Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD

Direct observations of compact objects, in the form of radiation spectra, gravitational waves from VIRGO/LIGO, and forthcoming direct imaging, are currently one of the primary source of information on the physics of plasmas in extreme astrophysical environments. The modeling of such physical phenomena requires numerical methods that allow for the simulation of microscopic plasma dynamics in presence of both strong gravity and electromagnetic fields. In Bacchini et al. (2018) we presented a detailed study on numerical techniques for the integration of free geodesic motion. Here we extend the study by introducing electromagnetic forces in the simulation of charged particles in curved spacetimes. We extend the Hamiltonian energy-conserving method presented in Bacchini et al. (2018) to include the Lorentz force and we test its performance compared to that of standard explicit Runge-Kutta and implicit midpoint rule schemes against analytic solutions. Then, we show the application of the numerical schemes to the integration of test particle trajectories in general relativistic magnetohydrodynamic (GRMHD) simulations, by modifying the algorithms to handle grid-based electromagnetic fields. We test this approach by simulating ensembles of charged particles in a static GRMHD configuration obtained with the Black Hole Accretion Code (BHAC)

Non-equilibrium dynamics in quantum simulators

This thesis summarizes a course of investigation of various aspects of non-equilibrium dynamics in isolated quantum systems which can be controlled to the extent that one can speak of not just realizing but rather simulating a desired physical effect. The first subject considered concerns a general question of relaxation in a large class of physical models. It is rigorously proven that equilibration can occur for arbitrary local observables despite the entire system being perfectly isolated. Various mechanisms responsible for convergence to local equilibrium are highlighted. These involve in particular the memory loss of non-Gaussian correlations following an interaction quench, a notion of Gaussian ergodicity and a proof of the emergence of translation invariance of correlations due to the presence of this symmetry in the Hamiltonian governing the evolution. These results provide the long time and large system size asymptotics facilitating a thermodynamic limit, but at the same time are relevant for state-of-the-art quantum simulation experiments with large numbers of ultra-cold atoms: A related effect has been observed in a one-dimensional phononic quantum field simulator and additionally a method is provided to study relaxation dynamics of this type in optical lattice quantum simulators. Within the second theme explored in this thesis a novel quantum read-out method is proposed and applied in continuous field quantum simulators which allowed for the first time to measure experimentally various thermodynamical properties of one-dimensional quasi-condensates. In particular, tomographic results concerning thermal properties, non-commuting observables, momentum and time-resolved occupation numbers of phonons are presented. Finally, ideas for practical benchmarking of the dynamics of certain closed quantum systems are put forward, based on the concept of a fidelity witness. It is demonstrated that fidelity, despite being a sensitive measure for large systems, can be efficiently estimated for non-equilibrium dynamics in coherent quantum simulators implementing paradigmatic models of condensed matter physics. The method developed has already found an independent application in studies of variational quantum circuits aiming at achieving so-called quantum chemistry accuracy using the Sycamore quantum processor. The fact that all three themes of research laid out in this thesis have found an experimental realization hints at a prognosis for future developments in physics that it will become standard that quantum simulators will realize experimentally novel theoretical ideas on demand and the time between theoretical insights and experimental observations will be dramatically shortened.Diese Dissertation fasst eine Reihe von Untersuchungen zu unterschiedlichen Aspekten von Nichtgleichgewichtsdynamik in isolierten Quantensystemen zusammen, die in einem Maße präzise kontrolliert werden können, dass man nicht nur von der Realisierung eines physikalischen Effektes, sondern von seiner Simulation sprechen kann. Das erste Thema befasst sich mit einer allgemeiner Frage der Relaxationdynamik in einer grosser Klasse von physikalischen Modellen. Es wird in diesem Rahmen rigoros bewiesen, dass eine Equilibrierung von beliebigen lokalen Observablen auch dann generisch vorliegen kann, wenn das System perfekt isoliert bleibt. Unterschiedliche Mechanismen werden herausgestellt, die für die Konvergenz zu lokalem Gleichgewicht verantwortlich sind. Dies betrifft insbesondere der Gedächtnisverlust von nicht-Gaußchen Korrelationen nach schnellen Änderungen von Wechselwirkungen, eine Begrifflichkeit von Gaußscher Ergodizität und der Beweis einer Emergenz von Translationsinvarianz in Situationen, in denen der Hamiltonoperator eine solche Symmetrie aufweist. Diese Resultate ergeben die Asymptotik eines Übergangs zu langen Zeiten und großen Systemen, die einen thermodynamischen Limes abbilden. Sie sind aber gleichermaßen relevant für moderne Quantensimulationsexperimente, wie sie derzeit mit großskaligen Systemen ultrakalter Atome durchgeführt werden: Ein artverwandter Effekt wurde in einem eindimensionalen Quantenfeldsimulator beobachtet. Aufbauend auf diesen Ergebnissen werden Methoden bereitgestellt zur Untersuchung der Nichtgleichgewichtsdynamik von Systemen ultrakalter Atome in optischen Gittern. Im zweiten Teil der Arbeit wird eine neuartige Auslesemethode vorgeschlagen und auf Quantensimulatoren kontinuierlicher Quantenfelder angewendet, die tatsächlich experimentell erprobt wurde, was erstmals erlaubte, verschiedene thermodynamische Eigenschaften von eindimensionalen Quasikondensaten experimentell zu vermessen. Insbesondere werden tomographische Resultate über thermische Eigenschaften präsentiert, über Erwartungswerte von nichtkommutierenden Observablen und auch Besetzungen von Phononenmoden, in Impuls und Zeit aufgelöst. Schließlich werden Ideen vorgestellt über die Zertifikation der Quantendynamik abgeschlossener Quantensysteme, basierende auf der Idee eines sogenannten Fidelitätszeugen. Es wird gezeigt, dass die Fidelität - eine inhärent fragile Größe für große Quantensysteme - effizient geschätzt werden kann für die Nichtgleichgewichtsdynamik kohärenter Quantensimulatoren, die paradigmatische Systeme aus der Physik der kondensierten Materie implementieren. Die so entwickelte Methode hat bereits eine unabhängige Anwendung gefunden in Studien variationeller Quantenschaltkreise, die darauf abzielen, das Genauigkeitsniveau der Quantenchemie zu erreichen, den Sycamore Quantenprozessor verwendend. Die Tatsache, dass alle drei in dieser Dissertation präsentierten theoretischen Forschungsrichtungen bereits experimentell realisiert werden konnten, deutet darauf hin, dass hier eine Prognose aufgegriffen werden kann, nach der es Standard wird, dass Quantensimulatoren theoretische Ideen gezielt aufgreifen können und die Zeit zwischen theoretischer Einsicht und experimenteller Bestätigung dramatisch verkürzt wird

