Hierarchical X-FEM for n-phase flow (n>2)

The eXtended Finite Element Method (X-FEM) has been successfully used in two-phase flow problems involving a moving interface. In order to simulate problems involving more than two phases, the X-FEM has to be further eXtended. The proposed approach is presented in the case of a quasi-static Stokes n-phase flow and it is based on using an ordered collection of level set functions to describe the location of the phases. A level set hierarchy allows describing triple junctions avoiding overlapping or “voids” between materials. Moreover, an enriched solution accounting for several simultaneous phases inside one element is proposed. The interpolation functions corresponding to the enriched degrees of freedom require redefining the associated ridge function accounting for all the level sets. The computational implementation of this scheme involves calculating integrals in elements having several materials inside. An adaptive quadrature accounting for the interfaces locations is proposed to accurately compute these integrals. Examples of the hierarchical X-FEM approach are given for a n-phase Stokes problem in 2 and 3 dimensions

Reply to comment by H. Lough, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, on the paper “Stream depletion predictions using pumping test data from a heterogeneous stream–aquifer system (a case study from the Great Plains, USA)”

1. General remark 2. The study by Kollet and Zlotnik (2003) 3. Remark on the explanation of the drawdown behavior 4. Remark on the re-analysis of the data from piezometer C2d 5. Summar

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the separability of the operator is addressed taking into account both the non-constant co

Transitions from Monotonicity to Chaos in Gas Mixture Dynamics in Pipeline Networks

The blending of hydrogen generated using clean energy into natural gas pipeline networks is proposed in order to utilize existing energy systems for their planned lifetime while reducing their reliance on fossil fuels. We formulate a system of partial differential equations (PDEs) that govern the flow dynamics of mixtures of gases in pipeline networks under the influence of time-varying compressor and regulator control actions. The formulation is derived for general gas networks that can inject or withdraw arbitrary time-varying mixtures of gases into or from the network at arbitrarily specified nodes. The PDE formulation is discretized in space to form a nonlinear control system which is used to prove that homogeneous mixtures are well-behaved and heterogeneous mixtures may be ill-behaved in the sense of monotone-ordering of solutions. We use numerical simulations to compute interfaces that delimit periodic and monotone system responses and show that any solution in the monotonic operating region eventually approaches a periodic orbit. Our results are demonstrated for examples of a single pipeline and a small test network

Spatially and Spectrally Resolved Observations of a Zebra Pattern in Solar Decimetric Radio Burst

We present the first interferometric observation of a zebra-pattern radio burst with simultaneous high spectral (~ 1 MHz) and high time (20 ms) resolution. The Frequency-Agile Solar Radiotelescope (FASR) Subsystem Testbed (FST) and the Owens Valley Solar Array (OVSA) were used in parallel to observe the X1.5 flare on 14 December 2006. By using OVSA to calibrate the FST the source position of the zebra pattern can be located on the solar disk. With the help of multi-wavelength observations and a nonlinear force-free field (NLFFF) extrapolation, the zebra source is explored in relation to the magnetic field configuration. New constraints are placed on the source size and position as a function of frequency and time. We conclude that the zebra burst is consistent with a double-plasma resonance (DPR) model in which the radio emission occurs in resonance layers where the upper hybrid frequency is harmonically related to the electron cyclotron frequency in a coronal magnetic loop.Comment: Accepted for publication in Ap

Proper generalised decomposition for the solution of geometrically parametrised Stokes flow problems

The ability to predict, and ultimately optimise, aerodynamic forces when the design variable is the geometric definition of the domain is of great importance in many areas of computational fluid dynamics. This problem is known to be extremely computationally intensive due to the vast number of configurations that must be tested and the high computational cost of each one of the simulations involved in the optimisation process. In this talk a novel approach for computing an off-line solution for a set of geometric parameters that define the computational domain will be presented. The proposed approach is based on the proper generalised decomposition and, contrary to similar approaches, the geometric parameters are the position of the control points that define the NURBS boundary representation. Examples involving the solution of Stokes flow problems in two and three dimensions will be used to demonstrate the potential of the proposed approach

CXCR2 deficient mice display macrophage-dependent exaggerated acute inflammatory responses

CXCR2 is an essential regulator of neutrophil recruitment to inflamed and damaged sites and plays prominent roles in inflammatory pathologies and cancer. It has therefore been highlighted as an important therapeutic target. However the success of the therapeutic targeting of CXCR2 is threatened by our relative lack of knowledge of its precise in vivo mode of action. Here we demonstrate that CXCR2-deficient mice display a counterintuitive transient exaggerated inflammatory response to cutaneous and peritoneal inflammatory stimuli. In both situations, this is associated with reduced expression of cytokines associated with the resolution of the inflammatory response and an increase in macrophage accumulation at inflamed sites. Analysis using neutrophil depletion strategies indicates that this is a consequence of impaired recruitment of a non-neutrophilic CXCR2 positive leukocyte population. We suggest that these cells may be myeloid derived suppressor cells. Our data therefore reveal novel and previously unanticipated roles for CXCR2 in the orchestration of the inflammatory response

