Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Understanding the Influence of Photon Energy on 6MV Non Reference Dosimetry and CT Dosimetry using TLD and OSLD

Measurement of the absorbed dose from ionizing radiation in medical applications is an essential component to providing safe and reproducible patient care. There are a wide variety of tools available for measuring radiation dose; this work focuses on the characterization of two common, solid-state dosimeters in medical applications: thermoluminescent dosimeters (TLD) and optically stimulated luminescent dosimeters (OSLD). There were two main objectives to this work. The first objective was to evaluate the energy dependence of TLD and OSLD for non-reference measurement conditions in a radiotherapy environment. The second objective was to fully characterize the OSLD nanoDot in a CT environment, and to provide validated calibration procedures for CT dose measurement using OSLD. Current protocols for dose measurement using TLD and OSLD generally assume a constant photon energy spectrum within a nominal beam energy regardless of measurement location, tissue composition, or changes in beam parameters. Variations in the energy spectrum of therapeutic photon beams may impact the response of TLD and OSLD and could thereby result in an incorrect measure of dose unless these differences are accounted for. In this work, we used a Monte Carlo based model to simulate variations in the photon energy spectra of a Varian 6MV beam; then evaluated the impact of the perturbations in energy spectra on the response of both TLD and OSLD using Burlin Cavity Theory. Energy response correction factors were determined for a range of conditions and compared to measured correction factors with good agreement. When using OSLD for dose measurement in a diagnostic imaging environment, photon energy spectra are often referenced to a therapy-energy or orthovoltage photon beam – commonly 250kVp, Co-60, or even 6MV, where the spectra are substantially different. Appropriate calibration techniques specifically for the OSLD nanoDot in a CT environment have not been presented in the literature; furthermore the dependence of the energy response of the calibration energy has not been emphasized. The results of this work include detailed calibration procedures for CT dosimetry using OSLD, and a full characterization of this dosimetry system in a low-dose, low-energy setting.

Ikaite of sediment cores from the Zaire deep-sea fan

Most concentration profiles of sulfate in continental margin sediments show constant or continuously increasing gradients from the benthic boundary layer down to the deep sulfate reduction zone. However, a very marked change in this gradient has been observed several meters below the surface at many locations, which has been attributed to anoxic sulfide oxidation or to non-local transport mechanisms of pore waters. The subject of this study is to investigate whether this feature could be better explained by non-steady state conditions in the pore-water system. To this end, data are presented from two gravity cores recovered from the Zaire deep-sea fan. The sediments at this location can be subdivided into two sections. The upper layer, about 10 m thick, consists of stratified pelagic deposits representing a period of continuous sedimentation over the last 190 kyr. It is underlain by a turbidite sequence measuring several meters in thickness, which contains large crystals of authigenic calcium carbonate (ikaite: CaCO3·6H2O). Ikaite delta13C values are indicative of a methane carbon contribution to the CO2 pool. Radiocarbon ages of these minerals, as well as of the adjacent bulk sediments, provide strong evidence that the pelagic sediments have overthrust the lower section as a coherent block. Therefore, the emplacement of a relatively undisturbed sediment package is postulated. Pore-water profiles show the depth of the sulfate-methane transition zone within the turbiditic sediments. By the adaptation of a simple transport-reaction model, it is shown that the change in the geochemical environmental conditions, resulting from this slide emplacement, and the development towards a new steady state are fully sufficient to explain all features related to the pore-water profiles, particularly, [SO4]2- and dissolved inorganic carbon (DIC). The model shows that the downslope transport took place about 300 yr ago.

