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SachComicWissen
(2018)
Klartext lesen! Unbedingt!
(2018)
Max im Comic
(2020)
Science Comics
(2021)
A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations
(2023)
For terminal value problems of fractional differential equations of order α∈(0,1) that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select the required initial values that solves such shooting problems quickly and accurately. Numerical experiments indicate that this new proportional secting technique converges very quickly and accurately to the solution. Run time measurements indicate a speedup factor of between 4 and 10 when compared to the standard bisection method.
The present article offers new evidence on the Unger playing-card making family of Győr,Western Transdanubia, as the result of a cross-disciplinary study. Mátyás Unger the Elder (1789-1862) andhis like-named son Mátyás the Younger (1824–1878) produced various types of playing-cards from theearly to mid-19th century. In particular, their cards, their iconography, design and production process will beanalysed. The family is best known for their cards with Sopron (Oedenburg) pattern. Also discussed will bethe role of Mátyás the Elder’s second eldest son Alajos Unger as a possible designer of the later Unger cards,which were of considerably higher quality than the earlier known ones by Mátyás Unger the Elder. Thehitherto little-known Alajos Unger was trained as a draughtsman and painter first at the National DrawingSchool of his hometown and then, between 1833 and 1842, at the Vienna Academy of Fine Arts, particularlyunder Leopold Kupelwieser (1796–1862). Finally an innovative outside-in bottom-up method for gainingfurther, reliable insight into 19thcentury artisanal playing-card manufacturing will be proposed to determinethe size, output and profitability of the Unger workshop based on material-flow simulation.
Alajos (Alois) Unger, who was descended from the well-known Unger playing- card making family from Győr, is a recently rediscovered Hungarian late Nazarene and late Romanticist artist. The son and brother of the playing-card makers Mátyás (Mathias) Unger the Elder (1789-1862) and Younger (1824-78), he was originally apprenticed in this craft as well and, as could be proved for the first time, designed the family’s playing-cards. First trained at the National Drawing School of his hometown under János Hofbauer (creator of The Castle of Dévény, Hungarian National Gallery), which apprentices and journeymen of the local crafts attended, Alajos Unger enrolled at the Vienna Academy of Fine Arts first in 1833 to train there as a draughtsman and then became a pupil of Leopold Kupelwieser (1796-1862) from 1836 until 1842. Among his classmates were the famous artists Eduard von Engerth (1818-97), Franz Josef Dobiaschofsky (1818-67), Ferenc Szoldatits (1820-1916) and August von Pettenkofen (1822-1889). In an art exhibition in Győr in 1903 the quality of Unger’s genre paintings displayed there was likened to those of the latter.
It has now been possible to demonstrate how strongly his art was rooted in the late Nazarene and late Romanticist tradition of the circle around his teacher. Overall, his style not only reflects the ’’literary-musical-artistic” orientation of Kupelwieser, but also the ”fairytale-like-poetical” variety represented by Joseph von Führich and particularly Moritz von Schwind.
Alajos Unger had until recently only been known by name, but with the present article, a fuller picture of the artist’s life and work has been presented. Thus, apart from the two oil paintings, which came into the possession of the Hungarian National Gallery in the 1970s, The Recapture ofRaab (1840) and a portrait of the artist and his family (1843), a series of hitherto unknown oilworks has been discovered: a portrait of an unknown lady (1836), now part of the art collection of the University of Pennsylvania, a copy of Cesare da Sesto’s La vierge au bas-relief (date unknown), the Baptism of Vajk (1842) and a Biedermeier picture clock depicting a patriotic scene from the opera Lucia di Lammermoor set against the backdrop of a veduta of Venice (1847). The portrait of Ferenc Hergeszell, a local politician from Unger’s hometown and later member of the Hungarian Diet, from 1841, now in the collection of the Flóris Römer Museum in Győr, also bears Unger’s painterly handwriting.
