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Spatio-Temporal Rainfall Estimation from Communication Satellite Data using Graph Neural Networks
http://hdl.handle.net/10993/51068
Title: Spatio-Temporal Rainfall Estimation from Communication Satellite Data using Graph Neural Networks
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<br/>Author, co-author: Krebs, Julian; Mishra, Kumar Vijay; Gharanjik, Ahmad; Mysore Rama Rao, Bhavani ShankarVisual Mathematical Dictionary
http://hdl.handle.net/10993/51050
Title: Visual Mathematical Dictionary
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<br/>Author, co-author: Perucca, AntonellaLëtzebuerger Mathematikerin bei der Weltraumagence ESA
http://hdl.handle.net/10993/51037
Title: Lëtzebuerger Mathematikerin bei der Weltraumagence ESA
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<br/>Author, co-author: Palmirotta, Guendalina
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<br/>Abstract: Eng Lëtzebuerger Mathematikerin schafft zanter e puer Woche fir d'europäesch Weltraumagence zu Darmstadt.
Déi jonk Fra entwéckelt Modeller fir d'Wieder am Weltall virauszesoen, fir esou d' Satellittesystemer viru Sonnestierm ze schützen. De Weltall passionéiert zanter, datt et d'Mënschheet gëtt. D’Dr. Guenda Palmirotta ass Mathematikerin a huet sech fréi fir dat interesséiert, wat ausserhalb vun der Äerd geschitt. Mam Job bei der Europäescher Weltraumagence geet en Dram an Erfëllung.
Zu Darmstadt entwéckelt d'Lëtzebuergerin Modeller fir d’Weltraumwieder virauszesoen. Bestëmmt gëtt dëst vun der Sonn an de Sonnestierm, déi kennen entstoen, déi fir Satellittesystemer e Problem kënnen duerstellen. Ee vun den Ziler ass et, an den nächste Joren d’Previsioune méi präzis ze maachen, ma och méi wäit am viraus kënne viraussoen, wat geschitt. Konkret ginn d’Modeller elo schonn agesat, fir d’Astronauten op der Internationaler Weltraumstatioun ze schützen.
Zu Darmstadt huet d'ESA een neien Iwwerwaachungszentral, wou nieft dem Weltraumwieder och aner Elementer vun der Weltraumsécherheet am A behale ginn. Esou zum Beispill de Weltraumschrott, mëttlerweil gëtt et vill Satellitten, déi net fonctionéieren a mat Aktive kéinte kollidéieren. Mat mathematesche Modeller sollen déi aktiv Satellitte gewarnt ginn a se esou hir Positioun fréizäiteg kënnen änneren.Spotlight on Young Researchers: Nature’s shapes as mathematical challenges
http://hdl.handle.net/10993/51036
Title: Spotlight on Young Researchers: Nature’s shapes as mathematical challenges
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<br/>Author, co-author: Palmirotta, Guendalina
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<br/>Abstract: In nature, we see hyperbolic forms in corals, flatworms, and many other species of reef organisms, such as sponges and kelps. The hyperbolic spaces are also of interest for mathematicians, who are looking to prove the solvability of invariant systems of differential equations in unusual spaces such as these.Machine learning force fields: towards modelling flexible molecules
http://hdl.handle.net/10993/50929
Title: Machine learning force fields: towards modelling flexible molecules
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<br/>Author, co-author: Vassilev Galindo, Valentin
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<br/>Abstract: Accurate modelling of chemical and physical interactions is crucial for obtaining thermodynamic and dynamical properties of any chemical system, enabling a myriad of possible applications. Many of these applications are computationally prohibitive when using advanced Computational Chemistry (CompChem) methods even on modern supercomputers. Because of this, machine learning (ML) force fields (FFs), combining the accuracy of state-of-the-art ab initio methods and the efficiency of classical FFs, are being increasingly used to reconstruct potential-energy surfaces (PESs) of molecules and solids. It is precisely the synergy of ML and CompChem that has revolutionized the field in the last decade, rising the applications to a qualitatively new level. Despite this great success, there are still many unsolved challenges. In this context, my thesis aims to investigate the capability of the existing MLFFs to provide simultaneously accurate and efficient models offering unprecedented insights into the (thermo)dynamics of realistic molecular systems.