MFCS\u2798 Satellite Workshop on Cellular Automata

For the 1998 conference on Mathematical Foundations of Computer Science (MFCS\u2798) four papers on Cellular Automata were accepted as regular MFCS\u2798 contributions. Furthermore an MFCS\u2798 satellite workshop on Cellular Automata was organized with ten additional talks. The embedding of the workshop into the conference with its participants coming from a broad spectrum of fields of work lead to interesting discussions and a fruitful exchange of ideas. The contributions which had been accepted for MFCS\u2798 itself may be found in the conference proceedings, edited by L. Brim, J. Gruska and J. Zlatuska, Springer LNCS 1450. All other (invited and regular) papers of the workshop are contained in this technical report. (One paper, for which no postscript file of the full paper is available, is only included in the printed version of the report). Contents: F. Blanchard, E. Formenti, P. Kurka: Cellular automata in the Cantor, Besicovitch and Weyl Spaces K. Kobayashi: On Time Optimal Solutions of the Two-Dimensional Firing Squad Synchronization Problem L. Margara: Topological Mixing and Denseness of Periodic Orbits for Linear Cellular Automata over Z_m B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata K. Morita, K. Imai: Number-Conserving Reversible Cellular Automata and Their Computation-Universality C. Nichitiu, E. Remila: Simulations of graph automata K. Svozil: Is the world a machine? H. Umeo: Cellular Algorithms with 1-bit Inter-Cell Communications F. Reischle, Th. Worsch: Simulations between alternating CA, alternating TM and circuit families K. Sutner: Computation Theory of Cellular Automat

Tackling the development of hormone therapy resistance in breast cancer through mathematical modelling

Patients suffering from estrogen-driven breast cancer frequently develop hardly predictable resistance to hormone therapy, which significantly complicates treatment. Current approaches for tackling this problem include cell models and clinical studies, both supported by sequencing technologies like RNA-seq, and offering different strengths and limitations. This dissertation addresses the challenge of predicting resistance to hormone therapy in breast cancer by merging advances in bioinformatics and Bayesian statistics, and applying them to two types of data – RNA-seq data and clinical data. First, we explore the statistical analysis of clinical data through Bayesian inference combined with enhanced Markov Chain Monte Carlo techniques, and introduce a novel algorithm for adaptive integration in prospective Modified Hamiltonian Monte Carlo (MHMC) methods. We demonstrate its positive effect on performance of MHMC in biomedical applications using clinical data of breast cancer patients. Next, we propose and implement an RNA-seq pipeline within our interactive web-app for the analysis of resistant breast cancer cell lines sequenced at CIC bioGUNE. Finally, we propose an original approach based on a Bayesian logistics regression model coupled with a simulated annealing-like algorithm for a combined analysis of RNA-seq and clinical data, and apply it to ad hoc data to obtain and validate in-silico and in-vitro a novel 6-gene signature for stratifying patient response to hormone therapy

The matter power spectrum in redshift space using effective field theory

The use of Eulerian 'standard perturbation theory' to describe mass assembly in the early universe has traditionally been limited to modes with k <= 0.1 h/Mpc at z=0. At larger k the SPT power spectrum deviates from measurements made using N-body simulations. Recently, there has been progress in extending the reach of perturbation theory to larger k using ideas borrowed from effective field theory. We revisit the computation of the redshift-space matter power spectrum within this framework, including for the first time for the full one-loop time dependence. We use a resummation scheme proposed by Vlah et al. to account for damping of the baryonic acoustic oscillations due to large-scale random motions and show that this has a significant effect on the multipole power spectra. We renormalize by comparison to a suite of custom N-body simulations matching the MultiDark MDR1 cosmology. At z=0 and for scales k <~ 0.4 h/Mpc we find that the EFT furnishes a description of the real-space power spectrum up to ~ 2%, for the ell=0 mode up to ~ 5% and for the ell = 2, 4 modes up to ~ 25%. We argue that, in the MDR1 cosmology, positivity of the ell = 0 mode gives a firm upper limit of k ~ 0.74 h/Mpc for the validity of the one-loop EFT prediction in redshift space using only the lowest-order counterterm. We show that replacing the one-loop growth factors by their Einstein-de Sitter counterparts is a good approximation for the ell = 0 mode, but can induce deviations as large as 2% for the ell = 2, 4 modes. An accompanying software bundle, distributed under open source licenses, includes Mathematica notebooks describing the calculation, together with parallel pipelines capable of computing both the necessary one-loop SPT integrals and the effective field theory counterterms