Altogether, the torso of the extraordinary work of a representative of a younger generation of Nazarenes, who promoted Hungarian national art, has been unveiled in the bicentenary of his birth. In addition to this, the role of Nazarene artists and that of their networks in the development of Hungarian art generally was investigated.
This paper will deals with the Nazarene Movement and its art in Hungary
with special reference to Alajos (Alois) Unger, a recently rediscovered artist of Hungary’s Reform Era, his links to Nazarene art, the relevance of (functional) semiotics in the interpretation of Nazarene works
and the influence of the Nazarene Movement on the arts and crafts of the 19th century. This includes the design of new playing-card patterns in Hungary
The Unger Family from Győr: The Social Semiotics, Political Iconography and Manufacture of their 19th Century Playing Cards Mátyás (Mathias) Unger the Elder (1789–1862) and his eponymous son Mátyás (Mathias) the Younger (1824–1878) from Győr are prominent in the history of the Hungarian playing cards. Due to more recent research, new details about the family and their playing cards have surfaced. This includes the fact that another son of Mátyás Unger the Elder was Alajos (Alois) Unger (1814–1848), an academic painter trained at the Vienna Academy of Arts, particularly under Leopold Kupelwieser and Johann Ender, in late Nazarene, late Romantic style.
New findings on the Unger playing cards are presented drawing on social semiotics and its relationship to political iconography, whereby cards are considered as text and the two categories of denotation and connotation pivotal. Change in connotation and meaning is analysed to provide further explanation for how the four season cards, i.e. Tell cards (magyar kártya), today‘s standard pattern, came about with lost Unger playing cards serving as a missing link. These Unger cards reflected the art policy of the Austrian Empire of the time as image propaganda for the Casa d’Austria linked with the pietas austriaca/hungarica, in line with Alajos Unger’s oil paintings. Over time, the connotation of the Tell cards changed into a clear anti-Habsburg stance. Further reasons for why this pattern became standard in Hungary and how the four seasoned Däuser cards, popularized by the Ungers, must have become part of it are also given. Against this background, a novel bottom-up material flow simulation approach is proposed to investigate the artisanal playing card production process, output and profitability of the small workshop of the Ungers together with a research agenda for adapting it to the building and conditions of the last known production site, all on the basis of a reconstruction.
Object of our interest is an elastic body Ω ⊂ ℝ3 which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field.
Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.
Discourse analysis has greatly relied on the tried and tested methods of data collection as well as on the use of traditional corpora. The question therefore arises as to how far the Internet has changed methodology in discourse analysis and to what degree it will do so in the future. A further issue that results from the possibilities the Web offers is whether traditional corpora will still be necessary to thoroughly investigate the structure and functioning of language and discourse, with regard to both native and non-native speech. In this paper the opportunities the Internet offers, the availability of tools to the researcher in using the Internet in DA but also the limits and dangers the linguist is prone to encounter will be investigated. And finally it will be discussed whether traditional empirical methods will still play any role in discourse analysis in future.
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of such representations have been proposed. Concentrating on Riemann-Liouville integrals whose order is in (0,1), we here present a general approach that comprises most of these variants as special cases and that allows a detailed investigation of the analytic properties of each variant. The availability of this information allows to choose concrete numerical methods for handling the representations that exploit the specific properties, thus allowing to construct very efficient overall methods.
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known variants of this approach is that they require the numerical approximation of some integrals over an unbounded integral whose integrand decays rather slowly, which implies that their numerical handling is difficult and costly. We present a novel variant of such a diffusive representation. This form also requires the numerical approximation of an integral over an unbounded domain, but the integrand decays much faster. This property allows to use well established quadrature rules with much better convergence properties.
This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights w:= exp (−Q) with finite moments and with smooth external fields Q:R→[0,∞), with varying smooth convex rate of increase for large argument. Our analysis relies in part on weighted polynomial interpolation at the zeros of orthonormal polynomials with respect to w2. We also study bounds for the first derivatives of a class of functions of the second kind for w2.
