# JLUdocs

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JLUdocs ist der Bereich für Open-Access-Publikationen von Mitgliedern und Angehörigen der JLU Gießen.

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### Auflistung JLUdocs nach Auflistung nach Organisationseinheit "FB 07 - Mathematik und Informatik, Physik, Geographie"

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Item 18. Theorietag "Automaten und Formale Sprachen" : Wettenberg-Launsbach bei Gießen 30. September - 2. Oktober 2008(2008) Holzer, Markus; Kutrib, Martin; Malcher, AndreasDer Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik. Er wird seit 1991 von Mitgliedern der Fachgruppe an wechselnden Orten in Deutschland und Österreich veranstaltet. Im Laufe des Theorietags findet auch die jährliche Fachgruppensitzung statt. Seit 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die bisherigen Austragungsorte waren Magdeburg (1991), Kiel (1992), Dagstuhl (1993), Herrsching (1994), Schloß Rauischholzhausen (1995), Cunnersdorf (1996), Barnstorf (1997), Riveris (1998), Schauenburg-Elmshagen (1999), Wien (2000), Wendgräben (2001), Wittenberg (2002), Herrsching (2003), Caputh (2004),Lauterbad (2005), Wien (2006) und Leipzig (2007). Der diesjährige Theorietag wird nach 13 Jahren wieder vom Institut für Informatik der Justus-Liebig-Universität Gießen ausgerichtet. Er findet mit dem vorangestellten Workshop über Selected Topics in Theoretical Computer Science vom 30. September bis zum 2. Oktober 2008 in Wettenberg-Launsbach bei Gießen statt. Teilnehmer aus Belgien, Deutschland, England, Frankreich, Italien, Österreich, Tschechien und Ungarn folgten der Einladung nach Mittelhessen.Item 3D Impedance Modelling of Metal Anodes in Solid-State Batteries − Incompatibility of Pore Formation and Constriction Effect in Physical-Based 1D Circuit Models(2022-09-08) Eckhardt, Janis K.; Fuchs, Till; Burkhardt, Simon; Klar, Peter J.; Janek, Jürgen; Heiliger, ChristianA non-ideal contact at the electrode/solid electrolyte interface of a solid-state battery arising due to pores (voids) or inclusions results in a constriction effect that severely deteriorates the electric transport properties of the battery cell. The lack of understanding of this phenomenon hinders the optimization process of novel components, such as reversible and high-rate metal anodes. Deeper insight into the constriction phenomenon is necessary to correctly monitor interface degradation and to accelerate the successful use of metal anodes in solid-state batteries. Here, we use a 3D electric network model to study the fundamentals of the constriction effect. Our findings suggest that dynamic constriction as a non-local effect cannot be captured by conventional 1D equivalent circuit models and that its electric behavior is not ad hoc predictable. It strongly depends on the interplay of the geometry of the interface causing the constriction and the microscopic transport processes in the adjacent phases. In the presence of constriction, the contribution from the non-ideal (porous) electrode/solid electrolyte interface to the impedance spectrum may exhibit two signals that cannot be explained when the porous interface is described by a physical-based (effective medium theory) 1D equivalent circuit model. In consequence, the widespread assumption of a single interface contribution to the experimental impedance spectrum may be entirely misleading and can cause serious misinterpretation.Item 5. Theorietag : "Automaten und Formale Sprachen" : Schloss Rauischholzhausen, 28./29.09.1995(1995) Kutrib, Martin; Worsch, ThomasItem A differential delay equation with a planar attractor(1991) Walther, Hans-OttoItem A Dry-Processed Al2O3/LiAlO2 Coating for Stabilizing the Cathode/Electrolyte Interface in High-Ni NCM-Based All-Solid-State Batteries(2022) Negi, Rajendra S.; Yusim, Yuriy; Pan, Ruijun; Ahmed, Shamail; Volz, Kerstin; Takata, Ryo; Schmidt, Franz; Henss, Anja; Elm, Matthias T.Item A first-order representation of stable models(1998) Eiter, Thomas; Lu, James; Subrahmanian, V.STuri (1991) introduced the important notion of a constrained atom: an atom with associated equality and disequality constraints on its arguments. A set of constrained atoms is a constrained interpretation. We investigate how nonground representations of both the stable model semantics and the wellfounded semantics may be obtained through Turi's approach. The practical implication of this is that the wellfounded model (or the set of stable models) may be partially precomputed at compiletime, resulting in the association of each predicate symbol in the program to a constrained atom. Algorithms to create such models are presented, both for the well founded case, and the case of stable models. Query processing reduces to checking whether each atom in the query is true in a stable model (resp. wellfounded model). This amounts to showing the atom is an instance of one of some constrained atom whose associated constraint is solvable. Various related complexity results are explored, and the impacts