The Navier-Stokes Equations with Particle Methods

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an accumulation point satisfying the Navier-Stokes equations in a weak sense.

Numerical Feasibility Study for Treated Wastewater Recharge as a Tool to Impede Saltwater Intrusion in the Coastal Aquifer of Gaza – Palestine

The ongoing depletion of the coastal aquifer in the Gaza strip due to groundwater overexploitation has led to the process of seawater intrusion, which is continually becoming a serious problem in Gaza, as the seawater has further invaded into many sections along the coastal shoreline. As a first step to get a hold on the problem, the artificial neural network (ANN)-model has been applied as a new approach and an attractive tool to study and predict groundwater levels without applying physically based hydrologic parameters, and also for the purpose to improve the understanding of complex groundwater systems and which is able to show the effects of hydrologic, meteorological and anthropogenic impacts on the groundwater conditions. Prediction of the future behaviour of the seawater intrusion process in the Gaza aquifer is thus of crucial importance to safeguard the already scarce groundwater resources in the region. In this study the coupled three-dimensional groundwater flow and density-dependent solute transport model SEAWAT, as implemented in Visual MODFLOW, is applied to the Gaza coastal aquifer system to simulate the location and the dynamics of the saltwater–freshwater interface in the aquifer in the time period 2000-2010. A very good agreement between simulated and observed TDS salinities with a correlation coefficient of 0.902 and 0.883 for both steady-state and transient calibration is obtained. After successful calibration of the solute transport model, simulation of future management scenarios for the Gaza aquifer have been carried out, in order to get a more comprehensive view of the effects of the artificial recharge planned in the Gaza strip for some time on forestall, or even to remedy, the presently existing adverse aquifer conditions, namely, low groundwater heads and high salinity by the end of the target simulation period, year 2040. To that avail, numerous management scenarios schemes are examined to maintain the ground water system and to control the salinity distributions within the target period 2011-2040. In the first, pessimistic scenario, it is assumed that pumping from the aquifer continues to increase in the near future to meet the rising water demand, and that there is not further recharge to the aquifer than what is provided by natural precipitation. The second, optimistic scenario assumes that treated surficial wastewater can be used as a source of additional artificial recharge to the aquifer which, in principle, should not only lead to an increased sustainable yield of the latter, but could, in the best of all cases, revert even some of the adverse present-day conditions in the aquifer, i.e., seawater intrusion. This scenario has been done with three different cases which differ by the locations and the extensions of the injection-fields for the treated wastewater. The results obtained with the first (do-nothing) scenario indicate that there will be ongoing negative impacts on the aquifer, such as a higher propensity for strong seawater intrusion into the Gaza aquifer. This scenario illustrates that, compared with 2010 situation of the baseline model, at the end of simulation period, year 2040, the amount of saltwater intrusion into the coastal aquifer will be increased by about 35 %, whereas the salinity will be increased by 34 %. In contrast, all three cases of the second (artificial recharge) scenario group can partly revert the present seawater intrusion. From the water budget point of view, compared with the first (do nothing) scenario, for year 2040, the water added to the aquifer by artificial recharge will reduces the amount of water entering the aquifer by seawater intrusion by 81, 77and 72 %, for the three recharge cases, respectively. Meanwhile, the salinity in the Gaza aquifer will be decreased by 15, 32 and 26% for the three cases, respectively.

How are Three-Deminsional Objects Represented in the Brain?

We discuss a variety of object recognition experiments in which human subjects were presented with realistically rendered images of computer-generated three-dimensional objects, with tight control over stimulus shape, surface properties, illumination, and viewpoint, as well as subjects' prior exposure to the stimulus objects. In all experiments recognition performance was: (1) consistently viewpoint dependent; (2) only partially aided by binocular stereo and other depth information, (3) specific to viewpoints that were familiar; (4) systematically disrupted by rotation in depth more than by deforming the two-dimensional images of the stimuli. These results are consistent with recently advanced computational theories of recognition based on view interpolation.

Three substituted 4-pyrazolylbenzoates: hydrogen-bonded supramolecular structures in one, two and three dimensions

The molecules of ethyl 4-(5-amino-3-methyl-1H-pyrazol-1yl) benzoate, C13H15N3O2, are linked by two independent N-H center dot center dot center dot O hydrogen bonds into a chain of edge-fused and alternating R-4(2)(8) and R-2(2)(20) rings. A combination of N-H center dot center dot center dot N and N-H center dot center dot center dot O hydrogen bonds links the molecules of methyl 4-(5-amino-3-tert-butyl-1H-pyrazol-1-yl) benzoate, C15H19N3O2, into sheets of alternating R-2(2)(20) and R-6(6)(32) rings. In 4-(5-amino-3-methyl-1H-pyrazol-1-yl) benzoic acid monohydrate, C11H11N3O2 center dot H2O, the molecular components are linked into a three-dimensional framework structure by a combination of five independent hydrogen bonds, two of O-H center dot center dot center dot N type and one each of O-H center dot center dot center dot O, N-H center dot center dot center dot O and N-H center dot center dot center dot N types