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory-efficient. Moreover, the method’s design is such that good convergence properties may be expected. In this paper, we commence a systematic investigation of these convergence properties.
We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on R, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional differential operators, in particular regarding the high computational complexity and the high memory requirements. The infinite state representation is an approach on which one can base numerical methods that overcome these obstacles. Such algorithms contain a number of parameters that influence the final result in nontrivial ways. Based on numerical experiments, we initiate a study leading to good choices of these parameters.
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results.
As in the embedded systems domain, energy efficiency has recently become one of the main design criteria in high performance computing. The European Union Horizon 2020 project READEX (Run-time Exploitation of Application Dynamism for Energy-efficient eXascale computing) has developed a tools-aided auto-tuning methodology inspired by system scenario based design. Applying similar concepts as those presented in earlier chapters of this book, the dynamic behavior of HPC applications is exploited to achieve improved energy efficiency and performance. Driven by a consortium of European experts from academia, HPC resource providers, and industry, the READEX project has developed the first generic framework of its kind for split design-time and run-time tuning while targeting heterogeneous systems at the Exascale level. Using a real-life boundary element application, energy savings of more than 30% can be shown.
This article describes fundamental approaches for the numerical handling of problems arising in fractional calculus. This includes, in particular, methods for approximately computing fractional integrals and fractional derivatives, where the emphasis is placed on Caputo operators, as well as solvers for the associated differential and integral equations.
This article describes the fundamentals of the theory of ordinary fractional differential equations of Caputo’s type. Starting from the existence and uniqueness of solutions and the well-posedness in general, the flow of topics continues via a derivation of explicit solution formulas for certain important classes of problems and the discussion of their smoothness properties to the stability properties of these solutions. The main focus is on initial value problems, but terminal value problems are briefly considered as well. In addition to dealing with standard single-order problems, the presentation also contains a short discussion of multiterm equations and multiorder systems.
Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can usually not be solved analytically. In this article, we provide a survey of the most important numerical methods. We restrict our attention to those types of fractional differential equations that are most important in the context of viscoelasticity, i.e., we discuss numerical methods for ordinary fractional differential equations and for certain types of time-fractional partial differential equations. Space-fractional partial differential equations are not discussed.
A note on the well-posedness of terminal value problems for fractional differential equations
(2018)
This note is intended to clarify some important points about the well-posedness of terminal value problems for fractional differential equations. It follows the recent publication of a paper by Cong and Tuan in this journal, in which a counter-example calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights, that a wide class of terminal value problems of fractional differential equations is well posed, and we identify those cases where the well-posedness question must be regarded as open.
Das Buch Programmieren in C++ für Elektrotechniker und Mechatroniker bietet einen Einstieg in die moderne Softwareentwicklung für Studierende der Ingenieurwissenschaften. Dabei wird ein durchgängiger Ansatz verfolgt, der, beginnend mit den Grundlagen der Programmierung, bis hin zu weiterführenden Themen, wie Hardware-nahe Programmierung, zahlreiche Themengebiete betrachtet und Studierende nicht nur für die Prüfung, sondern auch für den Arbeitsalltag vorbereitet. Da man Programmieren nur durch Üben erlernen kann, liefert das Buch einen umfangreichen Aufgabenkatalog.
Für Großunternehmen ist die Nachhaltigkeitskommunikation längst keine Nebendisziplin mehr. Was vor 20 Jahren noch als Nischenthema galt, ist heute eines der wichtigsten Strategiethemen für Unternehmen. Die Chemieindustrie steht vor der kommunikativen Herausforderung die Nachhaltigkeitsleistung aus den hoch komplexen Wertschöpfungsketten für eine breite Öffentlichkeit verständlich aufzubereiten. Eine Fokussierung auf wesentliche Kennzahlen und Themen ist dabei unerlässlich. Aufgrund der herausragenden Bedeutung des Themas für die Unternehmen, aber auch für die Gesellschaft an sich, bedarf es der Erstellung und Ausspielung von möglichst hochwertigem und zweckvollem Content seitens der Unternehmen.
