530 research outputs found
Vanishing cycles on Poisson varieties
We extend slightly the results of Evens-Mirkovi\'c, and "compute" the
characteristic cycles of Intersection Cohomology sheaves on the transversal
slices in the double affine Grassmannian and on the hypertoric varieties. We
propose a conjecture relating the hyperbolic stalks and the microlocalization
at a torus-fixed point in a Poisson variety.Comment: 7 page
Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach
We extend the calculation of relativistic bound-states of a fermion
anti-fermion pair in the Bethe-Salpeter formalism to the case of total angular
momentum . Together with results for this allows for the
investigation of Regge trajectories in this approach. We exemplify such a study
for ground and excited states of light unflavored mesons as well as strange
mesons within the rainbow-ladder approximation. For the - and
-meson we find a linear Regge trajectory within numerical accuracy.
Discrepancies with experiment in other channels highlight the need to go beyond
rainbow-ladder and to consider effects such as state mixing and more
sophisticated quark-antiquark interaction kernels.Comment: 11 pages, 8 figures, 2 tables. Minor typos corrected; accepted in
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Direct numerical simulation of gas transfer at the air-water interface in a buoyant-convective flow environment
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonThe gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been
carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution
of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the
temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident.
A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal
rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.Isambard Scholarshi
Pion cloud effects on baryon masses
In this work we explore the effect of pion cloud contributions to the mass of
the nucleon and the delta baryon. To this end we solve a coupled system of
Dyson-Schwinger equations for the quark propagator, a Bethe-Salpeter equation
for the pion and a three-body Faddeev equation for the baryons. In the
quark-gluon interaction we explicitly resolve the term responsible for the
back-coupling of the pion onto the quark, representing rainbow-ladder like pion
cloud effects in bound states. We study the dependence of the resulting baryon
masses on the current quark mass and discuss the internal structure of the
baryons in terms of a partial wave decomposition. We furthermore determine
values for the nucleon and delta sigma-terms.Comment: 9 pages, 4 figures, 2 tables. v2: Numerics corrected; results
updated; discussion extended. Version accepted for publication in Phys.Lett.
Beyond Rainbow-Ladder in a covariant three-body Bethe-Salpeter approach: Baryons
We report on recent results of a calculation of the nucleon and delta masses
in a covariant bound-state approach, where to the simple rainbow-ladder
gluon-exchange interaction kernel we add a pion-exchange contribution to
account for pion cloud effects. We observe good agreement with lattice data at
large pion masses. At the physical point our masses are too large by about five
percent, signaling the need for more structure in the gluon part of the
interaction.Comment: 4 pages, 3 figures, Proceedings of The 13th International Conference
on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2013), Rom
Hodge-to-de Rham degeneration for stacks
We introduce a notion of a Hodge-proper stack and extend the method of Deligne-Illusie to prove the Hodge-to-de Rham degeneration in this setting. In order to reduce the statement in characteristic to characteristic , we need to find a good integral model of a stack (a so-called spreading), which, unlike in the case of schemes, need not to exist in general. To address this problem we investigate the property of spreadability in more detail by generalizing standard spreading out results for schemes to higher Artin stacks and showing that all proper and some global quotient stacks are Hodge-properly spreadable. As a corollary we deduce a (non-canonical) Hodge decomposition of the equivariant cohomology for certain classes of varieties with an algebraic group action
Derived binomial rings I: integral Betti cohomology of log schemes
We introduce and study a derived version of the
binomial monad on the unbounded derived category of
-modules. This monad acts naturally on singular cohomology of any
topological space, and does so more efficiently than the more classical monad
. We compute all free derived binomial rings
on abelian groups concentrated in a single degree, in particular identifying
with via a different argument than in works of To\"en
and Horel. Using this we show that the singular cohomology functor
induces a fully faithful embedding of the
category of connected nilpotent spaces of finite type to the category of
derived binomial rings. We then also define a version of the derived binomial monad on the -category of -valued sheaves on a sufficiently nice topological space . As
an application we give a closed formula for the singular cohomology of an fs
log complex analytic space : namely we identify the pushforward
for the corresponding Kato-Nakayama space
with the free coaugmented derived
binomial ring on the 2-term exponential complex . This gives an extension of Steenbrink's formula and
its generalization by the second author to -coefficients.Comment: 61 pages, comments welcom
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