the purpose of model validation. To highlight the applicability to real-world processes and the possibility of coupling the model with existing physics-based simulation tools, the model is also (one-way) coupled with a multiphysics laser-material-interaction model to simulate competitive grain growth during laser beam welding of steel.

cond-mat.mtrl-sci↗

arXiv2023

A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells

We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We initially explore a single-protein model with a constraint equation governing the total resource available to the cell. The model is then extended to include three proteins that share a resource pool. Three approaches are considered at constant delay to numerically detect oscillations. First, we use a spectral element method to approximate the system as a discrete map and evaluate the stability of the linearized system about its equilibria by examining its eigenvalues. For the second method, we plot amplitudes of the simulation trajectories in 2D projections of the parameter space. We use a history function that is consistent with published experimental results to obtain metabolic oscillations. Finally, the spectral element method is used to convert the system to a boundary value problem whose solutions correspond to approximate periodic solutions of the system. Our results show that certain combinations of total resource available and the time delay, lead to oscillations. We observe that an oscillation region in the parameter space is between regions admitting steady states that correspond to zero and constant production. Similar behavior is found with the three-protein model where all proteins require the same production time. However, a shift in the protein production rates peaks occurs for low available resource suggesting that our model captures the shared resource pool dynamics.

math.DS↗

arXiv2022

Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness

In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using a finite-element method (FEM) allowed to model two-dimensional waveguide cross sections of arbitrary shape but only finite size. Here, we extend our FEM propagating-wave dynamic-matrix approach from finite waveguides to the important practical cases of infinitely-extended mono- and multilayers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of motion of magnetization is solved as an eigenvalue problem only on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution in multilayer systems, we introduce interlayer-exchange interaction into our FEM approach. With the calculation of dynamic dipolar fields being the main focus of this paper, we also extend the previously presented plane-wave Fredkin-Koehler method to calculate the dipolar potential of spin waves in infinite layers. The major benefit of this method is that it avoids the discretization of any non-magnetic material, such as non-magnetic spacers in multilayers. Therefore, the computational effort becomes completely independent on the spacer thicknesses. Furthermore, it keeps the resulting discretized eigenvalue problem sparse, which therefore, inherits a comparably low arithmetic complexity. As a validation of our method (implemented into the open-source finite-element micromagnetic package TetraX), we present results for various systems and compare them with theoretical predictions as well as with established finite-difference numerical methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems.

cond-mat.mes-hall↗

arXiv2022

Laminar Chaos

We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity remains almost constant, but its level varies chaotically from phase to phase. In scalar systems the periodic dynamics of the lengths and the chaotic dynamics of the intensity levels can be understood and also tuned via two one-dimensional maps, which can be deduced from the nonlinearity of the delay equation and from the delay variation, respectively.

nlin.CD↗

arXiv2021

The dynamics of a driven harmonic oscillator coupled to pairwise interacting Ising spins in random fields

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we investigated recently the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins in a random field. Although such a system does not produce hysteresis, we showed how to characterize the dynamics of such a piecewise-smooth system, especially in the case of a large number of spins [P. Zech, A. Otto, and G. Radons, Phys. Rev. E 101, 042217 (2020)]. In this paper we extend our model to spin dimers, thus pairwise interacting spins. We show in which cases two interacting spins can show elementary hysteresis and we give a connection to the Preisach model, which allows us to consider an infinite number of spin-pairs. This thermodynamic limit leads us to a dynamical system with an additional hysteretic force in the form of a generalized play operator. By using methods from general chaos theory, piecewise-smooth system theory and statistics we investigate the chaotic behavior of the dynamical system for a few spins and also in case of a larger number of spins by calculating bifurcation diagrams, Lyapunov exponents, fractal dimensions and self-averaging properties. We find that the fractal dimensions and the magnetization are in general not self-averaging quantities. We show, how the dynamical properties of the piecewise-smooth system for a large number of spins differs from the system in its thermodynamic limit.

nlin.CD↗

arXiv2021

Topological Feature Vectors for Chatter Detection in Turning Processes

Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays, and stochastic effects. Due to the nature of these models as well as the practical challenges which include time-varying parameters, the transition from numerical/analytical modeling of machining to the analysis of real cutting signals remains challenging. Some studies have focused on studying the time series of cutting processes using machine learning algorithms with the goal of identifying and predicting undesirable vibrations during machining referred to as chatter. These tools typically decompose the signal using Wavelet Packet Transforms (WPT) or Ensemble Empirical Mode Decomposition (EEMD). However, these methods require a significant overhead in identifying the feature vectors before a classifier can be trained. In this study, we present an alternative approach based on featurizing the time series of the cutting process using its topological features. We first embed the time series as a point cloud using Takens embedding. We then utilize Support Vector Machine, Logistic Regression, Random Forest and Gradient Boosting classifier combined with feature vectors derived from persistence diagrams, a tool from persistent homology, to encode chatter's distinguishing characteristics. We present the results for several choices of the topological feature vectors, and we compare our results to the WPT and EEMD methods using experimental turning data. Our results show that in two out of four cutting configurations the TDA-based features yield accuracies as high as 97%. We also show that combining Bezier curve approximation method and parallel computing can reduce runtime for persistence diagram computation of a single time series to less than a second thus making our approach suitable for online chatter detection.