of these results are discussed from the point of view of implementing systems that incorporate the stable and wellfounded semantics.Item A fundamental problem of hypothesis testing with finite inventory in e-commerce(2020) Bohle, Dennis; Marynych, Alexander; Meiners, MatthiasItem A kinetic Fokker-Planck algorithm for simulating multiscale gas flows(2022) Hepp, Christian; Heiliger, ChristianNumerical, aerodynamic analysis of spacecraft requires the modeling of rarefied hypersonic flows. Such flow regimes are usually dominated by broad shock waves and strong expansion flows. In such areas of the flow the gas is far from its equilibrium state and therefore conventional modeling approaches such as the Euler or Navier-Stokes equations cannot be used. Instead, non-equilibrium modeling approaches must be applied. While most non-equilibrium flow solvers are computationally expensive, a recently introduced kinetic Fokker-Planck (FP) method shows the potential of describing non-equilibrium flows with satisfactory accuracy and, at the same time, significantly reducing computational costs. However, the application of kinetic FP solvers was so far still limited to simple, single species gases. The aim of this study is to extend the capabilities of the kinetic FP approach for describing complex gas flows. Particular attention is paid to the modeling of non-equilibrium aerodynamics, as it is relevant for describing spacecraft related gas flows. Methods for describing polyatomic species as well as gas mixtures within the kinetic FP framework are constructed. All models are intensively validated by comparison to already established numerical methods, as well as in comparison to experimental studies. Excited energy states are modeled by a stochastic jump process described by a master equation. This approach allows the description of both continuous and discrete energy levels. Gas mixtures are modeled based on the hard-sphere and variable hard-sphere collision potentials. For both cases, FP models are constructed for an arbitrary number of species. The efficiency of the described models is investigated and different strategies are proposed to use kinetic FP methods efficiently. The expansion of synthetic air from an axially symmetric orifice is numerically reproduced using the developed models and results are compared with experimental measurements. Although the numerical simulations capture several magnitudes of Knudsen numbers, from the continuum flow in the reservoir up to the free-molecular far field, good agreement between simulation and experiment is seen.Item A Sensitivity Assessment of COSMO-CLM to Different Land Cover Schemes in Convection-Permitting Climate Simulations over Europe(2021) Zhang, Mingyue; Tölle, Merja H.; Hartmann, Eva; Xoplaki, Eleni; Luterbacher, JürgItem A surface-enhanced Raman-spectroscopic study: Verification of the interparticle gap dependence of field enhancement by triangulation of spherical gold nanoparticle trimers(2019) Dort, Katharina; Kroth, Kathrin; Klar, Peter J.Item A theorem on the amplitudes of periodic solutions of delay equations, with an application to bifurcation(1978) Walther, Hans-OttoItem A Time Hierarchy for Bounded One-Way Cellular Automata(2001) Klein, Andreas; Kutrib, MartinItem A uniqueness problem for a nonlinear differential delay equation(1985) Walther, Hans-OttoItem An ab initio approach to spin transport in magnetic tunnel junctions with disorder(2015) Franz, ChristianIn this work we investigate the spin(-dependent) transport in FeCo/MgO/FeCo magnetic tunnel junctions (MTJ) using advanced ab initio methods. Here, a special focus lies on the impact of the disordered alloy leads with varying Co concentration.The central effect in these MTJs is the dependence of the tunneling probability of the conduction electrons on their symmetry character (symmetry selection); this is a result of the epitaxial MgO barrier. In combination with the band structure of the ferromagnetic leads, this leads to a giant tunnel magnetoresistance (TMR) and highly spin-polarized currents. The latter are beneficial for the efficient generation of spin-transfer torque (STT) and other applications. These effects are illustrated in detail for the system with pure iron leads. We also discuss other effects that are important, e.g. the interface resonance states. The discussion is then extended to FeCo leads using a realistic description of the disordered alloys, which includes the effects of disorder scattering. We discuss the interplay of the coherent tunneling and the disorder scattering in the leads and also the effects of the band filling and their impact on the (spin) transport. The TMR and STT are investigated in the full concentration range and for a large range of bias voltages. Here, the consistent study of the MTJ with iron leads provides a starting point and a solid basis for the profound understanding of the observed dependencies. These are traced back to the underlying physical effects and contributing states using a combination of advanced techniques.The theoretical