Using the examples of molecular interactions that are pervasive in (bio)chemical systems, we show a counterintuitive effect of strengthening of such interactions, as well as an unexpected prevalence of quantum nuclear fluctuations over thermal contributions at room temperature. We reveal that, when dealing with complex PESs, the predictions of state-of-the-art ML models (BPNN, SchNet, GAP, and sGDML) greatly depend on the descriptor used, and on the region of the PES being sampled. Given the varying performance of MLFFs, we present a descriptor optimization scheme improving simultaneously the accuracy and efficiency of ML models. Our results show that the commonly employed strategies followed to construct both local and global descriptors need to be improved because the optimal descriptors are a non-trivial combination of local and global features. Therefore, the work presented in this thesis highlights the potential of MLFFs to provide insights into chemical systems while, at the same time, discloses the current limitations preventing the construction of accurate MLFFs for more realistic systems. Also, I propose the optimization of the description of interactions within an ML model as a valuable step towards obtaining efficient and accurate MLFFs of large and flexible molecules.
Overall, this thesis suggests that the full workflow for building ML models still needs significant elaboration. Despite this finding, the combination of CompChem and ML methods in atomistic modelling promises to enable us to solve multiple problems in different areas, such as medicine, materials design, pharmacology, energy production, environmental sciences, among others.A posteriori error estimation for finite element approximations of fractional Laplacian problems and applications to poro–elasticity
http://hdl.handle.net/10993/50928
Title: A posteriori error estimation for finite element approximations of fractional Laplacian problems and applications to poro–elasticity
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<br/>Author, co-author: Bulle, Raphaël
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<br/>Abstract: This manuscript is concerned with a posteriori error estimation for the finite element discretization of standard and fractional partial differential equations as well as an application of fractional calculus to the modeling of the human meniscus by poro-elasticity equations. In the introduction, we give an overview of the literature of a posteriori error estimation in finite element methods and of adaptive refine- ment methods. We emphasize the state–of–the–art of the Bank–Weiser a posteriori error estimation method and of the adaptive refinement methods convergence results. Then, we move to fractional partial differential equations. We give some of the most common discretization methods of fractional Laplacian operator based equations. We review some results of a priori error estimation for the finite element discretization of these equations and give the state–of–the–art of a posteriori error estimation. Finally, we review the literature on the use of the Caputo’s fractional derivative in applications, focusing on anomalous diffusion and poro-elasticity applications. The rest of the manuscript is organized as follow. Chapter 1 is concerned with a proof of the reliability of the Bank–Weiser estimator for three–dimensional problems, extending a result from the literature. In Chapter 2 we present a numerical study of the Bank–Weiser estimator, provide a novel implementation of the estimator in the FEniCS finite element software and apply it to a variety of elliptic equations as well as goal-oriented error estimation. In Chapter 3 we derive a novel a posteriori estimator for the L2 error induced by the finite element discretization of fractional Laplacian operator based equations. In Chapter 4 we present new theoretical results on the convergence of a rational approximation method with consequences on the approximation of fractional norms as well as a priori error estimation results for the finite element discretization of fractional equations. Finally, in Chapter 5 we provide an application of fractional calculus to the study of the human meniscus via poro-elasticity equations.; Ce manuscrit traite d’estimation d’erreur a posteriori pour la discrétisation d’équations aux dérivées partielles standard et fractionnaires par les méthodes éléments finis ainsi que de l’application de l’analyse fractionnaire à la modélisation du ménisque humain par les équations de poro-élasticité. Dans l’introduction, nous donnons un aperçu de la littérature sur l’estimation d’erreur a posteriori pour les méth- odes éléments finis et des méthodes de raffinement adaptatif. Nous insistons particulièrement sur l’état de l’art de la méthode d’estimation d’erreur a posteriori de
Bank-Weiser et sur les résultats de convergence des méthodes adaptatives. Ensuite, nous nous intéressons aux équations aux dérivées partielles fractionnaires. Nous présentons certaines méthodes de discrétisation d’équations basées sur l’opérateur Laplacien fractionnaire et donnons l’état de l’art sur l’estimation d’erreur a posteriori. Finalement, nous donnons un aperçu de la littérature concernant les applications de la dérivée fractionnaire au sens de Caputo en nous concentrant sur le phénomène de diffusion anormale et les applications en poro-élasticité.
