5,756 research outputs found
Linear Amplification in Nonequilibrium Turbulent Boundary Layers
Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating Nâ‚‚, Oâ‚‚, NO, N, and O as a mixture of chemically reacting gases.
Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale.
Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data.
Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.</p
Symmetries of Riemann surfaces and magnetic monopoles
This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions
Consistency of scalar and vector effective field theories
In the absence of a theory of everything, modern physicists need to rely on other predictive tools and turned to Effective Field Theories (EFTs) in a number of fields, including but not limited to statistical mechanics, condensed matter, particle physics, cosmology and gravity. The coefficients of an EFT can be constrained with high precision by experiments, which can involve high-energy particle colliders for instance but are generally left free from the theoretical point of view. The focus of this thesis is to use various consistency criteria to get theoretical constraints on the low-energy coefficients of EFTs. In particular, we construct a new model of massive spin-1 field by requiring that the theory is free of any ghostly degree of freedom. We then study its cosmological perturbations and ask that all propagating modes are stable and subluminal, reducing the space of viable cosmological solutions. Finally, we implement a method to get ‘causality bounds’, which are obtained by requiring infrared causality. This is imposed by forbidding any resolvable time advance in the EFT. We derive such ‘causality bounds’ for shift-symmetric and Galileon scalar EFTs, before turning to gauge-symmetric vector fields. We prove that our causality bounds can be competitive with positivity bounds and can even be used in scenarios that are out of reach of the positivity approach. The result of this thesis, by exploring several consistency criteria, is to provide compact causality bounds for low-energy EFT coefficients, in addition to constraints coming from the absence of ghosts, stability and cosmological viability.Open Acces
Simulation of heart growth in embryogenesis
The subject of this report is related to the finite element method and its application in the
simulation of a mouse heart in embryogenesis. The focus is on the malformation in criss-
cross heart which is caused by abnormal rotation of the ventricular mass along the long axis
of the heart during embryonic development. The project studies several growth patterns and
boundary conditions that may yield to the experimentaly observed development for regular and
criss-cross heart embryos.Incomin
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields
Deep Learning is having a remarkable impact on the design of Reduced Order
Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited
as a powerful tool for tackling complex problems for which classical methods
might fail. In this respect, deep autoencoders play a fundamental role, as they
provide an extremely flexible tool for reducing the dimensionality of a given
problem by leveraging on the nonlinear capabilities of neural networks. Indeed,
starting from this paradigm, several successful approaches have already been
developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs).
Nevertheless, when it comes to stochastic problems parameterized by random
fields, the current understanding of DL-ROMs is mostly based on empirical
evidence: in fact, their theoretical analysis is currently limited to the case
of PDEs depending on a finite number of (deterministic) parameters. The purpose
of this work is to extend the existing literature by providing some theoretical
insights about the use of DL-ROMs in the presence of stochasticity generated by
random fields. In particular, we derive explicit error bounds that can guide
domain practitioners when choosing the latent dimension of deep autoencoders.
We evaluate the practical usefulness of our theory by means of numerical
experiments, showing how our analysis can significantly impact the performance
of DL-ROMs
Mineral snowflakes on exoplanets and brown dwarfs
The diversity of exoplanets and brown dwarfs provides ideal atmospheric laboratories to investigate novel physico-chemical regimes. Furthermore, the atmospheres of exoplanets act as the history books of planetary system. However, as observational data improves, the contributions of cloud particles in exoplanet and brown dwarf atmospheres must be adequately accounted for. Microphysical modelling of cloud formation provides the best method to investigate the potentially observable properties of clouds in these atmospheres. Most observed gas-giant exoplanets have been suggested to host mineral clouds which could form `snowflake-like' structures through condensation and constructive collisions. Cloud particle porosity, size and number density are influenced by constructive and destructive collisions. In this thesis, we expand our kinetic non-equilibrium cloud formation model to explore the effects of non-compact, non-spherical cloud particles on cloud structure and their spectroscopic properties. Additionally, we investigate the effects on clouds of collisional growth and fragmentation. The impact of these affects is assessed on prescribed 1D (Tgas-Pgas) profiles in DRIFT-PHOENIX model atmospheres of brown dwarfs and