eess.SP↗

arXiv2021

Finite-element dynamic-matrix approach for spin-wave dispersions in magnonic waveguides with arbitrary cross section

We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally invariant along the waveguide. Our method is based on the propagating-wave dynamic-matrix approach by Henry et al. and extends it to arbitrary cross sections using a finite-element method. We solve the linearized equation of motion of the magnetization only in a single waveguide cross section which drastically reduces computational effort compared to common three-dimensional micromagnetic simulations. In order to numerically obtain the dipolar potential of individual spin-wave modes, we present a plane-wave version of the hybrid finite-element/boundary-element method by Frekdin and Koehler which, for the first time, we extend to a modified version of the Poisson equation. Our method is applied to several important examples of magnonic waveguides including systems with surface curvature, such as magnetic nanotubes, where the curvature leads to an asymmetric spin-wave dispersion. In all cases, the validity of our approach is confirmed by other methods. Our method is of particular interest for the study of curvature-induced or magnetochiral effects on spin-wave transport but also serves as an efficient tool to investigate standard magnonic problems.

cond-mat.mes-hall↗

arXiv2020

Non-perturbative signatures of non-linear Compton scattering

The probabilities of various elementary laser - photon - electron/positron interactions display in selected phase space and parameter regions typical non-perturbative dependencies such as $\propto {\cal P} \exp\{- a E_{crit} /E\}$, where ${\cal P}$ is a pre-exponential factor, $E_{crit}$ denotes the critical Sauter-Schwinger field strength, and $E$ characterizes the (laser) field strength. While the Schwinger process with $a = a_S \equiv π$ and the non-linear Breit-Wheeler process in the tunneling regime with $a = a_{n \ell BW} \equiv 4 m / 3 ω'$ (with $ω'$ the probe photon energy and $m$ the electron/positron mass) are famous results, we point out here that also the non-linear Compton scattering exhibits a similar behavior when focusing on high harmonics. Using a suitable cut-off $c > 0$, the factor $a$ becomes $a = a_{n \ell C} \equiv \frac23 c m /(p_0 + \sqrt{p_0^2 -m^2)}$. This opens the avenue towards a new signature of the boiling point of the vacuum even for field strengths $E$ below $E_{crit}$ by employing a high electron beam-energy $p_0$ to counter balance the large ratio $E_{crit} / E$ by a small factor $a$ to achieve $E / a \to E_{crit}$. In the weak-field regime, the cut-off facilitates a threshold leading to multi-photon signatures showing up in the total cross section at sub-threshold energies.

hep-ph↗

arXiv2020

The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields

We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable to show complex hysteresis. The system is a combination of a continuous (harmonic oscillator) and a discrete (RFIM) subsystem, which classifies it as a hybrid system. In this paper we focus on the hybrid nature of the system and consider only independent spins in quenched random local fields, which can already lead to complex dynamics such as chaos and multistability. We study the dynamic behavior of this system by using the theory of piecewise-smooth dynamical systems and discontinuity mappings. Specifically, we present bifurcation diagrams, Lyapunov exponents as well as results for the shape and the dimensions of the attractors and the self-averaging behavior of the attractor dimensions and the magnetization. Furthermore we investigate the dynamical behavior of the system for an increasing number of spins and the transition to the thermodynamic limit, where the system behaves like a driven harmonic oscillator with an additional nonlinear smooth external force.

nlin.CD↗

arXiv2020

Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos

Recently, it was shown that certain systems with large time-varying delay exhibit different types of chaos, which are related to two types of time-varying delay: conservative and dissipative delays. The known high-dimensional Turbulent Chaos is characterized by strong fluctuations. In contrast, the recently discovered low-dimensional Laminar Chaos is characterized by nearly constant laminar phases with periodic durations and a chaotic variation of the intensity from phase to phase. In this paper we extend our results from our preceding publication [J. D. Hart, R. Roy, D. Müller-Bender, A. Otto, and G. Radons, PRL 123 154101 (2019)], where it is demonstrated that Laminar Chaos is a robust phenomenon, which can be observed in experimental systems. We provide a time-series analysis toolbox for the detection of robust features of Laminar Chaos. We benchmark our toolbox by experimental time series and time series of a model system which is described by a nonlinear Langevin equation with time-varying delay. The benchmark is done for different noise strengths for both the experimental system and the model system, where Laminar Chaos can be detected, even if it is hard to distinguish from Turbulent Chaos by a visual analysis of the trajectory.

nlin.AO↗

arXiv2020

On Transfer Learning For Chatter Detection in Turning Using Wavelet Packet Transform and Empirical Mode Decomposition