prediction of the giant TMR (Butler 2001), i.e. a large increase in the resistance when switching the alignment of the magnetizations in the ferromagnetic leads from parallel to anti-parallel, has inspired a large interest in coherent MTJs. They are now widely used as magnetic field sensors, e.g. in the read heads of hard disk drives. MTJs are also used in MRAM, where the STT provides an efficient switching mechanism. Further, magnetic tunnel contacts are an important element in many proposed spintronic devices. While experiments usually consider FeCo alloys as lead material, the theoretical investigations so far only considered ordered materials.Here, we discuss the impact of the disordered leads of the MTJs based on ab initio calculations. The transport is described using non-equilibrium Green´s functions. For the disordered leads we use the coherent potential approximation, which provides an efficient and accurate description of the alloys including the effects of disorder scattering. These methods (including the necessary vertex corrections for transport calculations and the restricted alloy averages) are derived and discussed in this work. They provide a detailed picture of the transport processes in the presence of disorder.This shows that the disorder scattering interferes with the symmetry selection in the barrier leading to a reduction of the TMR. However, a detailed investigation reveals that the concentration dependence of the TMR (at zero bias voltage) is controlled by a combination of several effects including also band filling and interface resonance states. At higher bias voltages the TMR is increasingly influenced by minority states above the Fermi-energy with a high tunneling probability. For Co leads these lead to a fast decrease of the TMR with increasing bias voltage.The STT is a torque exerted on the magnetizations by electrons which cross the barrier at non-collinear alignment. The component of the STT in the plane spanned by the magnetizations is most important for the switching and can be accurately described by a model in terms of spin currents. This allows us to understand the concentration and bias dependence in terms of effects which are also observed for the TMR. In particular, this explains the observed linear bias dependence at low bias, which is independent of the concentration, and also the strong asymmetric deviations at large bias and high Co concentrations. The out-of-plane component is an even function of the bias voltage and shows a weak concentration dependence.Item Ab initio calculations of conduction band effective mass parameters of thermoelectric Mg2X1-xYx (X, Y = Si, Ge, Sn) alloys(2020) Guerra-Castro, Juan Manuel; Mahr, Carsten; Giar, Marcel; Czerner, Michael; Heiliger, ChristianItem Ab initio description of disorder effects in layered cathode active materials by the coherent potential approximation(2022) Eckhardt, Janis K; Risius, Philipp E; Czerner, Michael; Heiliger, ChristianDisorder effects in alloys are usually modeled by averaging various supercell calculations considering different positions of the alloy atoms. This approach, however, is only possible as long as the portion of the individual components of the alloy is sufficiently large. Herein, we present an ab initio study considering the lithium insertion material Li1−x[Ni0.33Co0.33Mn0.33]O2 as model system to demonstrate the power of the coherent potential approximation within the Korringa–Kohn–Rostoker Green's function method. This approach enables the description of disorder effects within alloy systems of any composition. It is applied in this study to describe the (de-)intercalation of arbitrary amounts of lithium from the cathode active material. Moreover, we highlight that using either fully optimized structures or experimental lattice parameters and atomic positions both lead to comparable results. Our findings suggest that this approach is also suitable for modeling the electronic structure of state-of-the-art materials such as high-nickel alloys.Item Ab initio description of lattice dynamics in oxide semiconductors(2017) Giar, MarcelAs non-toxic and sustainable materials the system of binary oxide semiconductors Cu2O, Cu4O3, and CuO is in the focus of current research, e.g., for solar-cell applications. The objective of this work is to analyse the vibrational and Raman spectroscopic properties of these binary semiconductors using ab initio methods (density functional theory).The phonon dispersions of polar semiconductors display a splitting in frequency of the longitudinal optical (LO) and transversal optical (TO) infrared active modes (LO-TO splitting) in the limit of vanishing phonon wave vector. This traces back to long-ranged dipole-dipole interactions present in these crystals. The theoretical treatment of these interactions requires the usage of certain correction schemes for the dynamical matrices. Two methods implementing these corrections [Phys. Rev. B 55, 10355 (1997) (Gonze s method); J. Phys.: Condens. Matter 22, 202201 (2010) (Wang s method)] are