Photometric and fundamental plane studies of galaxies

Determining the morphological parameters that describe galaxies has always been a challenging task. The studies on the correlations between different photometric as well as spectroscopic parameters of the galaxies help in understanding their structure, properties of the stars and gas which constitute the galaxy, the various physical and chemical processes which determine the properties, and galaxy formation and evolution. In the last few decades, the advent of Charge Coupled Devices (CCDs) and near infrared arrays ha\·e provided quick and reliable digitized data acquisition, in the optical and near infrared bands. This has provided an avalanche of data, which can be processed using sophisticated image analysis techniques to obtain information about the morphology of galaxies. The photometric analysis performed in this thesis involve the extraction of structural parameters of early type gala.xies imaged in the near infrared K (2.2ttm) band, obtaining correlations between these, parameters and using them to constrain the large scale properties of galaxi,~s.

Planar UWB Antenna with Modified Slotted Ground Plane

A compact coplanar waveguide-fed (CPW) monopole antenna for ultra-wideband wireless communication is presented. The proposed antenna comprises of a CPW-fed beveled rectangular patch with a modified slotted ground. The overall size of the antenna is 30 mm 27 mm 1.6 mm. The lower edge of the band is attained by properly decoupling the resonant frequencies due to the extended ground plane and the beveled rectangular patch of the antenna. The upper edge of the radiating band is enhanced by beveling the ground plane corners near the feed point. Experimental results show that the designed antenna operates in the 2.7–12 GHz band, for S11 10 dB with a gain of 2.7–5 dBi. Both the frequency domain and time domain characteristics of the antenna are investigated using antenna transfer function. It is observed that the antenna exhibits identical radiation patterns and reasonable transient characteristics over the entire operating band

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Boundary-layer ventilation by baroclinic lifecycles

Ventilation of the boundary layer has an important effect on local and regional air quality and is a prerequisite for long-range pollution transport. Once in the free troposphere, pollutants can alter the chemical composition of the troposphere and impact on the Earth's radiative forcing. Idealised baroclinic life cycles, LC1 and LC2, have been simulated in a three-dimensional dry hemispheric model in the presence of boundary-layer turbulent fluxes. A passive tracer is added to the simulations to represent pollution emitted at, or near, the surface. A simple conveyor-belt diagnostic is developed to objectively identify regions of the boundary layer that can be ventilated by either warm or cold conveyor belts. Transport of pollutants within and above the boundary layer is examined on synoptic scales. Three different physical mechanisms are found to interact with each other to ventilate pollutants out of the boundary layer. These mechanisms are turbulent mixing within the boundary layer, horizontal advection due to Ekman convergence and divergence within the boundary layer, and advection by the warm conveyor belt. The mass of tracer ventilated by the two life cycles is remarkably similar given the differences in frontal structure, suggesting that the large-scale baroclinicity is an effective constraint on ventilation.

Reactive Halogens in the Marine Boundary Layer (RHaMBLe): the tropical North Atlantic experiments

The NERC UK SOLAS-funded Reactive Halogens in the Marine Boundary Layer (RHaMBLe) programme comprised three field experiments. This manuscript presents an overview of the measurements made within the two simultaneous remote experiments conducted in the tropical North Atlantic in May and June 2007. Measurements were made from two mobile and one ground-based platforms. The heavily instrumented cruise D319 on the RRS Discovery from Lisbon, Portugal to São Vicente, Cape Verde and back to Falmouth, UK was used to characterise the spatial distribution of boundary layer components likely to play a role in reactive halogen chemistry. Measurements onboard the ARSF Dornier aircraft were used to allow the observations to be interpreted in the context of their vertical distribution and to confirm the interpretation of atmospheric structure in the vicinity of the Cape Verde islands. Long-term ground-based measurements at the Cape Verde Atmospheric Observatory (CVAO) on São Vicente were supplemented by long-term measurements of reactive halogen species and characterisation of additional trace gas and aerosol species during the intensive experimental period. This paper presents a summary of the measurements made within the RHaMBLe remote experiments and discusses them in their meteorological and chemical context as determined from these three platforms and from additional meteorological analyses. Air always arrived at the CVAO from the North East with a range of air mass origins (European, Atlantic and North American continental). Trace gases were present at stable and fairly low concentrations with the exception of a slight increase in some anthropogenic components in air of North American origin, though NOx mixing ratios during this period remained below 20 pptv. Consistency with these air mass classifications is observed in the time series of soluble gas and aerosol composition measurements, with additional identification of periods of slightly elevated dust concentrations consistent with the trajectories passing over the African continent. The CVAO is shown to be broadly representative of the wider North Atlantic marine boundary layer; measurements of NO, O3 and black carbon from the ship are consistent with a clean Northern Hemisphere marine background. Aerosol composition measurements do not indicate elevated organic material associated with clean marine air. Closer to the African coast, black carbon and NO levels start to increase, indicating greater anthropogenic influence. Lower ozone in this region is possibly associated with the increased levels of measured halocarbons, associated with the nutrient rich waters of the Mauritanian upwelling. Bromide and chloride deficits in coarse mode aerosol at both the CVAO and on D319 and the continuous abundance of inorganic gaseous halogen species at CVAO indicate significant reactive cycling of halogens. Aircraft measurements of O3 and CO show that surface measurements are representative of the entire boundary layer in the vicinity both in diurnal variability and absolute levels. Above the inversion layer similar diurnal behaviour in O3 and CO is observed at lower mixing ratios in the air that had originated from south of Cape Verde, possibly from within the ITCZ. ECMWF calculations on two days indicate very different boundary layer depths and aircraft flights over the ship replicate this, giving confidence in the calculated boundary layer depth.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.