The increasing availability of sensor data at machine tools makes automatic chatter detection algorithms a trending topic in metal cutting. Two prominent and advanced methods for feature extraction via signal decomposition are Wavelet Packet Transform (WPT) and Ensemble Empirical Mode Decomposition (EEMD). We apply these two methods to time series acquired from an acceleration sensor at the tool holder of a lathe. Different turning experiments with varying dynamic behavior of the machine tool structure were performed. We compare the performance of these two methods with Support Vector Machine (SVM), Logistic Regression, Random Forest Classification and Gradient Boosting combined with Recursive Feature Elimination (RFE). We also show that the common WPT-based approach of choosing wavelet packets with the highest energy ratios as representative features for chatter does not always result in packets that enclose the chatter frequency, thus reducing the classification accuracy. Further, we test the transfer learning capability of each of these methods by training the classifier on one of the cutting configurations and then testing it on the other cases. It is found that when training and testing on data from the same cutting configuration both methods yield high accuracies reaching in one of the cases as high as 94% and 95%, respectively, for WPT and EEMD. However, our experimental results show that EEMD can outperform WPT in transfer learning applications with accuracy of up to 95%.

eess.SP↗

arXiv2019

Time delay effects in the control of synchronous electricity grids

The expansion of inverter-connected generation facilities (i.e. wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change. Whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying power system and the control mechanisms that keep it close to a desired reference state, were not designed for such a low inertia system, this might make the system vulnerable to disturbances. In this paper, we will investigate whether the currently used control mechanisms are able to keep a low inertia system stable and how this is effected by the time delay between a frequency deviation and the onset of the control action. We integrate the control mechanisms used in continental Europe into a model of coupled oscillators which resembles the second order Kuramoto model. This model is then used to investigate how the interplay of changing inertia, network topology and delayed control effects the stability of the interconnected power system. To identify regions in parameter space that make stable grid operation possible, the linearized system is analyzed to create the system's stability chart. We show that lower and distributed inertia could have a beneficial effect on the stability of the desired synchronous state.

nlin.AO↗

arXiv2019

Chatter Detection in Turning Using Machine Learning and Similarity Measures of Time Series via Dynamic Time Warping

Chatter detection from sensor signals has been an active field of research. While some success has been reported using several featurization tools and machine learning algorithms, existing methods have several drawbacks such as manual preprocessing and requiring a large data set. In this paper, we present an alternative approach for chatter detection based on K-Nearest Neighbor (kNN) algorithm for classification and the Dynamic Time Warping (DTW) as a time series similarity measure. The used time series are the acceleration signals acquired from the tool holder in a series of turning experiments. Our results, show that this approach achieves detection accuracies that in most cases outperform existing methods. We compare our results to the traditional methods based on Wavelet Packet Transform (WPT) and the Ensemble Empirical Mode Decomposition (EEMD), as well as to the more recent Topological Data Analysis (TDA) based approach. We show that in three out of four cutting configurations our DTW-based approach attains the highest average classification rate reaching in one case as high as 99% accuracy. Our approach does not require feature extraction, is capable of reusing a classifier across different cutting configurations, and it uses reasonably sized training sets. Although the resulting high accuracy in our approach is associated with high computational cost, this is specific to the DTW implementation that we used. Specifically, we highlight available, very fast DTW implementations that can even be implemented on small consumer electronics. Therefore, further code optimization and the significantly reduced computational effort during the implementation phase make our approach a viable option for in-process chatter detection.

eess.SP↗

arXiv2018

Assisted Vacuum Decay by Time Dependent Electric Fields

We consider the vacuum decay by electron-positron pair production in spatially homogeneous, time dependent electric fields by means of quantum kinetic equations. Our focus is on the impact of various pulse shapes as envelopes of oscillating fields and the assistance effects in multi-scale fields, which are also seen in photons accompanying the creation and motion of pairs.

hep-ph↗

arXiv2017

Afterglow of the dynamical Schwinger process: soft photons amass

We consider the conversion of an electric field into photons as a secondary probe of the dynamical Schwinger process. In spatially homogeneous electric fields, quantum fluctuations of electron-positron ($e^+e^-$) pairs are lifted on the mass shell leaving asymptotically a small finite pair density. The $e^+e^-$ dynamics in turn couples to the quantized photon field and drives its on-shell mode occupation. The spectral properties of the emerging asymptotic photons accompanying the Schwinger process are calculated in lowest-order perturbation theory. Soft photons in the optical range are produced amass in the sub critical region, thus providing a promising discovery avenue, e.g. for laser parameters of the Extreme Light Initiative (ELI-NP) to be put in operation soon.

hep-ph↗

arXiv2017

From dynamical systems with time-varying delay to circle maps and Koopmanism

In the present paper we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay. The Koopman operator corresponds to an iterated map, called access map, which is defined by the iteration of the delayed argument of the delay equation. The dynamics of this one-dimensional iterated map determines the universality classes of the infinite-dimensional state dynamics governed by the delay differential equation. In this way, we connect the theory of time-delay systems with the theory of circle maps and the framework of the Koopman operator. In the present paper we extend our previous work [Otto, Müller, and Radons, Phys. Rev. Lett. 118, 044104 (2017)], by elaborating the mathematical details and presenting further results also on the Lyapunov vectors.

nlin.CD↗