Anisotropic eddy viscosity models
NASA Technical Reports Server (NTRS)
Carati, D.; Cabot, W.
1996-01-01
A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry.
Eddy viscosity measurements in a rectangular jet
NASA Technical Reports Server (NTRS)
Swan, David H.; Morrison, Gerald L.
1988-01-01
The flow field of a rectangular jet with a 2:1 aspect ratio was studied at a Reynolds number of 100,000 (Mach number 0.09) using three-dimensional laser Doppler velocimetry (LDV). Velocity gradients, Reynolds stress tensor components, and scalar eddy viscosities are presented for the major and minor axis planes of the jet. The eddy viscosity model was found to be applicable only in the direction of maximum mean velocity gradient.
Effects of Eddy Viscosity on Time Correlations in Large Eddy Simulation
NASA Technical Reports Server (NTRS)
He, Guowei; Rubinstein, R.; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.
Prediction of Transonic Vortex Flows Using Linear and Nonlinear Turbulent Eddy Viscosity Models
NASA Technical Reports Server (NTRS)
Bartels, Robert E.; Gatski, Thomas B.
2000-01-01
Three-dimensional transonic flow over a delta wing is investigated with a focus on the effect of transition and influence of turbulence stress anisotropies. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition or are fully turbulent are performed. To assess the effect of the turbulent stress anisotropy, comparisons are made between predictions from the algebraic stress model and the linear eddy viscosity models. Both transition location and turbulent stress anisotropy significantly affect the 3D flow field. The most significant effect is found to be the modeling of transition location. At a Mach number of 0.90, the computed solution changes character from steady to unsteady depending on transition onset. Accounting for the anisotropies in the turbulent stresses also considerably impacts the flow, most notably in the outboard region of flow separation.
Ekman Spiral in a Horizontally Inhomogeneous Ocean with Varying Eddy Viscosity
NASA Astrophysics Data System (ADS)
Chu, Peter C.
2015-10-01
The classical Ekman spiral is generated by surface wind stress with constant eddy viscosity in a homogeneous ocean. In real oceans, the eddy viscosity varies due to turbulent mixing caused by surface wind and buoyancy forcing. Horizontally inhomogeneous density produces vertical geostrophic shear which contributes to current shear that also affects the Ekman spiral. Based on similar theoretical framework as the classical Ekman spiral, the baroclinic components of the Ekman spiral caused by the horizontally inhomogeneous density are obtained analytically with the varying eddy viscosity calculated from surface wind and buoyancy forcing using the K-profile parameterization (KPP). Along with the three existing types of eddy viscosity due to pure wind forcing (zero surface buoyancy flux), such an effect is evaluated using the climatological monthly mean data of surface wind stress, buoyancy flux, ocean temperature and salinity, and mixed layer depth.
MHD Eddy Viscosity: Testing the Concept with the Solar-Wind/Magnetosphere Coupling Data Base
NASA Astrophysics Data System (ADS)
Borovsky, Joseph E.
2005-10-01
In Navier-Stokes fluids, the presence of upstream turbulence increases the viscous drag of an obstacle in a flow: this is known as the ``turbulence effect.'' The effect is explained by an eddy viscosity that enhances the viscous coupling, with the eddy viscosity controlled by the amplitude of the upstream turbulence. From solar-wind/magnetosphere data analysis it is known that activity in the Earth's magnetosphere is driven by the solar wind (chiefly as a consequence of reconnection, but also as a consequence of unexplained ``viscous effects''); the measured level of geomagnetic activity can be used as a measure of the strength of solar-wind/magnetosphere coupling. The solar wind is a turbulent flow with an MHD-turbulence amplitude that varies with time. We have statistically confirmed that there is a turbulence effect in solar-wind/magnetosphere coupling, where geomagnetic activity is observed to be greater when the solar-wind turbulence is louder. An expression for the MHD eddy viscosity of the turbulent solar wind that can be evaluated in terms of spacecraft-measured quantities is derived. Using this expression and a few decades of solar-wind measurements, cross correlations between geomagnetic activity and the eddy viscosity of the solar wind are performed. These cross correlations can yield (a) an experimental confirmation of the concept of MHD eddy viscosity and (b) a test of the validity, accuracy, and usefulness of the MHD-eddy-viscosity explanation of the turbulence effect in solar-wind/magnetosphere coupling.
