Search

We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on $\mathbb R^d$, generalizing known results for constant and linear Poisson structures to polynomial Poisson structures of arbitrary degree. We give several examples of nonlinear Poisson structures and construct explicit formal star products whose deformation parameter can be evaluated to any real value of $\hbar$, giving strict quantizations on the space of analytic functions on $\mathbb R^d$ with infinite radius of convergence. We also address further questions such as continuity of the classical limit $\hbar \to 0$, compatibility with *-involutions, and the existence of positive linear functionals. The latter can be used to realize the strict quantizations as *-algebras of operators on a pre-Hilbert space which we demonstrate in a concrete example., 45 pages, final version

This article presents an efficient nonlinear stochastic finite element method to solve stochastic elastoplastic problems. Similar to deterministic elastoplastic problems, we describe history-dependent stochastic elastoplastic behavior utilizing a series of (pseudo) time steps and go further to solve the corresponding stochastic solutions. For each time step, the original stochastic elastoplastic problem is considered as a time-independent nonlinear stochastic problem with initial values given by stochastic displacements, stochastic strains, and internal variables of the previous time step. To solve the stochastic solution at each time step, the corresponding nonlinear stochastic problem is transformed into a set of linearized stochastic finite element equations by means of finite element discretization and a stochastic Newton linearization, while the stochastic solution at each time step is approximated by a sum of the products of random variables and deterministic vectors. Each couple of the random variable and the deterministic vector is also used to approximate the stochastic solution of the corresponding linearized stochastic finite element equation that can be solved via a weakly intrusive method. In this method, the deterministic vector is computed by solving deterministic linear finite element equations, and corresponding random variables are solved by a non-intrusive method. Further, the proposed method avoids the curse of dimensionality successfully since its computational effort does not increase dramatically as the stochastic dimensionality increases. Four numerical cases are used to demonstrate the good performance of the proposed method.

We associate a complete intersection singularity to a graded matrix factorization of size two of a polynomial in three variables. We show that we get an inverse to the reduction of singularities considered by C.T.C.Wall. We study this for the full strongly exceptional collections in the triangulated category of graded matrix factorizations constructed by H.Kajiura, K.Saito, and the second author., Comment: 18 pages

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetry indices of finite-dimensional unitaries obtained by evaluating such matrix Schur functions at the symmetry protected points $\pm1$. The Schur representation fully covers the complete set of symmetry indices for 1D quantum walks with a group of symmetries realizing any of the symmetry types of the tenfold way. The main advantage of the Schur approach is its validity in the absence of translation invariance, which allows us to go beyond standard Fourier methods, leading to the complete classification of non-translation invariant phases for typical examples., 33 pages, 1 figure

In this paper, we deal with quasilinear Keller--Segel systems with indirect signal production, $$\begin{cases} u_t = \nabla \cdot ((u+1)^{m-1}\nabla u) - \nabla \cdot (u \nabla v), &x \in \Omega,\ t> 0,\\ 0 = \Delta v - \mu(t) + w, &x \in \Omega,\ t> 0,\\ w_t + w = u, &x \in \Omega,\ t> 0, \end{cases}$$ complemented with homogeneous Neumann boundary conditions and suitable initial conditions, where $\Omega\subset\mathbb R^n$ $(n\ge3)$ is a bounded smooth domain, $m\ge1$ and $$\mu(t) := \frac{1}{|\Omega|} w(\cdot, t) \qquad\mbox{for}\ t>0.$$ We show that in the case $m\ge2-\frac{2}{n}$, there exists $M_c>0$ such that if either $m>2-\frac{2}{n}$ or $\int_\Omega u_0 2^\frac{n}{2}n^{n-1}\omega_n$, then there exist radially symmetric initial data such that $\int_\Omega u_0 = M$ and the solution blows up in finite or infinite time, where the blow-up time is infinite if $m=2-\frac2n$. In particular, if $m=2-\frac{2}{n}$ there is a critical mass phenomenon in the sense that $\inf\left\{M > 0 : \exists u_0 \text{ with } \int_\Omega u_0 = M \text{ such that the corresponding solution blows up in infinite time}\right\}$ is a finite positive number., Comment: 18 pages

In this thesis we want to understand properties of families of stable sheaves. First we give a quick introduction to the topic. Then we look at three specific topics regarding families of stable sheaves: a) stability of wrong-way fibers, b) wrong-way fibers and integral functors and c) noncommutative surfaces and deformations. For each topic we collect known results and describe the state-of-the-art methods to study these properties. We end each section with open questions. Then we give a quick summary of our results answering some of the open questions.

