Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

Probing transitions and phase-ordering of charge-density waves

Due to their reduced dimensionality, surfaces and quasi two-dimensional materials exhibit numerous intriguing physical phenomena that drastically differ from the bulk. To resolve these effects and the associated dynamics at their intrinsic timescales requires experimental methodologies combining a high surface sensitivity with the essential temporal resolution. However, to date, there are still very few methods that facilitate investigation of the structural degrees of freedom of surfaces on the atomic scale along with a temporal resolution of femtoseconds or picoseconds. Addressing these challenges, this thesis covers the development and application of ultrafast low-energy electron diffraction in a backscattering geometry to study structural dynamics at surfaces. In this context, a central aspect is the development of a miniaturized and laser-driven electron source based on a nanometric needle photocathode. Using such a sharp metal tip, the photoemitted electron bunches offer a particularly high coherence and remarkably short pulse durations, which were also successfully implemented recently in ultrafast transmission electron microscopy, as well as in time-resolved transmission low-energy electron diffraction. Employing the capabilities of this novel technique, so-called transition metal dichalcogenides constitute an ideal prototype system. Specifically, in the present work, the transient structural disorder of charge-density waves at the surface of 1T-TaS2 has been examined. Following the optically induced transition between two temperature-dependent charge-density wave phases, this method enables the observation of a highly disordered transient state and the subsequent phase-ordering kinetics. More precisely, the temporal evolution of the growing charge-density correlation length is traced over several hundreds of picoseconds and found to obey a power-law scaling behavior. Due to the particular properties of the charge-density wave system at hand, the observed transient disorder can be explained by the ultrafast formation of topological defects and their subsequent annihilation. These results are complemented by a numerical modeling using a timedependent Ginzburg-Landau approach. Finally, two different excitation schemes demonstrating the possibility to study the relaxation of the investigated sample on the nanosecond and microsecond timescale are presented, as well as future prospects of ultrafast low-energy electron diffraction, including other promising surface sample systems

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

Dark matter in dense astrophysical objects

Tesis por compendio de publicaciones[ES] La materia oscura constituye la mayor parte de la materia en el modelo cosmológico aceptado para nuestro Universo. Las condiciones extremas en algunos objetos compactos tales como enanas blancas y estrellas de neutrones hacen de estos objetos muy buenos acretores de materia oscura debido al alto grado de compacidad, M/R, que presentan. Este hecho, unido a una sección eficaz de interacción finita entre la materia oscura y las partículas del modelo estándar, hace de estos objetos estelares sitios idóneos para encontrarla. En este trabajo de tesis doctoral se consideran diferentes modelos de materia oscura actualmente aceptados. En particular, se considera materia oscura fermiónica acretada en estrellas densas. Una vez dentro de estos objetos, dependiendo de la naturaleza de las partículas de materia oscura, éstas podrían proporcionar una fuente de energía que podría afectar a propiedades de las estrellas tales como el transporte de energía, la conductividad térmica, las emisividades o luminosidades de éstas. Además, si bien es cierto que el tema central de este trabajo es el estudio de distintos tipos de interacción de partículas de materia oscura dentro de objetos estelares compactos y analizar las posibles señales indirectas provenientes de ellos, también se ha analizado cómo puede eventualmente afectar el hecho de considerar una teoría general de gravedad modificada en las ecuaciones de estructura estelar. Considerando una aproximación perturbativa en el límite de campos gravitatorios débiles, se analizan los efectos de estas modificaciones de la gravedad en el radio, la masa y la luminosidad de estrellas de tipo solar y enanas blancas

Electronic self-organization in layered transition metal dichalcogenides

The interplay between different self-organized electronically ordered states and their relation to unconventional electronic properties like superconductivity constitutes one of the most exciting challenges of modern condensed matter physics. In the present thesis this issue is thoroughly investigated for the prototypical layered material 1T-TaS2 both experimentally and theoretically. At first the static charge density wave order in 1T-TaS2 is investigated as a function of pressure and temperature by means of X-ray diffraction. These data indeed reveal that the superconductivity in this material coexists with an inhomogeneous charge density wave on a macroscopic scale in real space. This result is fundamentally different from a previously proposed separation of superconducting and insulating regions in real space. Furthermore, the X-ray diffraction data uncover the important role of interlayer correlations in 1T-TaS2. Based on the detailed insights into the charge density wave structure obtained by the X-ray diffraction experiments, density functional theory models are deduced in order to describe the electronic structure of 1T-TaS2 in the second part of this thesis. As opposed to most previous studies, these calculations take the three-dimensional character of the charge density wave into account. Indeed the electronic structure calculations uncover complex orbital textures, which are interwoven with the charge density wave order and cause dramatic differences in the electronic structure depending on the alignment of the orbitals between neighboring layers. Furthermore, it is demonstrated that these orbital-mediated effects provide a route to drive semiconductor-to-metal transitions with technologically pertinent gaps and on ultrafast timescales. These results are particularly relevant for the ongoing development of novel, miniaturized and ultrafast devices based on layered transition metal dichalcogenides. The discovery of orbital textures also helps to explain a number of long-standing puzzles concerning the electronic self-organization in 1T-TaS2 : the ultrafast response to optical excitations, the high sensitivity to pressure as well as a mysterious commensurate phase that is commonly thought to be a special phase a so-called “Mott phase” and that is not found in any other isostructural modification