A normal stress subgrid-scale eddy viscosity model in large eddy simulation
NASA Technical Reports Server (NTRS)
Horiuti, K.; Mansour, N. N.; Kim, John J.
1993-01-01
The Smagorinsky subgrid-scale eddy viscosity model (SGS-EVM) is commonly used in large eddy simulations (LES) to represent the effects of the unresolved scales on the resolved scales. This model is known to be limited because its constant must be optimized in different flows, and it must be modified with a damping function to account for near-wall effects. The recent dynamic model is designed to overcome these limitations but is compositionally intensive as compared to the traditional SGS-EVM. In a recent study using direct numerical simulation data, Horiuti has shown that these drawbacks are due mainly to the use of an improper velocity scale in the SGS-EVM. He also proposed the use of the subgrid-scale normal stress as a new velocity scale that was inspired by a high-order anisotropic representation model. The testing of Horiuti, however, was conducted using DNS data from a low Reynolds number channel flow simulation. It was felt that further testing at higher Reynolds numbers and also using different flows (other than wall-bounded shear flows) were necessary steps needed to establish the validity of the new model. This is the primary motivation of the present study. The objective is to test the new model using DNS databases of high Reynolds number channel and fully developed turbulent mixing layer flows. The use of both channel (wall-bounded) and mixing layer flows is important for the development of accurate LES models because these two flows encompass many characteristic features of complex turbulent flows.
An alternative eddy-viscosity representation and its implication to turbulence modeling
NASA Astrophysics Data System (ADS)
Jakirlic, Suad; Jovanovic, Jovan; Basara, Branislav
2013-11-01
Large majority of turbulence models in the RANS framework (it holds also in the case of the LES method) is based on the eddy-viscosity rationale. The principle task of modeling the Reynolds stress tensor reduces to modeling the eddy-viscosity, representing, according to Boussinesq (1877), the ``coefficient of proportionality'' between the Reynolds stress and mean rate of strain tensors. In the present contribution an extended formulation based on the least square approach applied to the Boussinesq's correlation is presented. Furthermore, a Taylor-microscale-based formulation is derived originating from the equilibrium assumption related to the equality between the production and dissipation rates of kinetic energy of turbulence. Finally, an expression is proposed reflecting the Reynolds stress anisotropy influence on the eddy-viscosity damping by approaching the solid wall as well as including an appropriate length-scale switch accounting for the viscosity effects through inclusion of the Kolmogorov scales blended with those of the energy-containing eddies. The latter formulation is successfully applied in the framework of an instability-sensitive Reynolds stress model of turbulence. The afore-mentioned eddy-viscosity definitions are comparatively assessed in a series of wall-bounded flow configurations (including separation) in a Reynolds number range.
A new non-eddy viscosity subgrid-scale model and its application to channel flow
NASA Technical Reports Server (NTRS)
Shah, K. B.; Ferziger, J. H.
1995-01-01
To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky
Turbulent Eddy Viscosity and Large-Scale Convection in the Sun
NASA Technical Reports Server (NTRS)
Stothers, Richard B.
2000-01-01
It is suggested here that the laminar character of the large-scale deep convective flows appearing in numerical simulations of the Sun's convective envelope arises from the effect of turbulent eddy viscosity. Previously, M. Schwarzchild suggested the same idea to explain the observed surface granulation in the Sun.
NASA Astrophysics Data System (ADS)
Slepyshev, A. A.
2016-05-01
Free internal waves are considered in a Boussinesq approximation in the situation when horizontal eddy viscosity and diffusion in a vertically inhomogeneous flow are taken into account. The dispersion relation and wave damping factor are found in a linear approximation. The Stokes drift velocity is determined in the second order of smallness based on the wave amplitude. It has been indicated that the Stokes drift velocity, transverse with respect to the wave propagation direction, differs from zero if the flow-rate transverse component depends on the vertical coordinate. Vertical momentum fluxes differ from zero and can be comparable with or exceed the corresponding turbulent fluxes if eddy viscosity and diffusion are taken into account.