The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson–Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle θ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with θ only within an interval around 90°. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle.
The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off.
The interfacial premelting in ice/clay nano composites was studied by high energy X-ray diffraction. Below the melting point of bulk water, the formation of liquid water was observed for the ice/vermiculite and ice/kaolin systems. The liquid fraction is gradually increasing with temperature. For both minerals, similar effective premelting layer thicknesses of 2–3 nm are reached 3 K below the bulk melting point. For the quantitative description of the molten water fraction in wet clay minerals we developed a continuum model for short range interactions and arbitrary pore size distributions. This model quantitatively describes the experimental data over the entire temperature range. Model parameters were obtained by fitting using a maximum entropy (MaxEnt) approach. Pronounced differences in the deviation from Antonow's rule relating interfacial free energy between ice, water, and clay are observed for the charged vermiculite and uncharged kaolin minerals. The resultant parameters are discussed in terms of their ice nucleation efficiency. Using well defined and characterized ice/clay nano composite samples, this work bridges the gap between studies on single crystalline ice/solid model interfaces and naturally occurring soils and permafrost.
Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which additionally carry charges. This combination gives rise to a complex interplay of the underlying (anisotropic) contributions to the pair interactions. It promises interesting and distinctive structural and orientational properties to arise in systems of ILCs, combining properties of liquid crystals and ionic liquids. While previous theoretical studies have focused on the phase behavior of ILCs and the structure of the respective bulk phases, in the present study we provide new results, obtained within density functional theory, concerning (planar) free interfaces between an isotropic liquid L and two types of smectic-A phases (SA or SAW). We discuss the structural and orientational properties of these interfaces in terms of the packing fraction profile η(r) and the orientational order parameter profile S2(r) concerning the tilt angle α between the (bulk) smectic layer normal and the interface normal. The asymptotic decay of η(r) and of S2(r) towards their values in the isotropic bulk is discussed, too.
We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage VT for early (t≪τT) and late (t≫τT) times as compared to the relaxation time τT of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and VT) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τT regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, VT exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)].
Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.
The structure of dilute electrolyte solutions close to a surface carrying a spatially inhomogeneous surface charge distribution is investigated by means of classical density functional theory within the approach of fundamental measure theory. For electrolyte solutions, the influence of these inhomogeneities is particularly strong because the corresponding characteristic length scale is the Debye length, which is large compared to molecular sizes. Here, a fully three-dimensional investigation is performed, which accounts explicitly for the solvent particles, and thus provides insight into effects caused by ion–solvent coupling. The present study introduces a versatile framework to analyze a broad range of types of surface charge heterogeneities even beyond the linear response regime. This reveals a sensitive dependence of the number density profiles of the fluid components and of the electrostatic potential on the magnitude of the charge as well as on the details of the surface charge patterns at small scales.
Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve as a proxy for simple coacervation. First, a low-density density functional calculation reveals the dominance of two-particle configurations coupled by ion adsorption on neighboring macroions. Then a binary cell model, solved on the Debye-Hückel as well as the full nonlinear Poisson-Boltzmann level, unveils the charge symmetry breaking as inducing the phase separation between low- and high-density phases as a function of pH. These results can be identified as a charge symmetry broken complex coacervation between chemically identical macroions.
Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid–crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension that accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation–anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogens (i.e., liquid–crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and hexagonal crystal phases. We find that in the ordinary smectic-A phase, the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase, the small counterions accumulate in between the smectic layers. Due to this phenomenology, the wide smectic-A phase could be interesting for applications, which hinge on the presence of conductivity channels for mobile ions.
Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales
(2022)
The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.