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<br/>Commentary: This thesis was also submitted to obtain the degree of Docteur de l’Université de Bourgogne Franche–Comté en Mathématiques.Evaluation of the Multipath Environment Using Electromagnetic-Absorbing Materials at Continuous GNSS Stations
http://hdl.handle.net/10993/50896
Title: Evaluation of the Multipath Environment Using Electromagnetic-Absorbing Materials at Continuous GNSS Stations
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<br/>Author, co-author: Hunegnaw, Addisu; Teferle, Felix Norman
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<br/>Abstract: o date, no universal modelling technique is available to mitigate the effect of site-specific multipaths in high-precision global navigation satellite system (GNSS) data processing. Multipaths affect both carrier-phase and code/pseudorange measurements, and the errors can propagate and cause position biases. This paper presents the use of an Eccosorb AN-W-79 microwave-absorbing material mounted around a GNSS antenna that reflects less than −17 dB of normal incident energy above a frequency of 600 MHz. To verify the feasibility and effectiveness of the Eccosorb, we installed two close stations by continuously operating multi-GNSS (BeiDou, GLONASS, Galileo and GPS) in a challenging location. One station is equipped with the Eccosorb AN-W-79, covering a square area of 3.35 m2 around the antenna, and the second station operates without it. The standard deviation reductions from single point positioning estimates are significant for all the individual GNSS solutions for the station equipped with microwave-absorbing material. The reductions are as follows: for GPS, between 15% and 23%; for Galileo, between 22% and 45%; for GLONASS, 22%; and for BeiDou, 4%. Furthermore, we assess the influence of multipaths by analysing the linear combinations of code and carrier phase measurements for various GNSS frequencies. The Galileo code multipath shows a reduction of more than 60% for the station with microwave-absorbing material. For GLONASS, particularly for the GLOM3X and GLOM1P code multipath combinations, the reduction reaches 50%, depending on the observation code types. For BeiDou, the reduction is more than 30%, and for GPS, it reaches between 20% and 40%. The Eccosorb AN-W-79 microwave-absorbing material shows convincing results in reducing the code multipath noise level. Again, using microwave-absorbing material leads to an improvement between 15% and 60% in carrier phase cycle slips. The carrier-phase multipath contents on the post-fit residuals from the processed GNSS solutions show a relative RMS reduction of 13% for Galileo and 9% for GLONASS and GPS when using the microwave-absorbing material. This study also presents power spectral contents from residual signal-to-noise ratio time series using Morlet wavelet transformation. The power spectra from the antenna with the Eccosorb AN-W-79 have the smallest magnitude, demonstrating the capacity of microwave-absorbing materials to lessen the multipath influence while not eliminating it.Performance of early warning signals for disease re-emergence: A case study on COVID-19 data
http://hdl.handle.net/10993/50892
Title: Performance of early warning signals for disease re-emergence: A case study on COVID-19 data
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<br/>Author, co-author: Proverbio, Daniele; Kemp, Francoise; Magni, Stefano; Goncalves, Jorge
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<br/>Abstract: Developing measures for rapid and early detection of disease re-emergence is important to perform science-based risk assessment of epidemic threats. In the past few years, several early warning signals (EWS) from complex systems theory have been introduced to detect impending critical transitions and extend the set of indicators. However, it is still debated whether they are generically applicable or potentially sensitive to some dynamical charac- teristics such as system noise and rates of approach to critical parameter values. Moreover, testing on empirical data has, so far, been limited. Hence, verifying EWS performance remains a challenge. In this study, we tackle this question by analyzing the performance of common EWS, such as increasing variance and autocorrelation, in detecting the emer- gence of COVID-19 outbreaks in various countries. Our work illustrates that these EWS might be successful in detecting disease emergence when some basic assumptions are sat- isfied: a slow forcing through the transitions and not-fat-tailed noise. In uncertain cases, we observe that noise properties or commensurable time scales may obscure the expected early warning signals. Overall, our results suggest that EWS can be useful for active moni- toring of epidemic dynamics, but that their performance is sensitive to certain features of the underlying dynamics. Our findings thus pave a connection between theoretical and empiri- cal studies, constituting a further step towards the application of EWS indicators for inform- ing public health policies.STUDY OF COMPLEX FERROIC OXIDES BY LARGE-SCALE FIRST-PRINCIPLES SIMULATIONS