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J.
1994-01-01
A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.
Puleo, J.A.; Mouraenko, O.; Hanes, D.M.
2004-01-01
Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.
Convection without eddy viscosity: An attempt to model the interiors of giant planets
NASA Technical Reports Server (NTRS)
Ingersoll, A. P.
1986-01-01
In the theory of hydrostatic quasi-geostrophic flow in the Earth's atmosphere the principal results do not depend on the eddy viscosity. This contrasts with published theories of convection in deep rotating fluid spheres, where the wavelength of the fastest growing disturbance varies as E sup 1/3, where E, the Ekman number, is proportional to the eddy viscosity. A new theory of quasi-columnar motions in stably stratified fluid spheres attempts to capture the luck of the meteorologists. The theory allows one to investigate the stability of barotropic and baroclinic zonal flows that extend into the planetary interior. It is hypothesized that the internal heat Jupiter and Saturn comes out not radially but on sloping surfaces defined by the internal entropy distribution. To test the hypothesis one searches for basic states in which the wavelength of the fastest-growing disturbance remains finite as E tends to zero, and is which the heat flux vector is radially outward and poleward.
Predictions of axisymmetric free turbulent shear flows using a generalized eddy-viscosity approach
NASA Technical Reports Server (NTRS)
Morgenthaler, J. H.
1973-01-01
The generalized eddy viscosity approach is described and results are presented of test cases which show that predictions obtained by this approach are adequate for most engineering applications. Because of the importance of starting computations from the injection station where experimentally determined mean and turbulence parameters are rarely available, a very simple core model applicable to simple step-type (slug) profiles was developed. Agreement between predicted and experimental mean profiles was generally almost as good for calculations made by using this model throughout the core region and the transition model for all subsequent regions as predictions made by starting from experimental profiles in the transition region. The generalized eddy-viscosity model, which was developed in part through correlation of turbulence parameters, successfully predicted turbulent shear stress, turbulent intensity, and mean velocity profiles for a 0.040-inch-diameter microjet. Therefore, successful scaling by the model was demonstrated since data used in its development was for jet areas up to 90,000 times as large as the microjet and velocities only 1/20th as high.
NASA Astrophysics Data System (ADS)
Gravemeier, Volker; Wall, Wolfgang A.
2010-08-01
An algebraic variational multiscale-multigrid method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. Scale-separating operators generated by level-transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups (here, the smaller of the resolved scales) in a purely algebraic way. Thus, for scale separation, no additional discretization besides the basic one is required, in contrast to earlier approaches based on geometric multigrid methods. The proposed method is thoroughly validated via three numerical test cases of increasing complexity: a Rayleigh-Taylor instability, turbulent channel flow with a heated and a cooled wall, and turbulent flow past a backward-facing step with heating. Results obtained with the algebraic variational multiscale-multigrid method are compared to results obtained with residual-based variational multiscale methods as well as reference results from direct numerical simulation, experiments and LES published elsewhere. Particularly, mean and various second-order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small-scale subgrid-viscosity term within the algebraic multigrid framework instead of residual-based terms accounting for the subgrid-scale part of the non-linear convective term.
NASA Astrophysics Data System (ADS)
Holmberg, Andreas; Kierkegaard, Axel; Weng, Chenyang
2015-06-01
In this paper, a method for including damping of acoustic energy in regions of strong turbulence is derived for a linearized Navier-Stokes method in the frequency domain. The proposed method is validated and analyzed in 2D only, although the formulation is fully presented in 3D. The result is applied in a study of the linear interaction between the acoustic and the hydrodynamic field in a 2D T-junction, subject to grazing flow at Mach 0.1. Part of the acoustic energy at the upstream edge of the junction is shed as harmonically oscillating disturbances, which are conveyed across the shear layer over the junction, where they interact with the acoustic field. As the acoustic waves travel in regions of strong shear, there is a need to include the interaction between the background turbulence and the acoustic field. For this purpose, the oscillation of the background turbulence Reynold's stress, due to the acoustic field, is modeled using an eddy Newtonian model assumption. The time averaged flow is first solved for using RANS along with a k-ε turbulence model. The spatially varying turbulent eddy viscosity is then added to the spatially invariant kinematic viscosity in the acoustic set of equations. The response of the 2D T-junction to an incident acoustic field is analyzed via a plane wave scattering matrix model, and the result is compared to experimental data for a T-junction of rectangular ducts. A strong improvement in the agreement between calculation and experimental data is found when the modification proposed in this paper is implemented. Discrepancies remaining are likely due to inaccuracies in the selected turbulence model, which is known to produce large errors e.g. for flows with significant rotation, which the grazing flow across the T-junction certainly is. A natural next step is therefore to test the proposed methodology together with more sophisticated turbulence models.
Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L.
2014-06-10
We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are
Nonlinear eddy viscosity modeling and experimental study of jet spreading rates.
Heschl, C; Inthavong, K; Sanz, W; Tu, J
2014-02-01
Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence-driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS-based models that provide quick solutions but are known to fail in turbulent free shear and wall-affected flows. In order to cope with this deficiency, this study presents a nonlinear k-ε turbulence model and evaluates it along with linear k-ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling by entrainment through the well-known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence-driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations. PMID:23668473
NASA Technical Reports Server (NTRS)
Omori, S.; Gross, K. W.
1973-01-01
The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall hydrogen reacts with the combustion products, liberating an extensive amount of heat.
Laskowski, Gregory Michael
2005-12-01
Flows with strong curvature present a challenge for turbulence models, specifically eddy viscosity type models which assume isotropy and a linear and instantaneous equilibrium relation between stress and strain. Results obtained from three different codes and two different linear eddy viscosity turbulence models are compared to a DNS simulation in order to gain some perspective on the turbulence modeling capability of SIERRA/Fuego. The Fuego v2f results are superior to the more common two-layer k-e model results obtained with both a commercial and research code in terms of the concave near wall behavior predictions. However, near the convex wall, including the separated region, little improvement is gained using the v2f model and in general the turbulent kinetic energy prediction is fair at best.
Borovsky, Joseph E.
2006-05-15
The coefficient of magnetohydrodynamic (MHD) eddy viscosity of the turbulent solar wind is calculated to be {nu}{sub eddy}{approx_equal}1.3x10{sup 17} cm{sup 2}/s: this coefficient is appropriate for velocity shears with scale thicknesses larger than the {approx}10{sup 6} km correlation length of the solar-wind turbulence. The coefficient of MHD eddy viscosity is calculated again accounting for the action of smaller-scale turbulent eddies on smaller scale velocity shears in the solar wind. This eddy viscosity is quantitatively tested with spacecraft observations of shear flows in co-rotating interaction regions (CIRs) and in coronal-mass-ejection (CME) sheaths and ejecta. It is found that the large-scale ({approx}10{sup 7} km) shear of the CIR fractures into intense narrow ({approx}10{sup 5} km) slip zones between slabs of differently magnetized plasma. Similarly, it is found that the large-scale shear of CME sheaths also fracture into intense narrow slip zones between parcels of differently magnetized plasma. Using the solar-wind eddy-viscosity coefficient to calculate vorticity-diffusion time scales and comparing those time scales with the {approx}100-h age of the solar-wind plasma at 1 AU, it is found that the slip zones are much narrower than eddy-viscosity theory says they should be. Thus, our concept of MHD eddy viscosity fails testing. For the freestream turbulence effect in solar-wind magnetosphere coupling, the eddy-viscous force of the solar wind on the Earth's magnetosphere is rederived accounting for the action of turbulent eddies smaller than the correlation length, along with other corrections. The improved derivation of the solar-wind driver function for the turbulence effect fails to yield higher correlation coefficients between measurements of the solar-wind driver and measurements of the response of the Earth's magnetosphere.
NASA Technical Reports Server (NTRS)
Omori, S.
1973-01-01
The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion; that is, combustion alters the velocity profile as if the mass injection rate is increased, reducing the skin-friction as a result of a smaller velocity gradient at the wall. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall, hydrogen reacts with the combustion products, liberating an extensive amount of heat. The resulting large increase in temperature reduces the eddy viscosity in this region.