Angiorresonancia versus angiografía por sustracción digital en el seguimiento de aneurismas intracraneales embolizados. Comparación del desempeño diagnóstico

Introducción: La DSA es el método de elección para el seguimiento de pacientes con aneurismas intracraneales embolizados; esta se puede asociar a complicaciones incapacitantes o mortales. La MRA se ha propuesto como método alternativo por menor costo y menos morbi-mortalidad, aunque su desempeño diagnóstico permanece en discusión debido al desarrollo de nuevos protocolos, resonadores más potentes y nuevas aplicaciones de la DSA. Metodología: Exploramos la literatura hasta la actualidad y comparamos el desempeño diagnóstico de la MRA con la DSA para detectar flujo residual posterior a la embolización terapéutica de aneurismas intracraneales. Realizamos una revisión sistemática de la literatura y meta-análisis basados en 34 artículos detectados en la búsqueda que incluyó las bases de datos PubMed, Scopus, ScIELO y BVS. Resultados: La TOF-MRA demostró sensibilidad de 86.8% (84.3%-89.1%) y especificidad de 91.2% (89%-93.1%); la SROC para TOF-MRA demostró un AUC de 0.95. El desempeño de la CE-MRA demostró sensibilidad de 88.1% (84.6%-91.1%) y especificidad de 89.1% (85.7%-91.9%); la SROC presentó una AUC de 0.93. El análisis estratificado por potencia del resonador encontró que la TOF-MRA tiene mejor desempeño con el resonador de 3T, aunque no es estadísticamente significativo. La concordancia interobservador con TOF-MRA y CE-MRA fue moderada a muy buena. Discusión: El desempeño diagnóstico de la MRA en el seguimiento de aneurismas intracraneales embolizados demostró ser bueno, con sensibilidad mayor a 84%, siendo ligeramente mejor con TOF-MRA, sin lograr reemplazar la DSA. Sin embargo, los resultados deben ser evaluados con precaución por la heterogeneidad de los resultados de los estudios incluidos. (Abreviaturas: DSA: Angiografía por Sustracción Digital; MRA: Angiografía por Resonancia Magnética; TOF-MRA: Angiorresonancia por Tiempo de Vuelo; CE-MRA: Angiorresonancia contrastada).

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.

The global response to tropical heating in the Madden-Julian oscillation during the northern winter

A life cycle of the Madden–Julian oscillation (MJO) was constructed, based on 21 years of outgoing long-wave radiation data. Regression maps of NCEP–NCAR reanalysis data for the northern winter show statistically significant upper-tropospheric equatorial wave patterns linked to the tropical convection anomalies, and extratropical wave patterns over the North Pacific, North America, the Atlantic, the Southern Ocean and South America. To assess the cause of the circulation anomalies, a global primitive-equation model was initialized with the observed three-dimensional (3D) winter climatological mean flow and forced with a time-dependent heat source derived from the observed MJO anomalies. A model MJO cycle was constructed from the global response to the heating, and both the tropical and extratropical circulation anomalies generally matched the observations well. The equatorial wave patterns are established in a few days, while it takes approximately two weeks for the extratropical patterns to appear. The model response is robust and insensitive to realistic changes in damping and basic state. The model tropical anomalies are consistent with a forced equatorial Rossby–Kelvin wave response to the tropical MJO heating, although it is shifted westward by approximately 20° longitude relative to observations. This may be due to a lack of damping processes (cumulus friction) in the regions of convective heating. Once this shift is accounted for, the extratropical response is consistent with theories of Rossby wave forcing and dispersion on the climatological flow, and the pattern correlation between the observed and modelled extratropical flow is up to 0.85. The observed tropical and extratropical wave patterns account for a significant fraction of the intraseasonal circulation variance, and this reproducibility as a response to tropical MJO convection has implications for global medium-range weather prediction. Copyright © 2004 Royal Meteorological Society

Can climate models capture the structure of extratropical cyclones?