The oil painting The Recapture of Győr 1598 (1840) is one of the two works by Alajos Alois Unger (Győr 1814-1848) in the collection of the Hungarian National Gallery since the 1970s. It depicts a landmark event in the Ottoman Wars that had an immense impact on the whole of Christian Europe, but outside of Hungary it has been largely forgotten. In the past two decades, considerable insight was gained into the obscure painter Unger, his works, family and networks. Playing-card maker Mátyás Mathias Unger the Elder was his father and Alajos Unger must have been the designer behind the family’s prized playing-cards. Unger was trained at the Imperial Academy of Arts in Vienna between 1833 and 1842, particularly under Leopold Kupelwieser and Johann Ender. All this new insight enables a more detailed interpretation of this history painting frequently displayed and its religious and political meaning. It is part of an unusual cycle of patriotic Hungarian artwork glorifying the House of Habsburg.
Additive manufacturing processes, particularly Laser-Based Powder Bed Fusion of Metals (PBF-LB/M), enable the development of new application possibilities due to their manufacturing-specific freedom of design. These new fields of application require a high degree of component quality, especially in safety-relevant areas. This is currently ensured primarily via a considerable amount of downstream quality control. Suitable process monitoring systems promise to reduce this effort drastically. This paper introduces a novel monitoring method in order to gain process-specific thermal information during the manufacturing process. The Synchronized Path Infrared Thermography (SPIT) method is based on two synchronized galvanometer scanners allowing high-speed and high-resolution observations of the melt pool in the SWIR range. One scanner is used to steer the laser over the building platform, while the second scanner guides the field of view of an IR camera. With this setup, the melting process is observed at different laser powers, scan speeds and at different locations with respect to the laser position, in order to demonstrate the positioning accuracy of the system and to initially gain thermal process data of the melt pool and the heat-affected zone. Therefore, the SPIT system shows a speed independent overall accuracy of ±2 Pixel within the evaluated range. The system further allows detailed thermal observation of the melt pool and the surrounding heat-affected zone.
In recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will be shown here, through rigorous mathematical reasoning, that these non-singular kernel derivatives suffer from several drawbacks which should forbid their use. They fail to satisfy the fundamental theorem of fractional calculus since they do not admit the existence of a corresponding convolution integral of which the derivative is the left-inverse; and the value of the derivative at the initial time t = 0 is always zero, which imposes an unnatural restriction on the differential equations and models where these derivatives can be used. For the particular cases of the so-called Caputo-Fabrizio and Atangana-Baleanu derivatives, it is shown that when this restriction holds the derivative can be simply expressed in terms of integer derivatives and standard Caputo fractional derivatives, thus demonstrating that these derivatives contain nothing new.
Upper and lower estimates for the separation of solutions to fractional differential equations
(2022)
Given a fractional differential equation of order α∈(0,1] with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two solutions x1 and x2, say, of the same differential equation, both of which are assumed to be defined on a common interval [0, T], and provide upper and lower bounds for the difference x1(t)−x2(t) for all t∈[0,T] that are stronger than the bounds previously described in the literature.
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research.
Nowadays, additive manufacturing processes are becoming more and more appealing due to their production-oriented design guidelines, especially with regard to topology optimisation and minimal downstream production depth in contrast to conventional technologies. However, a scientific path in the areas of quality assurance, material and microstructural properties, intrinsic thermal permeability and dependent stress parameters inhibits enthusiasm for the potential degrees of freedom of the direct metal laser melting process (DMLS). Especially in quality assurance, post-processing destructive measuring methods are still predominantly necessary in order to evaluate the components adequately. The overall objective of these investigations is to gain process knowledge make reliable in situ statements about component quality and material properties based on the process parameters used and emission values measured. The knowledge will then be used to develop non-destructive tools for the quality management of additively manufactured components. To assess the effectiveness of the research design in relation to the objectives for further investigations, this pre-study evaluates the dependencies between the process parameters, process emission during manufacturing and resulting thermal diffusivity and the relative density of samples fabricated by DMLS. Therefore, the approach deals with additively built metal samples made on an EOS M290 apparatus with varying hatch distances while simultaneously detecting the process emission. Afterwards, the relative density of the samples is determined optically, and thermal diffusivity is measured using the laser flash method. As a result of this pre-study, all interactions of the within factors are presented. The process variable hatch distance indicates a strong influence on the resulting material properties, as an increase in the hatch distance from 0.11 mm to 1 mm leads to a drop in relative density of 57.4%. The associated thermal diffusivity also reveals a sharp decrease from 5.3 mm2/s to 1.3 mm2/s with growing hatch distances. The variability of the material properties can also be observed in the measured process emissions. However, as various factors overlap in the thermal radiation signal, no clear assignment is possible within the scope of this work.