NASA Technical Reports Server (NTRS)
Omori, S.
1973-01-01
As described in Vol. 1, the eddy viscosity is calculated through the turbulent kinetic energy, in order to include the history of the flow and the effect of chemical reaction on boundary layer characteristics. Calculations can be performed for two different cooling concepts; that is, transpiration and regeneratively cooled wall cases. For the regenerative cooling option, coolant and gas side wall temperature and coolant bulk temperature in a rocket engine can be computed along the nozzle axis. Thus, this computer program is useful in designing coolant flow rate and cooling tube geometry, including the tube wall thickness as well as in predicting the effects of boundary layers along the gas side wall on thrust performances.
NASA Astrophysics Data System (ADS)
Marras, Simone; Suckale, Jenny; Giraldo, Francis X.; Constantinescu, Emil
2016-04-01
We present the solution of the viscous shallow water equations where viscosity is built as a residual-based subgrid scale model originally designed for large eddy simulation of compressible [1] and stratified flows [2]. The necessity of viscosity for a shallow water model not only finds motivation from mathematical analysis [3], but is supported by physical reasoning as can be seen by an analysis of the energetics of the solution. We simulated the flow of an idealized wave as it hits a set of obstacles. The kinetic energy spectrum of this flow shows that, although the inviscid Galerkin solutions -by spectral elements and discontinuous Galerkin [4]- preserve numerical stability in spite of the spurious oscillations in the proximity of the wave fronts, the slope of the energy cascade deviates from the theoretically expected values. We show that only a sufficiently small amount of dynamically adaptive viscosity removes the unwanted high-frequency modes while preserving the overall sharpness of the solution. In addition, it yields a physically plausible energy decay. This work is motivated by a larger interest in the application of a shallow water model to the solution of tsunami triggered coastal flows. In particular, coastal flows in regions around the world where coastal parks made of mitigation hills of different sizes and configurations are considered as a means to deviate the power of the incoming wave. References [1] M. Nazarov and J. Hoffman (2013) "Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods" Int. J. Numer. Methods Fluids, 71:339-357 [2] S. Marras, M. Nazarov, F. X. Giraldo (2015) "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES" J. Comput. Phys. 301:77-101 [3] J. F. Gerbeau and B. Perthame (2001) "Derivation of the viscous Saint-Venant system for laminar shallow water; numerical validation" Discrete Contin. Dyn. Syst. Ser. B, 1:89?102 [4] F
NASA Technical Reports Server (NTRS)
Hickey, M. P.
1988-01-01
The chemical-dynamical model of Walterscheid et al. (1987), which describes wave-driven fluctuations in OH nightglow, was modified to include the effects of both eddy thermal conduction and viscosity, as well as the Coriolis force (with the shallow atmosphere approximation). Using the new model, calculations were performed for the same nominal case as used by Walterscheid et al. but with only wave periods considered. For this case, the Coriolis force was found to be unimportant at any wave period. For wave periods greater than 2 or 3 hours, the inclusion of thermal conduction alone greatly modified the results (in terms of a complex ratio 'eta' which expresses the relationship between the intensity oscillation about the time-averaged intensity and the temperature oscillation about the time-averaged temperature); this effect was reduced with the further inclusion of the eddy viscosity.
NASA Astrophysics Data System (ADS)
Chen, Wei; de Swart, Huib E.
2016-03-01
Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, "surface jumps" (vertical shear of tidal current amplitude has a subsurface maximum) and "subsurface jets" (maximum tidal current amplitude below the surface), respectively. The "surface jumps" and "subsurface jets" both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, "surface jumps" take place for low density stratification, while and "subsurface jets" occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.
NASA Astrophysics Data System (ADS)
Bidadi, Shreyas; Rani, Sarma L.