Composites of wind speeds, equivalent potential temperature, mean sea level pressure, vertical velocity, and relative humidity have been produced for the 100 most intense extratropical cyclones in the Northern Hemisphere winter for the 40-yr ECMWF Re-Analysis (ERA-40) and the high resolution global environment model (HiGEM). Features of conceptual models of cyclone structure—the warm conveyor belt, cold conveyor belt, and dry intrusion—have been identified in the composites from ERA-40 and compared to HiGEM. Such features can be identified in the composite fields despite the smoothing that occurs in the compositing process. The surface features and the three-dimensional structure of the cyclones in HiGEM compare very well with those from ERA-40. The warm conveyor belt is identified in the temperature and wind fields as a mass of warm air undergoing moist isentropic uplift and is very similar in ERA-40 and HiGEM. The rate of ascent is lower in HiGEM, associated with a shallower slope of the moist isentropes in the warm sector. There are also differences in the relative humidity fields in the warm conveyor belt. In ERA-40, the high values of relative humidity are strongly associated with the moist isentropic uplift, whereas in HiGEM these are not so strongly associated. The cold conveyor belt is identified as rearward flowing air that undercuts the warm conveyor belt and produces a low-level jet, and is very similar in HiGEM and ERA-40. The dry intrusion is identified in the 500-hPa vertical velocity and relative humidity. The structure of the dry intrusion compares well between HiGEM and ERA-40 but the descent is weaker in HiGEM because of weaker along-isentrope flow behind the composite cyclone. HiGEM’s ability to represent the key features of extratropical cyclone structure can give confidence in future predictions from this model.

Atmospheric factors governing banded orographic convection

Atmospheric factors Governing Banded Orographic Convection The three-dimensional structure of shallow orographic convection is investigated through simulations performed with a cloud-resolving numerical model. In moist flows that overcome a given topographic barrier to form statically unstable cap clouds, the organization of the convection depends on both the atmospheric structure and the mechanism by which the convection is initiated. Convection initiated by background thermal fluctuations embedded in the flow over a smooth mountain (without any small-scale topographic features) tends to be cellular and disorganized except that shear-parallel bands may form in flows with strong unidirectional vertical shear. The development of well-organized bands is favored when there is weak static instability inside the cloud and when the dry air surrounding the cloud is strongly stable. These bands move with the flow and distribute their cumulative precipitation evenly over the mountain upslope. Similar shear-parallel bands also develop in flows where convection is initiated by small-scale topographic noise superimposed onto the main mountain profile, but in this case stronger circulations are also triggered that create stationary rainbands parallel to the low-level flow. This second dominant mode, which is less sensitive to the atmospheric structure and the strength of forcing, is triggered by lee waves that form over small-scale topographic bumps near the upstream edge of the main orographic cloud. Due to their stationarity, these flow-parallel bands can produce locally heavy precipitation amounts.

Parcel theory in three dimensions and the calculation of SCAPE

Slantwise convective available potential energy (SCAPE) is a measure of the degree to which the atmosphere is unstable to conditional symmetric instability (CSI). It has, until now, been defined by parcel theory in which the atmosphere is assumed to be nonevolving and balanced, that is, two-dimensional. When applying this two-dimensional theory to three-dimensional evolving flows, these assumptions can be interpreted as an implicit assumption that a timescale separation exists between a relatively rapid timescale for slantwise ascent and a slower timescale for the development of the system. An approximate extension of parcel theory to three dimensions is derived and it is shown that calculations of SCAPE based on the assumption of relatively rapid slantwise ascent can be qualitatively in error. For a case study example of a developing extratropical cyclone, SCAPE calculated along trajectories determined without assuming the existence of the timescale separation show large SCAPE values for parcels ascending from the warm sector and along the warm front. These parcels ascend into the cloud head within which there is some evidence consistent with the release of CSI from observational and model cross sections. This region of high SCAPE was not found for calculations along the relatively rapidly ascending trajectories determined by assuming the existence of the timescale separation.

The power of NMR: in two and three dimensions

Two dimensional NMR experiments use a sequence of two or more pulses with a variable time delay to generate spectra. COSY spectra clarify where the protons are in a molecule. Two and three dimensional NMR are used to solve protein structures.

[Co(en)(3)][Sb12S19]: a new antimony sulfide with a zeolite-like structure containing one-dimensional channels

Solvothermal synthesis affords access to the first truly three-dimensional anti mony-sufide framework which contains one-dimensional circular channels.

Mapping fibre orientation in complex-shaped biological systems with micrometre resolution by scanning X-ray microdiffraction

A fully automated procedure to extract and to image local fibre orientation in biological tissues from scanning X-ray diffraction is presented. The preferred chitin fibre orientation in the flow sensing system of crickets is determined with high spatial resolution by applying synchrotron radiation based X-ray microbeam diffraction in conjunction with advanced sample sectioning using a UV micro-laser. The data analysis is based on an automated detection of azimuthal diffraction maxima after 2D convolution filtering (smoothing) of the 2D diffraction patterns. Under the assumption of crystallographic fibre symmetry around the morphological fibre axis, the evaluation method allows mapping the three-dimensional orientation of the fibre axes in space. The resulting two-dimensional maps of the local fibre orientations - together with the complex shape of the flow sensing system - may be useful for a better understanding of the mechanical optimization of such tissues.