314 research outputs found

    Neutrinos from horizon to sub-galactic scales

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    A first determination of the mass scale set by the lightest neutrino remains a crucial outstanding challenge for cosmology and particle physics, with profound implications for the history of the Universe and physics beyond the Standard Model. In this thesis, we present the results from three methodological papers and two applications that contribute to our understanding of the cosmic neutrino background. First, we introduce a new method for the noise-suppressed evaluation of neutrino phase-space statistics. Its primary application is in cosmological N-body simulations, where it reduces the computational cost of simulating neutrinos by orders of magnitude without neglecting their nonlinear evolution. Second, using a recursive formulation of Lagrangian perturbation theory, we derive higher-order neutrino corrections and show that these can be used for the accurate and consistent initialisation of cosmological neutrino simulations. Third, we present a new code for the initialisation of neutrino particles, accounting both for relativistic effects and the full Boltzmann hierarchy. Taken together, these papers demonstrate that with the combination of the methods described therein, we can accurately simulate the evolution of the neutrino background over 13.8 Gyr from the linear and ultra-relativistic regime at z=109z=10^9 down to the non-relativistic yet nonlinear regime at z=0z=0. Moreover, they show that the accuracy of large-scale structure predictions can be controlled at the sub-percent level needed for a neutrino mass determination. In a first application of these methods, we present a forecast for direct detection of the neutrino background, taking into account the gravitational enhancement (or indeed suppression) of the local density due to the Milky Way and the observed large-scale structure within 200 Mpc/h. We determine that the large-scale structure is more important than the Milky Way for neutrino masses below 0.1 eV, predict the orientation of the neutrino dipole, and study small-scale anisotropies. We predict that the angular distribution of neutrinos is anti-correlated with the projected matter density, due to the capture or deflection of neutrinos by massive objects along the line of sight. Finally, we present the first results from a new suite of hydrodynamical simulations, which includes the largest ever simulation with neutrinos and galaxies. We study the extent to which variations in neutrino mass can be treated independently of astrophysical processes, such as feedback from supernovae and black holes. Our findings show that baryonic feedback is weakly dependent on neutrino mass, with feedback being stronger for models with larger neutrino masses. By studying individual dark matter halos, we attribute this effect to the increased baryon density relative to cold dark matter and a reduction in the binding energies of halos. We show that percent-level accurate modelling of the matter power spectrum in a cosmologically interesting parameter range is only possible if the cosmology-dependence of feedback is taken into account

    Parametric Excitation of Coupled Nonlinear Microelectromechanical Systems

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    The commencement of the semi-conductor industry in the second half of the last century gave a surprising new outlook for engineered dynamical mechanical systems. It enabled, thanks to the continuously evolving microfabrication methods, the implementation of Micro Electromechanical systems (MEMS) followed by their nano-counterpart or NEMS. Nowadays M/NEMS constitute a massive portion of the small-scaled sensors industry, in addition to electrical, optical and telecommunication components. Since these tiny dynamical electromechanical systems involve sometimes couplings between degrees of freedom as well as nonlinearities, the theory of stability in dynamical systems plays a significant role in their design and implementation. From a practical point of view, the approach to stability problems often takes two different perspectives. The first one, most commonly in linear systems, aims to avoid any instability which could cause destructive consequences for mechanical structures or for electrical and electronic components. On the contrary in nonlinear systems, the second perspective aims to drive the system into regions of instability for the trivial solution, while searching for stable nontrivial steady-state solutions of the underlying differential equations. With the advent of micro and nanosystems, the second perspective could acquire increased importance. This is attributed to their capability to exhibit typical nonlinear behavior and higher amplitudes at normal operation conditions, when compared to macroscale systems. Higher amplitudes, in this sense, allows for a better amplification of an input excitation, and thereby higher sensitivity for miniature sensors and measurement devices. In addition, if the system parameters were time-periodic, the trivial solution could turn to be unstable at the so called parametric resonances. Known as parametric pumping in micro and nanosystems, the system’s response is usually amplified at these resonance frequencies for higher sensitivity and accuracy. For these reasons, this work is mainly focused on parametrically excited nonlinear systems. Nevertheless, a systematic approach is followed in this thesis, where the origins of destabilization are surveyed in time-invariant systems before proceeding to carry out a theoretical study on time-periodic systems in general, and time-periodic nonlinear systems in particular. Through this theoretical study, a novel idea for the M/NEMS industry is presented, namely the broadband parametric amplification using a bimodal excitation method. This idea is then implemented in microsystems, by investigating a particular example, that is the microgyorscope. Given the low-cost of this device in comparison with other inertial sensors, it is being currently enhanced to reach a relatively higher sensitivity and accuracy. To this end, the theoretical findings, including the mentioned idea, are implemented in this device and prove to contribute effectively to its performance. Moreover, an experimental investigation is carried out on an analogous microsystem. Through the experimental study, an electronic system is introduced to apply the proposed bimodal parametric excitation method on the microsystem. By comparing the stability charts in theory and experiment, the theoretical model could be validated. In conclusion, a theoretical study is carried out through this work on parametrically excited nonlinear systems, then implemented on microgyroscopes, and finally experimentally validated. Thereby, this work puts a first milestone for the utilization of the proposed excitation method in the M/NEMS industry