Spectral and spatial observations of microwave spikes and zebra structure in the short radio burst of May 29, 2003

The unusual radio burst of May 29, 2003 connected with the M1.5 flare in AR 10368 has been analyzed. It was observed by the Solar Broadband Radio Spectrometer (SBRS/Huairou station, Beijing) in the 5.2-7.6 GHz range. It proved to be only the third case of a neat zebra structure appearing among all observations at such high frequencies. Despite the short duration of the burst (25 s), it provided a wealth of data for studying the superfine structure with millisecond resolution (5 ms). We localize the site of emission sources in the flare region, estimate plasma parameters in the generation sites, and suggest applicable mechanisms for interpretating spikes and zebra-structure generation. Positions of radio bursts were obtained by the Siberian Solar Radio Telescope (SSRT) (5.7 GHz) and Nobeyama radioheliograph (NoRH) (17 GHz). The sources in intensity gravitated to tops of short loops at 17 GHz, and to long loops at 5.7 GHz. Short pulses at 17 GHz (with a temporal resolution of 100 ms) are registered in the R-polarized source over the N-magnetic polarity (extraordinary mode). Dynamic spectra show that all the emission comprised millisecond pulses (spikes) of 5-10 ms duration in the instantaneous band of 70 to 100 MHz, forming the superfine structure of different bursts, essentially in the form of fast or slow-drift fibers and various zebra-structure stripes. Five scales of zebra structures have been singled out. As the main mechanism for generating spikes (as the initial emission) we suggest the coalescence of plasma waves with whistlers in the pulse regime of interaction between whistlers and ion-sound waves. In this case one can explain the appearance of fibers and sporadic zebra-structure stripes exhibiting the frequency splitting.Comment: 11 pages, 5 figures, in press; A&A 201

Radioheliograph observations of microwave bursts with zebra structures

The so-called zebra structures in radio dynamic spectra, specifically their frequencies and frequency drifts of emission stripes, contain information on the plasma parameters in the coronal part of flare loops. This paper presents observations of zebra structures in a microwave range. Dynamic spectra were recorded by Chinese spectro-polarimeters in the frequency band close to the working frequencies of the Siberian Solar Radio Telescope. The emission sources are localized in the flare regions, and we are able to estimate the plasma parameters in the generation sites using X-ray data. The interpretation of the zebra structures in terms of the existing theories is discussed. The conclusion has been arrived that the preferred generation mechanism of zebra structures in the microwave range is the conversion of plasma waves to electromagnetic emission on the double plasma resonance surfaces distributed across a flare loop.Comment: 18 pages, 7 figure

New insights into the drainage of inundated ice-wedge polygons using fundamental hydrologic principles

The pathways and timing of drainage from the inundated centers of ice-wedge polygons in a warming climate have important implications for carbon flushing, advective heat transport, and transitions from methane to carbon dioxide dominated emissions. Here, we expand on previous research using a recently developed analytical model of drainage from a low-centered polygon. Specifically, we perform (1) a calibration to field data identifying necessary model refinements and (2) a rigorous model sensitivity analysis that expands on previously published indications of polygon drainage characteristics. This research provides intuition on inundated polygon drainage by presenting the first in-depth analysis of drainage within a polygon based on hydrogeological first principles. We verify a recently developed analytical solution of polygon drainage through a calibration to a season of field measurements. Due to the parsimony of the model, providing the potential that it could fail, we identify the minimum necessary refinements that allow the model to match water levels measured in a low-centered polygon. We find that (1) the measured precipitation must be increased by a factor of around 2.2, and (2) the vertical soil hydraulic conductivity must decrease with increasing thaw depth. Model refinement (1) accounts for runoff from rims into the ice-wedge polygon pond during precipitation events and possible rain gauge undercatch, while refinement (2) accounts for the decreasing permeability of deeper soil layers. The calibration to field measurements supports the validity of the model, indicating that it is able to represent ice-wedge polygon drainage dynamics. We then use the analytical solution in non-dimensional form to provide a baseline for the effects of polygon aspect ratios (radius to thaw depth) and coefficient of hydraulic conductivity anisotropy (horizontal to vertical hydraulic conductivity) on drainage pathways and temporal depletion of ponded water from inundated ice-wedge polygon centers. By varying the polygon aspect ratio, we evaluate the relative effect of polygon size (width), inter-annual increases in active-layer thickness, and seasonal increases in thaw depth on drainage. The results of our sensitivity analysis rigorously confirm a previous analysis indicating that most drainage through the active layer occurs along an annular region of the polygon center near the rims. This has important implications for transport of nutrients (such as dissolved organic carbon) and advection of heat towards ice-wedge tops. We also provide a comprehensive investigation of the effect of polygon aspect ratio and anisotropy on drainage timing and patterns, expanding on previously published research. Our results indicate that polygons with large aspect ratios and high anisotropy will have the most distributed drainage, while polygons with large aspect ratios and low anisotropy will have their drainage most focused near their periphery and will drain most slowly. Polygons with small aspect ratios and high anisotropy will drain most quickly. These results, based on parametric investigation of idealized scenarios, provide a baseline for further research considering the geometric and hydraulic complexities of ice-wedge polygons