In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S-Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD-controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker-structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement-frequency plane.

We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius-Schur indicators of those characters can be computed for p=2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius-Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups., Comment: 14 pages

It is a fun game to complete a partial character table of a finite group. We show that one can reconstruct a missing row or column from a given table. The proof relies on deep properties of fully ramified characters. Moreover, we extend a classification of groups with a "large" character degree started by Snyder and continued by Durfee and Jensen., 8 pages, typo corrected (thanks to \'Angel del R\'io)

Safe and efficient traffic systems constitute a cornerstone of modern life. This thesis provides a comprehensive treatment of the topic of risk in traffic systems. Based on an interdisciplinary research approach, novel models and methodologies are developed to investigate the impact of individual driving style, technological innovation, and traffic system design on safety and efficiency. For this purpose, perspectives and techniques from traffic modeling and insurance mathematics are combined. First, we develop a microscopic traffic model that can describe the occurrence of traffic accidents due to random misperception, a type of error that is relevant for both human drivers and sensors of autonomous vehicles. The model allows us to characterize the real-world tradeoff between safety and efficiency in case studies. Second, we generalize the microscopic traffic model to study the important scenario of an unsignalized urban intersection, a particularly accident-prone area. We apply the concept of random misperception to model the occurrence of accidents and discuss the numerical solution of the random ordinary differential equations involved using state-of-the-art methods. In case studies, we analyze the impact of driving styles on different types of conflicts; we also consider the important case of heterogeneous traffic participants where human drivers and autonomous vehicles coexist. Third, we devise a methodology that makes microscopic traffic models accessible for a statistical study of traffic accidents and corresponding financial losses. The approach enables comprehensive risk management for traffic systems: We study the impact of changes in the design of vehicles and transport systems on functionality and road safety, and price insurance contracts that cover residual risks. Fourth, we complement the above microscopic approaches with a macroscopic perspective: We investigate stochastic cell transmission models of traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation combines simulation, Gaussian process regression, and a stochastic exploration procedure.

In this article we will explore Dirichlet Laplace eigenvalues of balls with spherically symmetric metrics. We will compare any Dirichlet Laplace eigenvalue with the corresponding Dirichlet Laplace eigenvalue on balls in Euclidean space with the same radii. As a special case we shall show that the Dirichlet Laplace eigenvalues of balls with small radii on the sphere are smaller than the corresponding eigenvalues of the Euclidean balls with the same radii. The opposite correspondence is true for the Dirichlet Laplace eigenvalues of hyperbolic spaces.