    Cosmology with the Laser Interferometer Space Antenna

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    The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Nonautonomous Spectral Submanifolds for Model Reduction of Nonlinear Mechanical Systems under Parametric Resonance

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    We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization of SSMs and their reduced dynamics. We provide these results both for general first-order as well as second-order mechanical systems under periodic and quasiperiodic excitation using a multi-index based approach, thereby optimizing memory requirements and the computational procedure. We further provide theoretical results that simplify the SSM parametrization for general second-order dynamical systems. More practically, we show how the reduced dynamics on the SSM can be used to extract the resonance tongues and the forced response around the principal resonances in parametrically excited systems. In the case of two-dimensional SSMs, we formulate explicit expressions for computing the steady-state response as the zero-level set of a two-dimensional function for systems that are subject to external as well as parametric excitation. This allows us to parallelize the computation of the forced response over the range of excitation frequencies. We demonstrate our results on several examples of varying complexity, including finite-element type examples of mechanical systems. Furthermore, we provide an open-source implementation of all these results in the software package SSMTool

    Geometry and Topology in Memory and Navigation

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    Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyGeometry and topology offer rich mathematical worlds and perspectives with which to study and improve our understanding of cognitive function. Here I present the following examples: (1) a functional role for inhibitory diversity in associative memories with graph- ical relationships; (2) improved memory capacity in an associative memory model with setwise connectivity, with implications for glial and dendritic function; (3) safe and effi- cient group navigation among conspecifics using purely local geometric information; and (4) enhancing geometric and topological methods to probe the relations between neural activity and behaviour. In each work, tools and insights from geometry and topology are used in essential ways to gain improved insights or performance. This thesis contributes to our knowledge of the potential computational affordances of biological mechanisms (such as inhibition and setwise connectivity), while also demonstrating new geometric and topological methods and perspectives with which to deepen our understanding of cognitive tasks and their neural representations.doctoral thesi

    Primordial black holes and their gravitational-wave signatures

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    In the recent years, primordial black holes (PBHs) have emerged as one of the most interesting and hotly debated topics in cosmology. Among other possibilities, PBHs could explain both some of the signals from binary black hole mergers observed in gravitational wave detectors and an important component of the dark matter in the Universe. Significant progress has been achieved both on the theory side and from the point of view of observations, including new models and more accurate calculations of PBH formation, evolution, clustering, merger rates, as well as new astrophysical and cosmological probes. In this work, we review, analyse and combine the latest developments in order to perform end-to-end calculations of the various gravitational wave signatures of PBHs. Different ways to distinguish PBHs from stellar black holes are emphasized. Finally, we discuss their detectability with LISA, the first planned gravitational-wave observatory in space.Comment: 161 pages, 47 figures, comments welcom
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