http://hdl.handle.net/10993/50773
Title: STUDY OF COMPLEX FERROIC OXIDES BY LARGE-SCALE FIRST-PRINCIPLES SIMULATIONS
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<br/>Author, co-author: Pereira Gonçalves, Mauro António
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<br/>Abstract: The main goal of this thesis was to explore the possibility that ferroelectric materials, characterized by a spontaneous and switchable electric polarization, may present topologically non-trivial structures akin to the skyrmions that occur in their ferromagnetic counterparts. The main tool used in the investigation was atomistic simulation based of first-principles effective models (“second-principles methods”), applied to two model systems: ferroelectric PbTiO3 and ferroelectric/paraelectric superlattices made of PbTiO3 and SrTiO3. More precisely, the simulations were used to analyze multidomain configurations in these compounds, motivated by previous reports that they may present non-trivial structural features. The main finding of the thesis is that, indeed, a simple multidomain configuration in PbTiO3 – namely, a columnar nanodomain with polarization opposed to that of its surrounding matrix – is sufficient to generate a dipole texture – associated to the rotation of the polarization at the domain wall between nanodomain and matrix – with the topology of a skyrmion. This constitutes the first prediction of an electric skyrmion in a simple ferroelectric material. Further, it is shown that the properties and topology of this skyrmion can be tuned by external electric and elastic fields, as well as by temperature, obtaining novel effects such as topological and iso-topological phase transitions. Finally, the investigation of the PbTiO3/SrTiO3 superlattices reveals that the skyrmion structures can be obtained as the ground state solution for such systems. This latter study was developed in the context of a collaboration with experimental groups at UC Berkeley and elsewhere, which led to the first experimental confirmation of electric skyrmions. Hence, in conclusion, the theoretical work in this thesis has been an integral part of the discovery of electric skyrmions in ferroelectric materials.An a posteriori error estimator for the spectral fractional power of the Laplacian
http://hdl.handle.net/10993/50748
Title: An a posteriori error estimator for the spectral fractional power of the Laplacian
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<br/>Author, co-author: Bulle, Raphaël; Barrera, Olga; Bordas, Stéphane; Chouly, Franz; Hale, Jack
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<br/>Abstract: We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy.Quantifying some properties of curves and arcs on hyperbolic surfaces
http://hdl.handle.net/10993/50710
Title: Quantifying some properties of curves and arcs on hyperbolic surfaces
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<br/>Author, co-author: Doan, Nhat Minh
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<br/>Abstract: Motivated by the ergodicity of geodesic flow on the unit tangent bundle of a closed hyperbolic surface and its applications, this thesis includes three parts:
Part 1. We present a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly truncated orthogeodesic that are Y-dense on a given compact set on the surface.
Part 2. We investigate the terms arising in Luo-Tan’s identity, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two results. As a first application, we show how to deduce a theorem of Thurston which states, in particular for closed hyperbolic surfaces, that if a simple length spectrum "dominates" another, then in fact the two surfaces are isometric. As a second application, we show how to find upper bounds on the number of pairs of pants of bounded length that only depend on the boundary length and the topology of the surface. This is joint work with Hugo Parlier and Ser Peow Tan.