2015-01-01
Monotonically integrated large-eddy simulation (MILES) approach utilizes the dissipation inherent to shock-capturing schemes to emulate the role played by explicit subgrid-scale eddy diffusivity at the high-wavenumber end of the turbulent energy spectrum. In the current study, a novel formulation is presented for quantifying the numerical viscosity inherent to Roe-based second-order TVD-MUSCL schemes for the Euler equations. Using this formulation, the effects of numerical viscosity and dissipation rate on implicit large-eddy simulations of turbulent flows are investigated. At first, the three-dimensional (3-D) finite-volume extension of the original Roe's flux, including Roe's Jacobian matrix, is presented. The fluxes are then extended to second-order using van Leer's MUSCL extrapolation technique. Starting from the 3-D Roe-MUSCL flux, an expression is derived for the numerical viscosity as a function of flux limiter and characteristic speed for each conserved variable, distance between adjacent cell centers, and a scaling parameter. Motivated by Thornber et al. [16] study, the high numerical viscosity inherent to TVD-MUSCL schemes is mitigated using a z-factor that depends on local Mach number. The TVD limiters, along with the z-factor, were initially applied to the 1-D shock-tube and 2-D inviscid supersonic wedge flows. Spatial profiles of numerical viscosities are plotted, which provide insights into the role of these limiters in controlling the dissipative nature of Roe's flux while maintaining monotonicity and stability in regions of high gradients. Subsequently, a detailed investigation was performed of decaying homogeneous isotropic turbulence with varying degrees of compressibility. Spectra of numerical viscosity and dissipation rate are presented, which clearly demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of dissipation peak closer to the cut-off wavenumber
NASA Astrophysics Data System (ADS)
Elmekawy, Ahmed M. Nagib M.
When turbulent flow generates unsteady differential pressure over an aircraft's structure, this may generate buffeting, a random oscillation of the structure. The buffet phenomenon is observed on a wide range of fighter aircraft, especially fighters with twin-tail. More research is needed to better understand the physics behind the vortical flow over a delta wing and the subsequent tail buffet. This dissertation reports the modeling and simulation of a steady-state one-way fluid-structure interaction for the tail buffet problem observed on a F/A-18 fighter. The time-averaged computational results are compared to available experimental data. Next, computations are extended to simulate an unsteady two-way fluid-structure interaction problem of the tail buffet of a F/A-18 fighter. For the modeling herein, a commercial software ANSYS version 14.0, is employed. For the fluid domain, the unsteady Reynolds-averaged Navier Stokes (URANS) equations with different turbulent models are utilized. The first turbulence model selected is the modified Spalart-Allmaras model (SARRC) with a strain-vorticity based production and curvature treatment. The second turbulence model selected is the Non-linear Eddy Viscosity Model (NLEVM) based on the Wilcox k--o model. This model uses the formulation of an explicit algebraic Reynolds stress model. The structural simulation is conducted by a finite element analysis model with shell elements. Both SARRC and NLEVM turbulence models are in ANSYS software. The experimental data used for validation were conducted on a simplified geometry: a 0.3 Mach number flow past a 76-deg delta wing pitched to 30-deg. Two vertical tails were placed downstream of the delta wing. The present work is the first ever study of the tail buffet problem of the F/A-18 fighter with two-way fluid-structure interaction using the two advanced turbulence models. The steady-state, time-averaged, one-way fluid-structure interaction case of the present investigation indicates
Numerical investigation of algebraic oceanic turbulent mixing-layer models
NASA Astrophysics Data System (ADS)
Chacón-Rebollo, T.; Gómez-Mármol, M.; Rubino, S.
2013-11-01
In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski-Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.
A stochastic extension of the explicit algebraic subgrid-scale models
Rasam, A. Brethouwer, G.; Johansson, A. V.
2014-05-15
The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.
Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.
1995-01-01
A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.
NASA Astrophysics Data System (ADS)
Chakraborty, Nilanjan; Klein, Markus
2008-08-01
Flame surface density (FSD) based reaction rate closure is one of the most important approaches in turbulent premixed flame modeling. The algebraic models for FSD based on power laws often require information about the fractal dimension D and the inner cut-off scale ηi. In the present study, two three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames are analyzed among which the flame in one case belongs to the corrugated flamelet (CF) regime, whereas the other falls well within the thin reaction zone (TRZ) regime. It is found that D for the flame in the TRZ regime is greater than the value obtained for the flame in the CF regime. For the flame within the TRZ regime, the fractal dimension is found to be 7/3, which is the same as D for a material surface in a turbulent environment. For the flame in the CF regime, ηi is found to scale with the Gibson scale, whereas ηi is found to scale with the Kolmogorov length scale for the flame in the TRZ regime. Based on these observations a new algebraic model for FSD is proposed, where D and ηi are expressed as functions of Karlovitz number. The performances of the new and existing algebraic models for FSD are compared with the corresponding values obtained from DNS databases.