Boundary layer structure and decoupling from synoptic scale flow during NAMBLEX

This paper presents an overview of the meteorology and planetary boundary layer structure observed during the NAMBLEX field campaign to aid interpretation of the chemical and aerosol measurements. The campaign has been separated into five periods corresponding to the prevailing synoptic condition. Comparisons between meteorological measurements ( UHF wind profiler, Doppler sodar, sonic aneometers mounted on a tower at varying heights and a standard anemometer) and the ECMWF analysis at 10 m and 1100 m identified days when the internal boundary layer was decoupled from the synoptic flow aloft. Generally the agreement was remarkably good apart from during period one and on a few days during period four when the diurnal swing in wind direction implies a sea/land breeze circulation near the surface. During these periods the origin of air sampled at Mace Head would not be accurately represented by back trajectories following the winds resolved in ECMWF analyses. The wind profiler observations give a detailed record of boundary layer structure including an indication of its depth, average wind speed and direction. Turbulence statistics have been used to assess the height to which the developing internal boundary layer, caused by the increased surface drag at the coast, reaches the sampling location under a wide range of marine conditions. Sampling conducted below 10 m will be impacted by emission sources at the shoreline in all wind directions and tidal conditions, whereas sampling above 15 m is unlikely to be affected in any of the wind directions and tidal heights sampled during the experiment.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Wave-driven wind jets in the marine atmospheric boundary layer

The interaction between ocean surface waves and the overlying wind leads to a transfer of momentum across the air–sea interface. Atmospheric and oceanic models typically allow for momentum transfer to be directed only downward, from the atmosphere to the ocean. Recent observations have suggested that momentum can also be transferred upward when long wavelength waves, characteristic of remotely generated swell, propagate faster than the wind speed. The effect of upward momentum transfer on the marine atmospheric boundary layer is investigated here using idealized models that solve the momentum budget above the ocean surface. A variant of the classical Ekman model that accounts for the wave-induced stress demonstrates that, although the momentum flux due to the waves penetrates only a small fraction of the depth of the boundary layer, the wind profile is profoundly changed through its whole depth. When the upward momentum transfer from surface waves sufficiently exceeds the downward turbulent momentum flux, then the near-surface wind accelerates, resulting in a low-level wave-driven wind jet. This increases the Coriolis force in the boundary layer, and so the wind turns in the opposite direction to the classical Ekman layer. Calculations of the wave-induced stress due to a wave spectrum representative of fast-moving swell demonstrate upward momentum transfer that is dominated by contributions from waves in the vicinity of the peak in the swell spectrum. This is in contrast to wind-driven waves whose wave-induced stress is dominated by very short wavelength waves. Hence the role of swell can be characterized by the inverse wave age based on the wave phase speed corresponding to the peak in the spectrum. For a spectrum of waves, the total momentum flux is found to reverse sign and become upward, from waves to wind, when the inverse wave age drops below the range 0.15–0.2, which agrees reasonably well with previously published oceanic observations.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Developments in near infrared spectroscopy

Vibrational spectroscopy at high excitation is an important research frontier for two reasons. Firstly, the near infrared is proving to be an important area for the analytical applications of spectroscopy, and we would therefore like to understand how the spectra we observe relate to the molecular structure of the absorbing species. Secondly, there is a fundamental interest in understanding molecular dynamics and energy flow within a polyatomic molecule at high excitation, because this is the boundary between spectroscopy and chemistry through which we try to understand the details of a chemical reaction. In this presentation I shall survey recent progress in this field.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.