The six studies collected in this thesis deal with praxeological analyses of mathematical practices in a Signal Transmission module of an electrical engineering study programme. The research framework is the Anthropological Theory of the Didactic (ATD). Our analyses concern the introduction of the Dirac delta impulse in textbooks on signals and systems, the lecturer’s sample solution to an exercise on the envelope demodulator, and the lecturer’s sample solution and the students’ solutions to an exercise on amplitude modulation. Three research foci are developed in the collected studies. The first focus is The subject-specific reconstruction of mathematical practices (Hochmuth & Peters, 2021; Peters & Hochmuth, 2021). We analyse two exercises and the corresponding sample solutions given by the lecturer and students’ solutions. Based on methodological developments we were able to reconstruct aspects of two different mathematical discourses as well as how they interact within the analysed practices. We also propose a graphical representation of the results of our analyses. The second focus is The epistemological and philosophical relationship between mathematics and electrical engineering (Hochmuth & Peters, 2020, 2022). Our aim is to gain a better understanding of the mathematical practices involved in the introduction of the Dirac delta impulse in a textbook on signals and systems. We realised that certain mathematical steps could be better understood from an engineering point of view if historical-philosophical studies of the relationship between physics and mathematics were also taken into account. Here, we are not referring to the philosophical positions of students or lecturers. We are referring to philosophical studies that focus on the societal aspects that play a role in the historical concrete formation of practices. The case of the Dirac impulse is well suited to illustrate the fruitfulness of such studies for subject-specific analyses. Finally, the third focus is Revisiting the relationship between mathematics and electrical engineering, on how ideas for the development of teaching can be derived from the other two perspectives (Peters, 2022; Peters & Hochmuth, 2022). Looking back at our previous studies, we show how our research findings allow for a conceptualisation of the relationship between mathematics and engineering that differs from the standard application and modelling approaches. We also focus on the phenomenon of disconnectedness of the mathematical practices in mathematics service courses and engineering courses.Based on our analyses of engineering mathematical practices, we develop the idea of modifying exercises from a mathematics service course. The key feature of this approach is that it is an alternative to the usual approaches that propose the use of engineering application examples or the use of modelling tasks.

Modern complex drilling systems contain communication nodes like sensors, actuators, and controllers, spread along the lower end of a drill string. Here, temperatures of more than 150 °C and pressure levels up to 200 MPa are present. These environmental conditions and mechanical shocks, are extremely challenging for the reliable use of electronic components. A powerline communication system is designed and evaluated to establish a robust communication channel with low amounts of wiring. This system can operate on highly distorted physical transmission channels by adding redundancy at the sender that can then be used to correct errors at the receiver. In order to synchronize the real-time clocks among different powerline stations, a new preamble extension approach that enables precise time synchronization between multiple bus nodes is added. After design and verification, this system was manufactured in XFAB 180 nm Silicon-On-Insulator (SOI) technology allowing operating temperatures of up to 175 °C. The die size is 5.25 mm × 5.25 mm and contains a complete HomePlug 1.0 communication stack with an environment for boot, interfacing, and debugging. Its data rate reaches 6.1 Mbit/s using the fastest transmission mode and the theoretical maximum of 0.55 Mbit/s in the robust OFDM (ROBO) mode, which is of particular interest for harsh environment applications. After verifying the fabricated die, a Printed Circuit Board (PCB) for climate chamber evaluation was designed and fitted. Measurements in this chamber carried out a maximum ambient temperature of 190 °C for communication with a minimum self-heating of the die of 20 °C measured at room temperature. In combination, this is 35 °C above the specification of the technology process. The timing synchronization evaluation showed a precision of 55.6 ns over the temperature range from -30 °C to 185 °C, which is as low as 1.5 clock cycles. Power measurements of up to 190 °C have shown an average power consumption increase of only 63μW/K below 150 °C and a maximum increase of 394μW/K above 150 °C. To the best of the authors’ knowledge, this is the first high-temperature evaluation of a powerline communication ASIC, which is particularly designed for a drilling system's harsh environment.

First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moment and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.

We refine Cossec and Dolgachev's classification of extra-special Enriques surfaces, providing a complete and concise proof., 9 pages

We discuss when law-invariant convex functionals “collapse to the mean”. More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures. © 2021 The Author(s)

Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset Delta of a finite group G is called a p-base (where p is a prime) if Delta generates a p-group and C_G(Delta) is p-nilpotent. Building on results of Halasi-Mar\'oti, we prove that p-solvable groups possess p-bases of size 3 for every prime p. For other prominent groups we exhibit p-bases of size 2. In fact, we conjecture the existence of p-bases of size 2 for every finite group. Finally, the notion of p-bases is generalized to blocks and fusion systems., Comment: 8 pages, appears in Arch. Math

[no abstract available]