Simulated Bromoform emission and concentration using the ocean biogeochemistry model MPIOM/HAMOCC forced by 6-hourly NCEP data

Bromoform (CHBr3) is one important precursor of atmospheric reactive bromine species that are involved in ozone depletion in the troposphere and stratosphere. In the open ocean bromoform production is linked to phytoplankton that contains the enzyme bromoperoxidase. Coastal sources of bromoform are higher than open ocean sources. However, open ocean emissions are important because the transfer of tracers into higher altitude in the air, i.e. into the ozone layer, strongly depends on the location of emissions. For example, emissions in the tropics are more rapidly transported into the upper atmosphere than emissions from higher latitudes. Global spatio-temporal features of bromoform emissions are poorly constrained. Here, a global three-dimensional ocean biogeochemistry model (MPIOM-HAMOCC) is used to simulate bromoform cycling in the ocean and emissions into the atmosphere using recently published data of global atmospheric concentrations (Ziska et al., 2013) as upper boundary conditions. Our simulated surface concentrations of CHBr3 match the observations well. Simulated global annual emissions based on monthly mean model output are lower than previous estimates, including the estimate by Ziska et al. (2013), because the gas exchange reverses when less bromoform is produced in non-blooming seasons. This is the case for higher latitudes, i.e. the polar regions and northern North Atlantic. Further model experiments show that future model studies may need to distinguish different bromoform-producing phytoplankton species and reveal that the transport of CHBr3 from the coast considerably alters open ocean bromoform concentrations, in particular in the northern sub-polar and polar regions.

Geochemistry of sediments cores in the Mediterranean Sea

We investigated five time-equivalent core sections (180-110 kyr BP) from the Balearic Sea (Menorca Rise), the easternmost Levantine Basin and southwest, south, and southeast of Crete to reconstruct spatial patterns of productivity during deposition of sapropels S5 and S6 in the Mediterranean Sea. Our indicators are Ba, total organic carbon and carbonate contents. We found no indications of Ba remobilization within the investigated core intervals, and used the accumulation rate of biogenic Ba to compute paleoproductivity. Maximum surface water productivity (up to 350 g C/m2/yr) was found during deposition of S5 (isotope stage 5e) but pronounced spatial variability is evident. Coeval sediment intervals in the Balearic Sea show very little productivity change, suggesting that chemical and biological environments in the eastern and western Mediterranean basins were decoupled in this interval. We interpret the spatial variability as the result of two different modes of nutrient delivery to the photic zone: riverderived nutrient input and shoaling of the pycnocline/nutricline to the photic zone. The productivity increase during the formation of S6 was moderate compared to S5 and had a less marked spatial variability within the study area of the eastern Mediterranean Sea. Given that S6 formed during a glacial interval, glacial boundary conditions such as high wind stress and/or cooler surface water temperatures apparently favored lateral and vertical mixing and prevented the development of the spatial gradients within the Eastern Mediterranean Sea (EMS) observed for S5. A non-sapropel sediment interval with elevated Ba content and depleted 18O/16O ratios in planktonic foraminifer calcite was detected between S6 and S5 that corresponds to the weak northern hemisphere insolation maximum at 150 kyr. At this time, productivity apparently increased up to five times over surrounding intervals, but abundant benthic fauna show that the deep water remained oxic. Following our interpretation, the interval denotes a failed sapropel, when a weaker monsoon did not force the EMS into permanent stratification. The comparison of interglacial and glacial sapropels illustrates the relevance of climatic boundary conditions in the northern catchment in determining the facies and spatial variability of sapropels within the EMS.

Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems.

The estimation of truncation error by tau-estimation revisited

The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the @t-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.

A regular perturbation approach to surface tension driven flows

Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed

Estudio y desarrollo de un preproceso basado en la difusión no lineal para la segmentación en imágenes