employed. Gonze s method, which is traditionally in the framework of density function perturbation theory, is shown to be applicable together with the real space method. Both correction schemes are compared using the insulator CaF2 as test system. The evolution of the phonon frequencies of the modes showing LO-TO splitting close to the Brillouin zone centre in many cases is better described by Gonze s method. Wang s method, on the contrary, can introduce artificial features in the phonon dispersion.The phonon dispersion and derived quantities of all three copper oxide phases are calculated and compared to experiment. It becomes particularly clear that the corrections following Gonze s method are necessary to obtain agreement with experimentally determined phonon dispersions. Good agreement with experiment is obtained for the vibrational contributions to the specific heat and the entropy. Based on Gonze s method the velocities of sound are calculated along several directions also yielding good accordance with experiment.The focus of the Raman spectroscopy investigations is on Cu4O3 and CuO. Cu4O3 is not too extensively studied theoretically as well as experimentally, and for CuO different crystal structures must be considered for room temperature (RT) and low temperatures (LT) (below 213 K). While group theory predicts three Raman active modes for CuO at RT additional modes appear in the experimental LT Raman spectrum [Phys. Rev. B 52, R13130 (1995)]. The appearance of the extra Raman active modes can be explained by a local symmetry lowering of the atomic positions compared to the RT structure owing to a change in the antiferromagnetic ordering. Additional measured Raman active modes can be identified in the calculations; more extra modes are calculated than measured, while each of those not visible in experiment shows a small intensity in the calculated Raman spectrum. Additionally, a rather different behaviour of the Raman intensities of the modes common to both the RT and the LT structures as a function of the laser energy is found. For Cu4O3 the dependence of the Raman intensities on the crystal orientation and the chosen polarisations are investigated in detail. Particularly, the totally symmetric A1g mode has noteworthy angular intensity dependence since it depends on the relative phase of the complex-valued Raman tensor elements. The effect of hydrostatic pressure is also studied showing that the frequencies of the Raman active modes are very sensitive to the exerted pressure.Item Ab initio Description of Materials Properties: An Application to Thermoelectric and Raman Scattering Phenomena(2019) Guerra-Castro, Juan ManuelThe need of efficient and sustainable alternatives to raw materials for technological applications has driven an intense research effort in the field of materials science. The scientific strategies aim to replace or supplement conventional power production by alternative technologies like thermoelectric generators or solar cells. During my doctoral track, within the Research Training Group (RTG) 2204 "substitute materials for sustainable energy technologies", I performed theoretical - ab initio - calculations of materials properties. For that purpose, I used density functional theory (DFT) techniques to find the energy eigenvalues of the physical quantum system, and the charge density. My calculations allow me to determine the electronic parameters of thermoelectric materials, and the Raman spectral properties of graphene. For thermoelectric conversion, I studied magnesium silicide that shows enhanced thermoelectric performance when silicon is substituted by germanium or tin. Within the KKR formalism, I studied the full-relativistic effects on the electronic bands. For treating substitutional alloy systems, I used the in-site (single-cell) coherent potential approximation (CPA) to map a band structure for any intermediate composition and thereby to extract the electronic parameters. These results allow me to interpret the structural instability found in intermediate alloys, the variation of band gaps, and parabolic band effective masses with the composition. This change is nearly linear for substitutions between silicon and germanium, but non-linear terms - or deviations from Vegard´s law - appear when silicon or germanium is substituted by tin. At a particular intermediate composition, I describe the degeneracy of the conduction bands that has been shown to enhance the electronic transport properties of the n-type samples, not present in the substitution between silicon and germanium. For the interpretation of the Raman spectra in graphene samples, I compute the phonon frequencies and electronic band structures. Graphene, besides its rich physical properties, present a cheaper and more efficient alternative for carbon-based technologies. Raman spectra is a powerful method to characterize defects in these materials, i.e., boundaries, stacking, ripples, etc., through the scattering of an external light source. For non-crystalline materials, a defect-induced Raman