Let K be a field of characteristic 0 and let G and H be connected commutative algebraic groups over K. Let Mor0(G,H) denote the set of morphisms of algebraic varieties G → H that map the neutral element to the neutral element. We construct a natural retraction from Mor0(G,H) to Hom(G,H) (for arbitrary G and H) which commutes with the composition and addition of morphisms. In particular, if G and H are isomorphic as algebraic varieties, then they are isomorphic as algebraic groups. If G has no non-trivial unipotent group as a direct factor, we give an explicit description of the sets of all morphisms and isomorphisms of algebraic varieties between G and H. We also characterize all connected commutative algebraic groups over K whose only variety automorphisms are compositions of automorphisms of algebraic groups with translations.

We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in $$\mathbb {C}^n$$ C n . As an application we discuss semi-simplicity and the spectral invariance of these algebras. The different function Hilbert spaces are dealt with in parallel in successive chapters so that a direct comparison of the results is possible. As a new aspect of the theory we define commutative Toeplitz algebras over spaces of functions in infinitely many variables and present some structural results. The paper concludes with a short list of open problems in this area of research.

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability., Corrected a statement in Section 6.3

We exhibit a precise connection between N\'eron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to compute Beilinson--Bloch heights in higher dimensions., Comment: 21 pages. Updated references and took referee comments into account. Final version

This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

We introduce a generalized concept of solutions for reaction–diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.

This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds., A new appendix

[no abstract available]

[no abstract available]

Let $X$ be a semistable curve and $L$ a line bundle whose multidegree is uniform, i.e., in the range between those of the structure sheaf and the dualizing sheaf of $X$. We establish an upper bound for $h^0(X,L)$, which generalizes the classic Clifford inequality for smooth curves. The bound depends on the total degree of $L$ and connectivity properties of the dual graph of $X$. It is sharp, in the sense that on any semistable curve there exist line bundles with uniform multidegree that achieve the bound., Added Corollary 4.5 and Lemma 4.10, as well as some changes in presentation following a referee report. 19 pages, 4 Figures. Final version, to appear in Math. Z

[no abstract available]

In characteristic 0 irreducible tensor products of representations of symmetric and alternating groups have been described by Zisser and by Bessenrodt and Kleshchev. In positive characteristic a classification conjecture for such products for symmetric groups was formulated by Gow and Kleshchev. Parts of the conjecture were proved shortly after in papers of Bessenrodt and Kleshchev and of Graham and James. However many cases in characteristic 2 for n even were still open. For alternating groups in characteristics p at least irreducible tensor products have been described in a paper of Bessenrodt and Kleshchev, though not for smaller p. In the submitted papers I consider the still open cases, completing the classification of irreducible tensor products of representations of symmetric and alternating groups up to a certain class of tensor products for alternating groups in characteristic 2.

[no abstract available]

In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any characteristic. Following Severi's original idea, this gives a new proof of the irreducibility of the moduli space of smooth projective curves of a given genus in positive characteristic. It is the first proof that involves no reduction to the characteristic zero case. As a further consequence, we generalize Zariski's theorem to positive characteristic and show that a general reduced planar curve of a given geometric genus is nodal., 36 pages, 9 figures. v2: Minor changes throughout the paper. v3: Added two references. Final version, to appear in Publ. Math. IH\'ES

In this work we classify the multiplicity-free Kronecker products of irreducible characters of the alternating groups.

This article considers a coupled finite and boundary element method for an interface problem for the acoustic wave equation. Well-posedness, a priori and a posteriori error estimates are discussed for a symmetric space-time Galerkin discretization related to the energy. Numerical experiments in three dimensions illustrate the performance of the method in model problems.

