Rings, Shells, and Arc Structures Around B[e] Supergiants. I. Classical Tools of Nonlinear Hydrodynamics

An important aspect of the assessment of climate models is the representation of fast physical processes, which have a strong impact on climate projections. Since these fast processes also have a strong impact on weather forecasts, there is potential in using numerical weather prediction (NWP)‐based methodologies in climate model assessments.Two NWP‐based methods have been proposed in the literature. The first is referred to as the ‘initial tendency’ approach and assesses the systematic departure in the first few hours of short climate model resolution forecasts from the weather trajectory. For this method, the forecast model needs data assimilation capabilities to create initial conditions consistent with the model physics. The second approach is referred to as the ‘transpose‐AMIP’ method. This makes use of analyses produced with a different forecast model to initiate weather forecasts with a climate model. It is generally recommended that errors are diagnosed after a few forecast days to minimise the impact of the non‐native initial conditions.Here we compare these two methods in one NWP model over the subtropical South Pacific, which encompasses climatologically important regimes and transitions between them. The impact of the non‐native initial conditions is compared with the impact of an error introduced in the convection scheme.Results show that care is needed in the design and evaluation of transpose‐AMIP‐style experiments if model errors are to be disentangled from, at short lead‐times, the initial shock of using non‐native initial conditions and, at longer lead‐times, the complicating effects of interactions and the growth of chaos. On the other hand, the initial tendency approach is able to identify the introduced model error. This provides some evidence that it might be worthwhile for climate centres to explore the use of data assimilation.

In this thesis I present three separate studies on three different topics in General Relativity. The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a laser-interferometer gravitational-wave detector. The black hole is assumed to have been strongly perturbed, perhaps by coalescence with a binary companion, and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured mass and angular momentum arise from the unavoidable presence of noise in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. It is also found that the errors in the mass and angular momentum are highly correlated. The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell. This analysis is expected to be helpful in understanding the behavior during collapse of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time, as measured by a distant observer or by one riding on the shell. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The picture is completed with a numerical simulation that follows the collapse from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in the direction parallel to the symmetry axis, and infinitely compressed in the azimuthal direction. The gravitational waves emitted from the collapse are also analyzed. The last study focuses on a different kind of phenomenon, namely, the consequences of the existence of closed timelike curves in a spacetime that contains a wormhole. One might expect that the closed timelike curves would cause difficulty for the initial value problem for systems that evolve in such a spacetime: a system with apparently well-posed initial conditions might have no self-consistent solutions to its evolution equations. We study the simple case of a macroscopic, classical particle with a hard-sphere potential (a billiard ball), and we focus attention on initial conditions for which the evolution, if followed naively, is self- inconsistent: the ball enters one mouth of the wormhole and then comes out of the other mouth at an earlier time, then collides with its younger self, preventing itself from ever entering the first mouth. We find, surprisingly, that for all such dangerous initial conditions, there are an infinite number of self-consistent evolutionary solutions, involving a glancing collision and any number of wormhole traversals. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.

L-stable Simpson’s 3/8 rule and Burgers’ equation

This work discusses the soliton solutions for the fractional complex Ginzburg–Landau equation in Kerr law media. It is a particularly fascinating model in this context as it is a dissipative variant of the Hamiltonian nonlinear Schrödinger equation with solutions that create localized singularities in finite time. The ϕ6-model technique is one of the generalized methodologies exerted on the fractional complex Ginzburg–Landau equation to find the new solitary wave profiles. As a result, solitonic wave patterns develop, including Jacobi elliptic function, periodic, dark, bright, single, dark-bright, exponential, trigonometric, and rational solitonic structures, among others. The assurance of the practicality of the solitary wave results is provided by the constraint condition corresponding to each achieved solution. The graphical 3D and contour depiction of the attained outcomes is shown to define the pulse propagation behaviors while imagining the pertinent data for the involved parameters. The sensitive analysis predicts the dependence of the considered model on initial conditions. It is a reliable and efficient technique used to generate generalized solitonic wave profiles with diverse soliton families. Furthermore, we ensure that all results are innovative and mark remarkable impacts on the prevailing solitary wave theory literature.

A numerical model describing the dynamics of the surface gravity waves and acoustic waves induced in the ocean by small dynamic deformations of the bottom is developed. The model is based on the linear potential theory. The model represents a combination of two dynamically coupled blocks: deep-water and shallow. The deep-water block solves a three-dimensional problem of potential wave theory in the sigma-spherical coordinates; the shallow block solves a two-dimensional problem of shallow water theory in the spherical coordinates. The results of testing the numerical model using the analytical solution of the problem for the flat horizontal bottom are presented. A comparative analysis of the simulation results of tsunamis on November 15, 2006 and January 13, 2007 on the Central Kuril Islands with the use of the newly developed and conventional long-wave models is performed.