En esta Tesis Doctoral se aborda la utilización de filtros de difusión no lineal para obtener imágenes constantes a trozos como paso previo al proceso de segmentación. En una primera parte se propone un formulación intrínseca para la ecuación de difusión no lineal que proporcione las condiciones de diseño necesarias sobre los filtros de difusión. A partir del marco teórico propuesto, se proporciona una nueva familia de difusividades; éstas son obtenidas a partir de técnicas de difusión no lineal relacionadas con los procesos de difusión regresivos. El objetivo es descomponer la imagen en regiones cerradas que sean homogéneas en sus niveles de grises sin contornos difusos. Asimismo, se prueba que la función de difusividad propuesta satisface las condiciones de un correcto planteamiento semi-discreto. Esto muestra que mediante el esquema semi-implícito habitualmente utilizado, realmente se hace un proceso de difusión no lineal directa, en lugar de difusión inversa, conectando con proceso de preservación de bordes. Bajo estas condiciones establecidas, se plantea un criterio de parada para el proceso de difusión, para obtener imágenes constantes a trozos con un bajo coste computacional. Una vez aplicado todo el proceso al caso unidimensional, se extienden los resultados teóricos, al caso de imágenes en 2D y 3D. Para el caso en 3D, se detalla el esquema numérico para el problema evolutivo no lineal, con condiciones de contorno Neumann homogéneas. Finalmente, se prueba el filtro propuesto para imágenes reales en 2D y 3D y se ilustran los resultados de la difusividad propuesta como método para obtener imágenes constantes a trozos. En el caso de imágenes 3D, se aborda la problemática del proceso previo a la segmentación del hígado, mediante imágenes reales provenientes de Tomografías Axiales Computarizadas (TAC). En ese caso, se obtienen resultados sobre la estimación de los parámetros de la función de difusividad propuesta. This Ph.D. Thesis deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. I have first shown an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, I have proposed a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. It has also proved that the proposed filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edgepreserving process. Under the conditions established for the diffusivity and using a stopping criterion I for the diffusion time, I have obtained piecewise constant images with a low computational effort. The whole process in the one-dimensional case is extended to the case where 2D and 3D theoretical results are applied to real images. For 3D, develops in detail the numerical scheme for nonlinear evolutionary problem with homogeneous Neumann boundary conditions. Finally, I have tested the proposed filter with real images for 2D and 3D and I have illustrated the effects of the proposed diffusivity function as a method to get piecewise constant images. For 3D I have developed a preprocess for liver segmentation with real images from CT (Computerized Tomography). In this case, I have obtained results on the estimation of the parameters of the given diffusivity function.

SERBA: a B.I.E. program with linear elements for 2-D elastostatics analysis

The great developments that have occurred during the last few years in the finite element method and its applications has kept hidden other options for computation. The boundary integral element method now appears as a valid alternative and, in certain cases, has significant advantages. This method deals only with the boundary of the domain, while the F.E.M. analyses the whole domain. This has the following advantages: the dimensions of the problem to be studied are reduced by one, consequently simplifying the system of equations and preparation of input data. It is also possible to analyse infinite domains without discretization errors. These simplifications have the drawbacks of having to solve a full and non-symmetric matrix and some difficulties are incurred in the imposition of boundary conditions when complicated variations of the function over the boundary are assumed. In this paper a practical treatment of these problems, in particular boundary conditions imposition, has been carried out using the computer program shown below. Program SERBA solves general elastostatics problems in 2-dimensional continua using the boundary integral equation method. The boundary of the domain is discretized by line or elements over which the functions are assumed to vary linearly. Data (stresses and/or displacements) are introduced in the local co-ordinate system (element co-ordinates). Resulting stresses are obtained in local co-ordinates and displacements in a general system. The program has been written in Fortran ASCII and implemented on a 1108 Univac Computer. For 100 elements the core requirements are about 40 Kwords. Also available is a Fortran IV version (3 segments)implemented on a 21 MX Hewlett-Packard computer,using 15 Kwords.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surfacefilm of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological nonequilibrium thermodynamics for a general nonisothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analyzed.

Hexagonal patterns in a model for rotating convection

We study a model equation that mimics convection under rotation in a fluid with temperature- dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kuppers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and os- cillating hexagons quite well, and include the Busse?Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

High-accuracy adaptive simulations of a Petri dish exposed to electromagnetic radiation

This paper analyses numerically the electric field distribution of a liquid contained in a Petri dish when exposed to electromagnetic waves excited in a rectangular waveguide. Solutions exhibit high-gradients due to the presence of the dielectric liquid contained in the dish. Furthermore, electromagnetic fields within the dielectric have a dramatically lower value than on the remaining part of the domain, which difficults its simulation. Additionally, various singularities of different intensity appear along the boundary of the Petri dish. To properly reproduce and numerically study those effects, we employ a highly-accurate hp-adaptive finite element method. Results of this study demonstrate that the electric field generated within the circular Petri dish is non-homogeneous, and thus, a better shape, size, or location of the dish is needed to achieve an equally distributed radiation enabling the uniform growth of cell cultives.