On the seven dimensional Euclidean sphere S7 we compare two subriemannian structures with regards to various geometric and analytical properties. The first structure is called trivializable and the underlying distribution HT is induced by a Clifford module structure of R8. More precisely, HT is rank 4, bracket generating of step two and generated by globally defined vector fields. The distribution HQ of the second structure is of rank 4 and step two as well and obtained as the horizontal distribution in the quaternionic Hopf fibration S3↪ S7→ S4. Answering a question in: Markina and Godoy Molina (Rev Mat Iberoam 27(3), 997–1022, 2011) we first show that HQ does not admit a global nowhere vanishing smooth section. In both cases we determine the Popp measures [20], the intrinsic sublaplacians ΔsubT and ΔsubQ and the nilpotent approximations. We conclude that both subriemannian structures are not locally isometric and we discuss properties of the isometry group. By determining the first heat invariant of the sublaplacians it is shown that both structures are also not isospectral in the subriemannian sense.

In this paper, we derive, from a general Simonenko's local principle, Fredholm criteria for restriction to isotypical components. More precisely, we give a full proof, of the equivariant local principle for restriction to isotypical components of invariant pseudodifferential operators announced in \cite{BCLN2}. Furthermore, we extend this result by relaxing the hypothesis made in the preceding quoted paper., Comment: arXiv admin note: text overlap with arXiv:2004.01543

[no abstract available]

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena. © 2021 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.

The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of H-matrices. Under a technical assumption on the mesh, we prove that root exponential convergence in the block rank can be achieved, if the block structure conforms to a standard admissibility criterion.

[no abstract available]

This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.

[no abstract available]

A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the deflection of the plate is derived. The latter paves the way for the construction of energy minimizers and also provides the Euler–Lagrange equation satisfied by these minimizers. A by-product is the monotonicity of the electrostatic energy with respect to the deflection.

Cryogenic turning can be used to produce deformation-induced martensite in metastable austenitic steels. Martensite exhibits a higher hardness than austenite and increases the wear resistance of the workpiece. In order to reliably induce a desired martensite content in the subsurface zone during the turning process, a non-destructive, contactless and real-time testing method is necessary. Eddy current testing is an electromagnetic method that is non-destructive, non-contact and real-time capable. Furthermore, eddy current testing has been integrated into production processes many times. Eddy current testing can be used to detect the transformation of paramagnetic austenite to ferromagnetic α′-martensite based on the change in magnetic and electrical properties. Thus, the newly formed subsurface can be characterized and the manufacturing process can be monitored. The objective of this study was to understand the correlation of eddy current testing signals with newly formed α′-martensite in the subsurface of AISI 304 and to quantify the amount formed. The measurements were performed within a machining center. Several methods for reference measurement of martensite content are known in the literature. However, depending on the method used, large discrepancies may occur between the determined contents. Therefore, different analytical methods were used for reference measurements to determine the total martensite content in the subsurface. Metallographic sections, magnetic etching, Mössbauer spectroscopy, and X-ray diffraction with two different analytical methods were employed. Based on the correlation between the eddy current testing signals and the α′-martensite content in the subsurface, process control of the manufacturing process can be achieved in the future.

[no abstract available]

Flexoelectricity is a universal electro-mechanical coupling effect that occurs in dielectrics of all symmetric groups and becomes dominant at the micro- and nano-scales. It plays an important role in evaluating micro-electro-mechanical systems (MEMS) such as energy harvesters which convert vibrational energy to electric energy. At finer length scales, micro-inertia effects significantly contribute to the behavior of flexoelectric materials due to the mechanical dispersion. Hence, to properly characterize the vibrational behavior of MEMS, a reliable theoretical approach is required accounting for all possible phenomena that affect the output of the system such as voltage or power density. In this work, we present a consistent (dynamic) model and associated computational framework for flexoelectric structures to study the characteristics of the vibrational behavior of energy harvesters showing the dominance of the flexoelectric effect at micro- and nano-scales. In this context, we quantify the impact of the micro-inertia length scale and the flexoelectric dynamic parameter on both frequency and time responses of energy harvesters.

[no abstract available]

We prove that the centralizer of a Coxeter element in an irreducible Coxeter group is the cyclic group generated by that Coxeter element., Comment: 10 pages; v2: minor corrections and revision of section 4

With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick’s law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring U, j-characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At T = 1123.15 K and j = 8000 A/m2, 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.