Part 3. Inspired by a number theoretic application of Bridgeman’s identity, the combinatorial proof of McShane’s identity by Bowditch and its generalized version by Labourie and Tan, we describe a tree structure on the set of orthogeodesics and give a combinatorial proof of Basmajian’s identity in the case of surfaces. We also introduce the notion of orthoshapes with associated identity relations and indicate connections to length equivalent orthogeodesics and a type of Cayley-Menger determinant. As another application, dilogarithm identities following from Bridgeman’s identity are computed recursively and their terms are indexed by the Farey sequence.On regime shifts in biological research
http://hdl.handle.net/10993/50708
Title: On regime shifts in biological research
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<br/>Author, co-author: Proverbio, DanieleTime-Dependent Screening Explains the Ultrafast Excitonic Signal Rise in 2D Semiconductors
http://hdl.handle.net/10993/50686
Title: Time-Dependent Screening Explains the Ultrafast Excitonic Signal Rise in 2D Semiconductors
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<br/>Author, co-author: Smejkal, Valerie; Libisch, Florian; Molina-Sanchez, Alejandro; Trovatello, Chiara; Wirtz, Ludger; Marini, Andrea
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<br/>Abstract: We calculate the time evolution of the transient reflection signal in an MoS2 monolayer on a SiO2/Si substrate using first-principles out-of-equilibrium real-time methods. Our simulations provide a simple and intuitive physical picture for the delayed, yet ultrafast, evolution of the signal whose rise time depends on the excess energy of the pump laser: at laser energies above the A- and B-exciton, the pump pulse excites electrons and holes far away from the K valleys in the first Brillouin zone. Electron–phonon and hole–phonon scattering lead to a gradual relaxation of the carriers toward small Active Excitonic Regions around K, enhancing the dielectric screening. The accompanying time-dependent band gap renormalization dominates over Pauli blocking and the excitonic binding energy renormalization. This explains the delayed buildup of the transient reflection signal of the probe pulse, in excellent agreement with recent experimental data. Our results show that the observed delay is not a unique signature of an exciton formation process but rather caused by coordinated carrier dynamics and its influence on the screening.Exciton band structure of molybdenum disulfide: from monolayer to bulk
http://hdl.handle.net/10993/50685
Title: Exciton band structure of molybdenum disulfide: from monolayer to bulk
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<br/>Author, co-author: Fugallo, Giorgia; Cudazzo, Pier Luigi; Gatti, Matteo; Sottile, Francesco
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<br/>Abstract: Exciton band structures analysis provides a powerful tool to identify the exciton character of
materials, from bulk to isolated systems, and goes beyond the mere analysis of the optical spectra.
In this work, we focus on the exciton properties of molybdenum sisulfide (MoS 2 ) by solving the ab
initio many-body Bethe–Salpeter equation, as a function of momentum, to obtain the excitation
spectra of both monolayer and bulk MoS 2 . We analyse the spectrum and the exciton dispersion on
the basis of a model excitonic Hamiltonian capable of providing an efficient description of the
excitations in the bulk crystal, starting from the knowledge of the excitons of a single layer. In this
way, we obtain a general characterization of both bright and darks excitons in terms of the interplay
between the electronic band dispersion (i.e. interlayer hopping) and the electron–hole exchange
interaction. We identify for both the 2D and the 3D limiting cases the character of the
lowest-energy excitons in MoS 2 , we explain the effects and relative weights of both band dispersion
and electron–hole exchange interaction and finally we interpret the differences observed when
changing the dimensionality of the system.Collective electronic excitations in charge density wave systems: The case of CuTe
http://hdl.handle.net/10993/50684
Title: Collective electronic excitations in charge density wave systems: The case of CuTe
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<br/>Author, co-author: Cudazzo, Pier Luigi; Wirtz, Ludger
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<br/>Abstract: The study of neutral electronic excitations directly probed by electron energy loss spectroscopy experiments allows obtaining important insight about the physical origin of the charge density wave (CDW) transition in solids. In particular it allows us to disentangle purely phononic mechanisms from the excitonic insulator scenario which is associated to a purely electronic mechanism. As a matter of fact, while the the loss function of the excitonic insulators should display negative dispersive features associated to the softening of neutral electronic excitations at the CDW wave vector above the critical temperature, no softening is expected when the driving force is purely phononic. Here we perform a microscopic analysis of the dynamical charge response of CuTe, a material