mode, or the D-mode, is activated involving phonons away from the zone center. I compute the Raman shifts of the D mode using a resonant process that involves the intra-valley inelastic dispersion with a phonon and the elastic scattering of the defect, which explains very well the dispersion observed for different light energies. For small size samples, I describe the effect of the boundary on the Raman spectrum using a phonon-confinement model that relax the phonon conservation rules and broadens the Raman signals. In general, my calculations show a very good agreement with available experimental trends and provide intermediate data not yet reached. Therefore, these findings have served to interpret the experiments and to predict new possible results.Item Ab initio description of transport in nanostructures including electron-phonon coupling(2018) Mahr, Carsten EberhardThe ongoing trends toward miniaturization and exploitation of non-classical degrees of freedom severely challenge the available methods for the theoretical description of electronic devices, because in realistic situations both quantum-mechanical effects as well as phase-breaking scattering events must be taken into account. The objective of this work is to assist the endeavor to improve electronic and spintronic appliances by implementing a numerical scheme making predictive nanoscale device modeling from first principles affordable.A thorough mathematical and physical discussion regarding the treatment of phase-breaking scattering events - particularly those due to the electron-phonon interaction - in ab initio electronic transport calculations yields the basis for the advocated computational scheme. This method is characterized by the usage of suitable additional self-energies in the Keldysh formulation of the non-equilibrium Green´s function formalism (NEGF) as implemented in a Korringa-Kohn-Rostoker (KKR) electronic structure code. The evaluation of the transmission probability is performed by means of the Landauer-Büttiker theory. Depending on the problem at hand, we propose two methods to obtain the necessary energy-resolved electron-phonon self-energies: In case of non-magnetic metals, a wave-vector integration of bulk self-energies obtained from third-party codes is introduced. Alternatively, we describe a self-energy fitting procedure to spin-resolved ab initio resistivity data. If the effects of thermal expansion are taken into account (e.g., in the framework of the Debye-Grüneisen theory), we show that the suggested method provides very accurate results for the temperature-dependence of electronic transport properties in both complex nanostructures as well as bulk-like macroscopic devices up to very high temperatures.We verify the correctness of the implementation and study the validity of the calculational scheme by carefully analyzing the required numerical precisions in the bulk-like metallic systems copper, aluminum, and - to some extent - iron. The electron-phonon induced electron linewidth is calculated. Subsequently, we evaluate the temperature-dependent resistivity and compare to both experimental data and to results obtained using other methods based on first principles, notably the lowest-order variational approximation (LOVA) to the Boltzmann formalism and the alloy analogy. For all three materials we find the Landauer formula to be valid in the considered temperature regime of up to 900 K. Further, in the limit of macroscopic device lengths, Ohm´s law emerges. In the studies on copper and aluminum, the strong influence of thermal expansion on the resistivity is traced back to the vibrational degrees of freedom. This provides evidence for the validity of the quasi-harmonic approximation in case of simple metals and illustrates the importance of accurate phonon calculations. We argue that GGA exchange-correlation functionals are hence to be preferred over local approximations if experimental lattice constants are used. In the low temperature regime, however, small deviations of the Fermi surface triangulation used in the wave-vector integration determine the accuracy of the results.In order to study the applicability of the proposed method in the context of complex nanostructures, the understanding of the mechanisms giving rise to resonant tunneling in Fe/MgO double barrier magnetic tunnel junctions is confirmed and improved: The strong localization of Δ1 quantum well states mimics the one-dimensional situation and induces strong asymmetric peaks in the energy-resolved transmission. These peaks are palmed off with increasing temperature and become more symmetric in energy. We show that the resonant behavior in the current-voltage characteristics reduces likewise and in accordance with experimental data. This is related to an increase of the electron linewidth on the one hand, and a broadening of the electron distribution functions on the other hand. Further, and still in accordance with the experiment, phase-breaking scattering in the metallic leads is found to decrease the resistance of the device.