First time right is one major goal in powder based 3D metal printing. Reaching this goal is driven by reducing life cycle costs for quality measures, to minimize scrap rate and to increase productivity under optimal resource efficiency. Therefore, monitoring the state of the powder bed for each printed layer is state of the art in selective laser melting. In the most modern approaches the quality monitoring is done by computer vision systems working with an interference on trained neural networks with images taken after exposure and after recoating. There are two drawbacks of this monitoring method: First, the sensor signals - the image of the powder bed - give no direct height information. Second, the application of this method needs to be trained and labeled with reference images for several cases. The novel approach presented in this paper uses a laser line scanner attached to the recoating machine. With this new concept, a direct threshold measure can be applied during the recoating process to detect deviations in height level without prior knowledge. The evaluation can be done online during recoating and feedback to the controller to monitor each individual layer. Hence, in case of deviations the location in the printing plane is an inherent measurement and will be used to decide which severity of error is reported. The signal is used to control the process, either by starting the recoating process again or stopping the printing process. With this approach, the sources of error for each layer can be evaluated with deep information to evaluate the cause of the error. This allows a reduction of failure in the future, which saves material costs, reduces running time of the machine life cycle phase in serial production and results in less rework for manufactured parts. Also a shorter throughput time per print job results, which means that the employee can spent more time to other print jobs and making efficient use of the employee’s work force. In summary, this novel approach will not only reduce material costs but also operating costs and thus optimize the entire life cycle cost structure. The paper presents a first feasibility and application of the described approach for test workpieces in comparison to conventional monitoring systems on an EOS M290 machine.
Production companies are getting more and more aware of the relevancy of energy costs and the environmental impact of their manufactured products. Hence, the knowledge about the energy intensity of new process technologies as metal printing becomes increasingly crucial. Therefore, data about the energy intensity of entire process chains allow a detailed assessment of the life cycle costs and environmental impact of metal printed parts. As metal printing with Laser Powder Bed Fusion (LPBF) is applied from rapid prototyping to serial manufacturing processes more and more, sustainability data are useful to support a valid scale-up scenario and energetic improvements of the 3D-printing machinery as well as peripheral aggregates used in the process chain. The contribution aims to increase the transparency of the LPBF process chain in terms of its energy consumption. Therefore a generalized model to assess sustainability aspects of metal printed parts is derived. For this purpose, the LPBF process chain with the essential pre-, main- and post-processes is evaluated regarding its energy intensity. Here, the sub-processes, for example wet and dry cleaning of the printer, sieving of the metal powder or sand-blasting of the part are analyzed as well as the main printing process. Based on the derived experimental data from an installed, industry-like process chain, a model is created, which tends to generalize the experimental findings to evaluate other metal printed parts and process chain variants in terms of their energy intensity.
FHWS Science Journal (5, 1)
(2021)
[D]ie Beiträge im vorliegenden FHWS Science Journal [dienen] dazu, einen Ein- und Überblick über eine Auswahl erfolgreicher Maßnahmen zu geben, die im Rahmen des BEST-FIT-Projektes entwickelt wurden und die erarbeiteten Methoden, Konzepte und Ergebnisse mit interessierten Lehrenden zu teilen. Nur wenn es gelingt, erfolgreiche Maßnahmen auch nach dem Ende der Förderperiode an der FHWS weiterzuführen und auf weitere Studiengänge und Fakultäten zu übertragen, können die Ziele von BEST-FIT und insgesamt des Qualitätspakts Lehre nachhaltig und dauerhaft erreicht und gesichert werden.
