Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Cold surge episodes over southeastern Brazil - a potential vorticity perspective

Most intense cold surges and associated frost events in southern and southeastern Brazil are characterized by a large amplitude trough over South America extending toward tropical latitudes and a ridge to the west of it over the Pacific Ocean. In this study, potential vorticity (PV) streamers serve to examine the flow condition leading to cold surges. Case studies suggest that several PV anomalies are related to cold surge episodes: (1) the potential vorticity unit (2-PVU) isoline upstream of South America becomes progressively more distorted prior and during the cold surge episode, indicating a flow situation which is conducive for Rossby wave breaking and hence a flow which strongly deviates from zonality; (2) the initial stage of a cold surge episode is characterized by a northward bulging of high-PV air to the east of the Andes, resulting in a PV streamer whose northern end reaches Uruguay and southeastern Brazil; the strong PV gradient on its western flank constitutes a flow configuration that induces and maintains the transport of sub-Antarctic air toward the subtropics; (3) a distinct negative PV anomaly, a blocking, originates over the eastern South Pacific, upstream of the South America sector. A composite analysis of 27 cold surges is performed for stratospheric PV streamer frequency on several isentropic surfaces. It reveals that equatorward wave breaking over South America and the western South Atlantic represents an important potential component of the dynamics of intense cold surges. The indications are most pronounced around the isentropic levels of 320 K and immediately before the day with largest temperature drops over subtropical Brazil.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Warm Conveyor Belts in the ERA-Interim Dataset (1979–2010): Part I: Climatology and Potential Vorticity Evolution

A global climatology of warm conveyor belts (WCBs) is presented for the years 1979–2010, based on trajectories calculated with Interim ECMWF Re-Analysis (ERA-Interim) data. WCB trajectories are identified as strongly ascending air parcels (600 hPa in 2 days) near extratropical cyclones. Corroborating earlier studies, WCBs are more frequent during winter than summer and they ascend preferentially in the western ocean basins between 25° and 50° latitude. Before ascending, WCB trajectories typically approach from the subtropics in summer and from more midlatitude regions in winter. Considering humidity, cloud water, and potential temperature along WCBs confirms that they experience strong condensation and integrated latent heating during the ascent (typically >20 K). Liquid and ice water contents along WCBs peak at about 700 and 550 hPa, respectively. The mean potential vorticity (PV) evolution shows typical tropospheric values near 900 hPa, followed by an increase to almost 1 potential vorticity unit (PVU) at 700 hPa, and a decrease to less than 0.5 PVU at 300 hPa. These low PV values in the upper troposphere constitute significant negative anomalies with amplitudes of 1–3 PVU, which can strongly influence the downstream flow. Considering the low-level diabatic PV production, (i) WCBs starting at low latitudes (<40°) are unlikely to attain high PV (due to weak planetary vorticity) although they exhibit the strongest latent heating, and (ii) for those ascending at higher latitudes, a strong vertical heating gradient and high absolute vorticity are both important. This study therefore provides climatological insight into the cloud diabatic formation of significant positive and negative PV anomalies in the extratropical lower and upper troposphere, respectively.

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O(N) sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For N ≥ 3 this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For N = 2 we determine the critical point and present boson and fermion masses in the critical regime.

Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

Comparison of the capacity of enamel matrix derivative gel and enamel matrix derivative in liquid formulation to adsorb to bone grafting materials.

BACKGROUND The use of an enamel matrix derivative (EMD) has been shown to enhance periodontal regeneration (e.g., formation of root cementum, periodontal ligament, and alveolar bone). However, in certain clinical situations, the use of EMD alone may not be sufficient to prevent flap collapse or provide sufficient stability of the blood clot. Data from clinical and preclinical studies have demonstrated controversial results after application of EMD combined with different types of bone grafting materials in periodontal regenerative procedures. The aim of the present study is to investigate the adsorption properties of enamel matrix proteins to bone grafts after surface coating with either EMD (as a liquid formulation) or EMD (as a gel formulation). METHODS Three different types of grafting materials, including a natural bone mineral (NBM), demineralized freeze-dried bone allograft (DFDBA), or a calcium phosphate (CaP), were coated with either EMD liquid or EMD gel. Samples were analyzed by scanning electron microscopy or transmission electron microscopy (TEM) using an immunostaining assay with gold-conjugated anti-EMD antibody. Total protein adsorption to bone grafting material was quantified using an enzyme-linked immunosorbent assay (ELISA) kit for amelogenin. RESULTS The adsorption of amelogenin to the surface of grafting material varied substantially based on the carrier system used. EMD gel adsorbed less protein to the surface of grafting particles, which easily dissociated from the graft surface after phosphate-buffered saline rinsing. Analyses by TEM revealed that adsorption of amelogenin proteins were significantly farther from the grafting material surface, likely a result of the thick polyglycolic acid gel carrier. ELISA protein quantification assay demonstrated that the combination of EMD liquid + NBM and EMD liquid + DFDBA adsorbed higher amounts of amelogenin than all other treatment modalities. Furthermore, amelogenin proteins delivered by EMD liquid were able to penetrate the porous surface structure of NBM and DFDBA and adsorb to the interior of bone grafting particles. Grafting materials coated with EMD gel adsorbed more frequently to the exterior of grafting particles with little interior penetration. CONCLUSIONS The present study demonstrates a large variability of adsorbed amelogenin to the surface of bone grafting materials when enamel matrix proteins were delivered in either a liquid formulation or gel carrier. Furthermore, differences in amelogenin adsorption were observed among NBM, DFDBA, and biphasic CaP particles. Thus, the potential for a liquid carrier system for EMD, used to coat EMD, may be advantageous for better surface coating.