that displays a low-temperature Peierls-like CDW instability. By means of first-principles time-dependent density functional calculations of the loss function, we characterize the plasmon dispersion along the different directions, highlighting the role of the intrinsic structural anisotropy and the effects of the crystal local fields that are responsible for the periodic reappearance of the spectra of the first Brillouin zone as well as the formation of an acousticlike plasmon. Finally, we demonstrate that also in this system, in analogy with other materials displaying excitonic insulator instability, the low energy region of the loss function presents negative dispersive structures at momentum transfer close to the CDW wave vector. This is a feature common to both excitonic insulator transition and Peierls distortion that further highlights how the difference between the two mechanisms is at most quantitative.Excitonic-insulator instability and Peierls distortion in one-dimensional semimetals
http://hdl.handle.net/10993/50683
Title: Excitonic-insulator instability and Peierls distortion in one-dimensional semimetals
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<br/>Author, co-author: Barborini, Matteo; Calandra, Matteo; Mauri, Francesco; Wirtz, Ludger; Cudazzo, Pier Luigi
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<br/>Abstract: The charge density wave instability in one-dimensional semimetals is usually explained through a Peierls-like mechanism, where the coupling of electrons and phonons induces a periodic lattice distortion along certain modes of vibration, leading to a gap opening in the electronic band structure and to a lowering of the symmetry of the lattice. In this work, we study two prototypical Peierls systems: the one-dimensional carbon chain and the monatomic hydrogen chain with accurate ab initio calculations based on quantum Monte Carlo and hybrid density functional theory. We demonstrate that in one-dimensional semimetals at T=0, a purely electronic instability can exist independently of a lattice distortion. It is induced by spontaneous formation of low energy electron-hole pairs resulting in the electronic band gap opening, i.e., the destabilization of the semimetallic phase is due to an excitonic mechanism.Electronic structure of TiSe2 from a quasi-self-consistent G0W0 approach
http://hdl.handle.net/10993/50682
Title: Electronic structure of TiSe2 from a quasi-self-consistent G0W0 approach
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<br/>Author, co-author: Hellgren, Maria; Baguet, Lucas; Calandra, Matteo; Mauri, Francesco; Wirtz, Ludger
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<br/>Abstract: n a previous work, it was shown that the inclusion of exact exchange is essential for a first-principles description of both the electronic and the vibrational properties of TiSe2, M. Hellgren et al. [Phys. Rev. Lett. 119, 176401 (2017)]. The GW approximation provides a parameter-free description of screened exchange but is usually employed perturbatively (G0W0), making results more or less dependent on the starting point. In this work, we develop a quasi-self-consistent extension of G0W0 based on the random phase approximation (RPA) and the optimized effective potential of hybrid density functional theory. This approach generates an optimal G0W0 starting point and a hybrid exchange parameter consistent with the RPA. While self-consistency plays a minor role for systems such as Ar, BN, and ScN, it is shown to be crucial for TiS2 and TiSe2. We find the high-temperature phase of TiSe2 to be a semimetal with a band structure in good agreement with experiment. Furthermore, the optimized hybrid functional agrees well with our previous estimate and therefore accurately reproduces the low-temperature charge-density-wave phase.Low-cost GNSS for Meteorology: A receiver comparison
http://hdl.handle.net/10993/50648
Title: Low-cost GNSS for Meteorology: A receiver comparison
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<br/>Author, co-author: Monteiro, Cristiano; Hunegnaw, Addisu; Teferle, Felix Norman
<br/>
<br/>Abstract: GNSS, particularly the GPS and GLONASS satellite constellations are commonly used
for accurate estimation of atmospheric parameters. The high accuracy is accomplished by sophisticated analysis methods and expensive high-end receivers and antennas along with precise products and bias corrections. The recent market introduction of low-cost dual frequency
receivers that can produce raw data from multiple constellations offers an insight into the potential use of these receivers for meteorological applications. Here we demonstrate that GPS and GLONASS
measurements from a low-cost dual-frequency receiver can be used to estimate the Zenith Total Delay ( ZTD) commensurate to meteorological applications.Multi-GNSS Slant Wet Delay Retrieval Using Multipath Mitigation Maps
http://hdl.handle.net/10993/50647
Title: Multi-GNSS Slant Wet Delay Retrieval Using Multipath Mitigation Maps
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<br/>Author, co-author: Hunegnaw, Addisu; Ejigu, Yohannes Getachew; Teferle, Felix Norman; Elgered, Gunnar
<br/>