The initial stage of dam-break flow of two immiscible fluids. Linear analysis of global flow

The classification theory of Riemann surfaces is generalized to Riemanniann-manifolds in the conformally invariant case. This leads to the study of the existence ofA-harmonic functions of typen with various properties and to an extension of the definition of the classical notions with inclusionsOG⊂OHP⊂OHB⊂OHD. In the classical case the properness of the inclusions were proved rather late, in the 50's by Ahlfors and Toki. Our main objective is to show that such inclusions are proper also in the generalized case.

Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic function

In this paper, we obtain gradient continuity estimates for viscosity solutions of [Formula: see text] in terms of the scaling critical [Formula: see text]-norm of [Formula: see text], where [Formula: see text] is the normalized [Formula: see text]-Laplacian operator. Our main result corresponds to the borderline gradient continuity estimate in terms of the modified Riesz potential [Formula: see text]. Moreover, for [Formula: see text] with [Formula: see text], we also obtain [Formula: see text] estimates. This improves one of the regularity results in [A. Attouchi, M. Parviainen and E. Ruosteenoja, [Formula: see text] regularity for the normalized [Formula: see text]-Poisson problem, J. Math. Pures Appl. (9) 108(4) (2017) 553–591], where a [Formula: see text] estimate was established depending on the [Formula: see text]-norm of [Formula: see text] under the additional restriction that [Formula: see text] and [Formula: see text]. We also mention that differently from the approach in the above paper, which uses methods from divergence form theory and nonlinear potential theory, the method in this paper is more non-variational in nature, and it is based on separation of phases inspired by the ideas in [L. Wang, Compactness methods for certain degenerate elliptic equations, J. Differential Equations 107(2) (1994) 341–350]. Moreover, for [Formula: see text] continuous, our approach also gives a somewhat different proof of the [Formula: see text] regularity result.

Approximation in Sobolev spaces and nonlinear potential theory

Pointwise gradient bounds via Riesz potentials, such as those available for the linear Poisson equation, actually hold for general quasilinear degenerate equations of p-Laplacean type. The regularity theory of such equations completely reduces to that of the classical Poisson equation up to the C1-level.

<div class="htmlview paragraph">This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analysis is based on a linearization of the non-uniform potential mean flow. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.</div>

Nonlinear potential theory in metric spaces

The quest of deciphering the true nature of dark energy has proven to be one of the most exciting in recent times in cosmology. Various ideas have been put forward in this regard besides the usual cosmological constant approach, ranging from scalar field based models like Quintessence and Phantom dark energy to various modified gravity approaches as well. A very interesting idea then is to consider scalar field dark energy models in quantum gravitationally corrected cosmologies with the RS-II Braneworld being one of the most well known in this regard. So in this work, we consider RS-II Braneworld based scalar field dark energy models and try to look out for the existence of finite time singularities in these regimes both through a dynamical system perspective, for which we employ the Goriely–Hyde singularity analysis method, and a physical perspective. Our approach is general in the sense that it is not limited to any particular class of potentials or for any constrained parameter region for the brane tension and is valid for both Quintessence and phantom dark energy regimes. We firstly show through Goriely–Hyde procedure that finite time singularities can exist in these models for a limited set of initial conditions and that this result would hold irrespective of any consideration given to the swampland dS conjecture. We then discuss the physical nature of the singularities that can occur in this regime, where we use a well motivated ansatz for the Hubble parameter and show that these models of dark energy can allow for weak singularities like those of Type III and Type IV and can also allow for strong singularities like the Big Rip (Type I).

This paper numerically investigates the energy evolution of the focused wave and its correlation with input parameters for the wave generation. The focused wave is numerically generated based on the fully nonlinear potential wave theory which is solved by the Quasi Arbitrary Lagrangian Eulerian-Finite Element Method. The investigation is performed by dividing the generated wave energy into three categories according to their frequency intervals, i.e., the initially assigned frequency interval [f1fN], the frequencies lower (f < f1) and higher (f > fN) than the initial interval. The amount of the generated energy falling into three energy categories and the energy distribution in the initial frequency interval are analysed against amplitude parameters and frequency bands under three amplitude spectra. Four indicators are proposed to indicate the actual energy variations comparing to the initial design. It is found that for all the three frequency intervals the energies increase when the amplitude parameters increases or the given frequency shifts towards the lower frequency domain. The choice of wave amplitude spectrum plays a significant role to maintain the distribution of the energy in the design frequency range and to minimise the energies out of the design frequency range. The results from the second-order wave group theory are used to assist analyses of the mechanism of the energy evolution alongside the focused wave generation. It is found that the lower-frequency energy in the vicinity of the focusing point is dominated by the second-order difference waves, whereas the higher-frequency energy is mainly produced by the wave flap. The waves which are higher than the second-order and the complex interactions not considered by the second-order wave theory are found significantly disturbing the energy distribution in the originally assigned wave-frequency interval.