Eine alte Ödenburger Bürgerfamilie namens Unger: ihre Geschichte vom 16. bis ins 20. Jahrhundert
(2020)
Der vorliegende Beitrag skizziert die Geschichte der Ödenburger/Soproner Bürgerfamilie Unger vom 16. bis zum 20. Jahrhundert. Bereits Anfang des 17. Jahrhunderts ist ein Mitglied der Familie als äußerer Stadtrat belegt und immer wieder tauchten Mitglieder als Honoratioren auf und wurden ab dem 19. Jahrhundert häufiger als Beamte tätig. Außerdem übersiedelte ein Teil der Familie im 19. Jahrhundert für einige Zeit nach Raab/Győr, wo Mathias Mátyás Unger der Ältere (1789-1862) und der Jüngere (1824-1878) als Erste überhaupt landesweite Bekanntheit mit ihren patriotischen ungarischen Spielkarten erreichten. Dabei unterstützte sie als Designer der an der Wiener Akademie v.a. unter Leopold Kupelwieser und Johann Ender ausgebildete akademische Maler Alois Alajos Unger (1814-1848).
Unboxing YouTube
(2019)
Die sozialen Medien haben die Welt verändert und die politische Kommunikation umgewälzt. Fake News, Halbwahrheiten, Hetze und Verschwörungstheorien, die über die sozialen Medien abgefeuert werden, haben es politisch extremen Kräften weltweit erleichtert, Gesellschaften tief zu spalten. Twitter, Facebook und YouTube haben aber auch den Trend zur inhaltlichen Verkürzung und dramaturgischen Zuspitzung stark beschleunigt. Gleichzeitig lässt sich beobachten, dass diese Medien für Jugendliche und Kinder zur primären Quelle für Informationen, Unterhaltung und Zeitvertreib geworden sind. Doch was wird dort eigentlich „gesendet“, welche Botschaften werden vermittelt?
Unsere OBS-Studie über YouTube geht diesen Fragen nach, klärt aber auch grundsätzlich über die Funktionsweise der beliebten Videoplattform auf. So zeigt sie etwa, dass die populärsten Videomacher, die so genannten Influencer, oft überwunden geglaubte Geschlechter-Stereotypen propagieren und von professionellen Agenturen gemanagt werden – mit dem Ziel, möglichst hohe Werbeeinnahmen zu generieren. YouTube, das zeigt der historische Überblick, ist schon lange nicht mehr das demokratische Mitmach-Amateurportal, als das es sich gerne präsentiert, sondern ein profitorientiertes (Werbe)Unternehmen. Passend dazu weist die Studie nach, dass die meisten deutschen Top-100-Influencer neben trivialer Unterhaltung einen platten Konsumismus predigen. Viele Kinder und Jugendliche halten die dort gezeigte, oft nicht gekennzeichnete Werbung inzwischen für „normal“, zudem stehen Kinder als „Mini-Influencer“ verstärkt selbst vor der Kamera. Welche Schlüsse müssen daraus für den Umgang mit und die Regulierung von YouTube gezogen werden? Und wie sind die Versuche der Öffentlich-Rechtlichen zu bewerten, mit dem Projekt „funk“ die YouTube-affine junge Zielgruppe auch zukünftig noch zu erreichen? Auf diese und weitere Fragen gibt die Studie erste Antworten.
Translating Manga
(2008)
Numerical Simulation of Electro-Quasi-static Fields Using Advanced Subspace Projection Techniques
(2006)
Reuse, Recycle, Reduce (3R)
(2009)
Reuse, Recycle, Reduce (3R)
(2006)