<br/>Abstract: The conventional Global Navigation Satellite System (GNSS) processing is typically contaminated with errors due to atmospheric variabilities, such as those associated with the mesoscale phenomena. These errors are manifested in the parameter estimates, including station coordinates and atmospheric products. To enhance the accuracy of these GNSS products further, a better understanding of the local-scale atmospheric variability is necessary. As part of multi-GNSS processing, station coordinates, carrier phase ambiguities, orbits, zenith total delay (ZTD) and horizontal gradients are the main parameters of interest. Here, ZTD is estimated as the average zenith delay along the line-of-sight to every observed GNSS satellite mapped to the vertical while the horizontal gradients are estimated in NS and EW directions and provide a means to partly account for the azimuthally inhomogeneous atmosphere. However, a better atmospheric description is possible by evaluating the slant path delay (SPD) or slant wet delay (SWD) along GNSS ray paths, which are not resolved by ordinary ZTD and gradient analysis. SWD is expected to provide better information about the inhomogeneous distribution of water vapour that is disregarded when retrieving ZTD and horizontal gradients. Usually, SWD cannot be estimated directly from GNSS processing as the number of unknown parameters exceeds the number of observations. Thus, SWD is generally calculated from ZTD for each satellite and may be dominated by un-modelled atmospheric delays, clock errors, unresolved carrier-phase ambiguities and near-surface multipath scattering. In this work, we have computed multipath maps by stacking individual post-fit carrier residuals incorporating the signals from four GNSS constellations, i.e. BeiDou, Galileo, Glonass and GPS. We have selected a subset of global International GNSS Service (IGS) stations capable of multi-GNSS observables located in different climatic zones. The multipath effects are reduced by subtracting the stacked multipath maps from the raw post-fit carrier phase residuals. We demonstrate that the multipath stacking technique results in significantly reduced variations in the one-way post-fit carrier phase residuals. This is particularly evident for lower elevation angles, thus, producing a retrieval method for SWD that is less affected by site-specific multipath effects. We show a positive impact on SWD estimation using our multipath maps during increased atmospheric inhomogeneity as induced by severe weather events.Intermolecular Interactions in Static Electric Fields Studied with Quantum Mechanics and Quantum Electrodynamics
http://hdl.handle.net/10993/50627
Title: Intermolecular Interactions in Static Electric Fields Studied with Quantum Mechanics and Quantum Electrodynamics
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<br/>Author, co-author: Karimpour, Mohammad Reza
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<br/>Abstract: In the present work, the interactions between neutral molecular systems subject to external static electric fields are studied. To comprehensively explore the effects of external fields on intermolecular interactions, the two most reliable frameworks in the subject, namely molecular quantum mechanics and quantum electrodynamics are employed while atomic and molecular responses are modeled using quantum Drude oscillators (QDO). In the first part of the work, the focus is to understand the interplay between dispersion and field-induced forces in two-body systems for both nonretarded and retarded ranges of inter-species distances. To identify the origin and the mechanism responsible for different field-induced interactions, a complementary approach based on classical electrodynamics with a zero-point radiation field, namely stochastic electrodynamics, is employed. The results show that neglecting higher-order contributions coming from field-induced hyperpolarizabilities of atoms, the dispersion interaction remains unchanged by the external uniform static field, for both regimes. However, using an external static field one can control the magnitude and characteristics of intermolecular interactions. The second part of the work is devoted to the extension of the study to many-body interacting systems. There, the total interaction energy in systems with many interacting atoms or molecules is obtained by extending the well-established theory of many-body dispersion (MBD) interactions to the presence of external static electric fields. Diagonalization of the Hamiltonian of the system in the nonretarded regime and in the framework of quantum mechanics yields the total energy of the interacting system in terms of the corresponding normal mode frequencies. Subtraction of the energy of the non-interacting QDOs-in-fields from the total energy of the interacting system results in the many-body interaction energy. The impact of the field-induced many-body contributions is investigated for a benzene dimer as well as for two carbyne chains. Varying the number of carbon atoms per chain demonstrates the significance of the field-induced many-body terms in the interplay between dispersion and field-induced interactions. Such contributions can be of great importance for controlling delamination and self-assembly of materials in static electric fields.