exoplanets. We utilise Mie theory and effective medium theory to study cloud optical depths, where we additionally represent non-spherical cloud particles with a statistical distribution of hollow spheres. We find that micro-porosity can affect the distribution of cloud particles in an exoplanet atmosphere, and that irregular particle shape impacts the optical depth in the near- and mid-infrared. However, we also find that cloud particle collisions driven by turbulence result in fragmentation of cloud particles for exoplanet atmospheres, which also impacts optical depths in the optical and mid-infrared regions. The global distribution and properties of clouds is also important as observations begin to allow for treating exoplanets in their full 3D nature. We therefore apply a hierarchical approach to global cloud formation modelling. We also apply our 1D cloud formation model to profiles extracted from results of 3D General Circulation Models (GCM) for the gas-giant exoplanet WASP-43b and the ultra-hot Jupiter HAT-P-7b, revealing a dramatic difference in the distribution of clouds between these types of exoplanets as a result of stellar radiation heating the day-side of the ultra-hot planets. This results in an asymmetry in cloud structures for the terminators of WASP-43b and more significantly for HAT-P-7b, observable in the optical depth of the clouds at these points, further complicating retrieval of cloud properties from spectra."This work was supported by the Science and Technology Facilities Council (STFC), UK [grant number 2093954]; and the Österreichische Akademie der Wissenschaften."--Fundin
"Le present est plein de l’avenir, et chargé du passé" : Vorträge des XI. Internationalen Leibniz-Kongresses, 31. Juli – 4. August 2023, Leibniz Universität Hannover, Deutschland. Band 3
[No abstract available]Deutschen Forschungsgemeinschaft (DFG)/Projektnr. 517991912VGH VersicherungNiedersächsisches Ministerium für Wissenschaft und Kultur (MWK
Historical Burdens on Physics
When learning physics, one follows a track very similar to the historical path of the evolution of this science: one takes detours, overcomes superfluous obstacles and repeats mistakes, one learns inappropriate concepts and uses outdated methods. In the book, more than 200 articles present and analyze such obsolete concepts methods. All articles have the same structure: 1. subject, 2. deficiencies, 3. origin, 4. disposal. The articles had originally appeared as columns in various magazines. Accordingly, we had tried to write them in an easily understandable way
Synthesis, Characterization, and Simulation of Two-Dimensional Materials
ABSTRACT
SYNTHESIS, CHARACTERIZATION, AND SIMULATION OF TWO-DIMENSIONAL MATERIALS
by
Lawrence Hudy
The University of Wisconsin-Milwaukee, 2023Under the Supervision of Professor Michael Weinert
This dissertation focuses on my journey through many aspects of surface science leading to the first principles investigation of transition metal dichalcogenides studying the impact of defects, twist, and decreasing interlayer separation to probe their effect on the electronic properties of these materials. My journey started out learning many aspects of material science such as methods for material synthesis and characterization but later ended on simulation of material properties using density functional theory. In the first experiments, we focus on two-dimensional material synthesis, mostly involving graphene, where we see that polymer transferred graphene forms a Schottky junction when interfaced with a semiconductor. From atomic force microscopy and scanning tunneling microscopy we see that polymer transferred graphene is not entirely flat and forms ripples and ridges on the surface. Scanning tunneling spectroscopy and temperature dependent current-voltage measurements help to show that the behavior of these graphene Schottky diodes are not ideal. The observed temperature dependent Schottky barrier height can be explained using a distribution of barriers with varying barrier heights. The theoretical studies focus on various transition metal dichalcogenides, composed of MoSe2 and WSe2, using their monolayer and their homo and hetero bilayer counterparts. The first studies observed that adding defects alters the electronic band structure, and in particular, a copper dopant creates impurity states at the Fermi level and induces a significant magnetic moment in the material. The resulting occupied unpaired spin states are the key contributor to the creation of the magnetic moment in this material. Next, we see that twisted bilayer transition metal dichalcogenides, specifically bilayers composed of MoSe2 and WSe2, where we observe pressure induced flat bands and real space localization. Using a commensurate set of twist angles and varying interlayer spacing led to the discovery of flat bands and real space localization. These flat bands are a result of forcing the bilayers to interact causing a localization in real space. It is only under special conditions where the closest chalcogens, along with the nearest metal atoms, form a hybridized state that contribute to the flat bands in the energy band diagram. These findings help to highlight the impact impurities can have on transition metal dichalcogenides and the role of twist and interlayer separation has on the formation of flat bands as well as real space localization in these materials
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