On continuum driven winds from rotating stars

We study the dynamics of continuum driven winds from rotating stars, and develop an approximate analytical model. We then discuss the evolution of stellar angular momentum, and show that just above the Eddington limit, the winds are sufficiently concentrated towards the poles to spin up the star. A twin-lobe structure of the ejected nebula is seen to be a generic consequence of critical rotation. We find that if the pressure in such stars is sufficiently dominated by radiation, an equatorial ejection of mass will occur during eruptions. These results are then applied to {\eta}-Carinae. We show that if it began its life with a high enough angular momentum, the present day wind could have driven the star towards critical rotation, if it is the dominant mode of mass loss. We find that the shape and size of the Homunculus nebula, as given by our model, agree with recent observations. Moreover, the contraction expected due to the sudden increase in luminosity at the onset of the Great Eruption explains the equatorial "skirt" as well.Comment: 8 pages, 4 figure

Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation

A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlev´e II reduction of a resonant NLS equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uniaxial propagation of magneto-acoustic waves. A B¨acklund transformation is employed in the iterative generation of novel classes of solutions to the cold plasma system which involve either Yablonski-Vorob’ev polynomials or classical Airy function

The Unitary Gas and its Symmetry Properties

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typo

Matching of spacetimes theory applied to rotating stars and quadratic gravity

233 p.Este resumen contiene un repaso breve de las actividades de investigación que se han llevado a cabo durante el desarrollo de la presente tesis doctoral, realizada con la ayuda predoctoral del Gobierno Vasco (BFI-2011-250) durante los años 2012-2015 en el departamento de Física Teórica e Historia de la Ciencia de la UPV/EHU, bajo la dirección de R.Vera. La primera parte del resumen está dedicada a explicar los problemas que se han abordado, cómo se ha hecho o qué métodos se han empleado y qué resultados hemos obtenido

On surface water waves and tsunami propagation

In dieser Arbeit werden die reibungslosen Bewegungsgleichungen für wasser Wellen mit physikalischer Motivation eingeführt. Es folgt ein Studium der Eigenschaften dieser Gleichungen, die durch anwendung asymptotischer Näherungen zur Korteweg-de Vries Gleichung führen. Schließlich wird die Korteweg-de Vries Gleichung hinsichtlich ihrer Anwendung im Bereich der Tsunami Modellierung untersucht.This work introduces the inviscid governing equations for water waves from a physically motivated standpoint, in as accessible a manner as possible. From there, certain asymptotic regimes are explored, leading to the Korteweg-de Vries equation. Elaborations are made on applications to tsunami modeling, while taking care to point out shortcomings in the analytical approach as well as unresolved difficulties in reconciling the intriguing nature of water with mathematics

Effects of finite Rossby radius on vortex-boundary interactions

The effect of the finite Rossby radius on vortex motion is examined in a two-dimensional inviscid incompressible fluid, assuming quasigeostrophic dynamics in a single layer of fluid with reduced gravity for two geophysically significant problems: a vortex near a gap in a wall and a pair of steady translating vortices. For the motion of a point vortex near a gap in an infinite barrier, a key parameter determining the behaviour of the vortex is a, the ratio of the Rossby radius of deformation and the half-width of the gap. For large a, depending on the location of the vortex, a vortex sheet is placed either over the gap (gap method) or over the two semi-infinite barriers (barrier method). When the vortex sheet is over the gap, numerical inaccuracies are encountered when the vortex is close to the gap, therefore the conjugate (barrier) method is used. Both integral equations contain singularities which can be de-singularised and solved iteratively using the known exact solution in rigid-lid limit, i.e. a → ∞. For large a, there is only slight deviation from the analytical (a → ∞) trajectories. For smaller a, the integral equation from the conjugate method is solved by numerically approximating the integral equation into a system of linear equations and solving using matrix inversion. The integral equation is further simplified by splitting into even and odd parts, thus reducing the problem to the half plane. It is also found that decreasing a, increases the tendency for vortices to pass through the gap. Background flows influence vortex trajectories and are incorporated by modifying the conjugate method integral equation. These equations are solved using the matrix method. Streamlines for uniform symmetric and anti-symmetric (which has no analogy in the rigid-lid limit) flow through the gap are computed and their effect on the vortex trajectories are found. The motion of finite area patches of constant vorticity near a gap in a wall is computed using the matrix method in conjunction with contour dynamics. For fixed a, vortex patches are normalised to travel at the same speed as a point vortex. The normalisation is non-trivial and depends nonlinearly on the patch area and a. In the rigid-lid limit, it reduces to the ‘usual’ normalisation based on the patch circulation. For near circular patches, the trajectory of the centroid of the patches also follows the trajectory of the point vortices. When the patch becomes distorted the agreement is not so close. The splitting and joining of contours is also computed using contour surgery and some examples showing this sudden change of behaviour is presented. The next problem determines the effect of the Rossby radius of deformation, on steady translating vortex pairs or, equivalently, a patch in steady translation near a wall. The velocities for the normalised vortex patch are compared to the velocity of a point vortex located at the centroid of the patch. It is found there is good agreement for a range of patch sizes. When the patches are sufficiently far from the wall, decreasing the Rossby radius makes the steadily translating shapes more circular. However, when close to the wall, the effect of the Rossby radii results in patches deforming greatly, forming long slug-like shapes. These are shown to be stable using a time dependent contour dynamics code. Background flows are also incorporated and give different vortical shapes for finite Rossby radii flows, ranging from slug-like to tear-drop in shape

ELASTO-CAPILLARITY IN FIBROUS MATERIALS

Current advances in the manufacture of nanoporous and nanofibrous materials with high absorption capacity open up new opportunities for the development of fiber-based probes and sensors. Pore structures of these materials can be designed to provide high suction pressure and fast wicking. During wicking, due to the strong capillary action, the liquids exert stresses on the fiber network, thus the stressed state of dry and wet parts of the material differs. In this work the effect of stress reduction in fibrous materials due to the presence of wetting liquid in the pore structure is studied in details for both static and dynamic cases. It is suggested that this effect can be used for liquid monitoring and the examples of one and two dimensional probes are provided. To open a discussion an illustrative example of a single capillary is considered and the effect of a moving meniscus on the stress distribution along capillary walls is demonstrated. Then the similar effects are analyzed in yarns and fabrics. A yarn that can capture an aerosol droplet is considered as a promising sensing element that could monitor the stresses caused by wetting fronts. It is shown that the stress transfer between dry and wet parts of the yarn upon liquid wicking significantly depends on the boundary conditions. The stress distribution in the yarn with clamped ends is discussed. The elasto-capillary problem is resolved for 2D case of a freely suspended self-reconfigurable material. It is shown that the classical Bernoulli problem of a freely suspended fabric can be used for the analysis of stresses in the fibrous matrix. The theoretical conclusions on elasto-capillarity are supported by experimental results on tensile testing of fibrous materials. The results show that the elasto-capillary effect is pronounced in the porous samples with the pore sizes smaller than 10 microns

Variational Methods for Evolution

The workshop brought together researchers from geometry, nonlinear functional analysis, calculus of variations, partial differential equations, and stochastics around a common topic: systems whose evolution is driven by variational principles such as gradient or Hamiltonian systems. The talks covered a wide range of topics, including variational tools such as incremental minimization approximations, Gamma convergence, and optimal transport, reaction-diffusion systems, singular perturbation and homogenization, rate-independent models for visco-plasticity and fracture, Hamiltonian and hyperbolic systems, stochastic models and new gradient structures for Markov processes or variational large-deviation principles