NASA Technical Reports Server (NTRS)
Baurle, R. A.
2015-01-01
Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit
NASA Technical Reports Server (NTRS)
Baldwin, B. S.; Maccormack, R. W.
1976-01-01
Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.
Production and destruction of eddy kinetic energy in forced submesoscale eddy-resolving simulations
NASA Astrophysics Data System (ADS)
Mukherjee, Sonaljit; Ramachandran, Sanjiv; Tandon, Amit; Mahadevan, Amala
2016-09-01
We study the production and dissipation of the eddy kinetic energy (EKE) in a submesoscale eddy field forced with downfront winds using the Process Study Ocean Model (PSOM) with a horizontal grid resolution of 0.5 km. We simulate an idealized 100 m deep mixed-layer front initially in geostrophic balance with a jet in a domain that permits eddies within a range of O(1 km-100 km). The vertical eddy viscosities and the dissipation are parameterized using four different subgrid vertical mixing parameterizations: the k - ɛ , the KPP, and two different constant eddy viscosity and diffusivity profiles with a magnitude of O(10-2m2s-1) in the mixed layer. Our study shows that strong vertical eddy viscosities near the surface reduce the parameterized dissipation, whereas strong vertical eddy diffusivities reduce the lateral buoyancy gradients and consequently the rate of restratification by mixed-layer instabilities (MLI). Our simulations show that near the surface, the spatial variability of the dissipation along the periphery of the eddies depends on the relative alignment of the ageostrophic and geostrophic shear. Analysis of the resolved EKE budgets in the frontal region from the simulations show important similarities between the vertical structure of the EKE budget produced by the k - ɛ and KPP parameterizations, and earlier LES studies. Such an agreement is absent in the simulations using constant eddy-viscosity parameterizations.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
ERIC Educational Resources Information Center
Pavelle, Richard; And Others
1981-01-01
Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)
NASA Astrophysics Data System (ADS)
Read, Nicholas
2015-03-01
Viscosity is a transport coefficient relating to transport of momentum, and usually thought of as the analog of friction that occurs in fluids and solids. More formally, it is the response of the stress to the gradients of the fluid velocity field, or to the rate of change of strain (derivatives of displacement from a reference state). In general, viscosity is described by a fourth-rank tensor. Invoking rotation invariance, it reduces to familiar shear and bulk viscosity parts, which describe dissipation, but it can also contain an antisymmetric part, analogous to the Hall conductivity part of the conductivity tensor. In two dimensions this part is a single number, the Hall viscosity. Symmetry of the system under time reversal (or, in two dimensions, reflections) forces it to vanish. In quantum fluids with a gap in the bulk energy spectrum and which lack both time reversal and reflection symmetries the Hall viscosity can be nonzero even at zero temperature. For integer quantum Hall states, it was first calculated by Avron, Seiler, and Zograf, using a Berry curvature approach, analogous to the Chern number for Hall conductivity. In 2008 this was extended by the present author to fractional quantum Hall states and to BCS states in two dimensions. I found that the general result is given by a simple formula ns / 2 , where n is the particle number density, and s is the ``orbital spin'' per particle. The spin s is also related to the shift S, which enters the relation between particle number and magnetic flux needed to put the ground state on a surface of non-trivial topology with introducing defect excitations, by S = 2 s ; the connection was made by Wen and Zee. The values of s and S are rational numbers, and are robust--unchanged under perturbations that do not cause the bulk energy gap to collapse--provided rotation as well as translation symmetry are maintained. Hall viscosity can be measured in principle, though a simple way to do so is lacking. It enters various
Computation of turbulent boundary layer flows with an algebraic stress turbulence model
NASA Technical Reports Server (NTRS)
Kim, Sang-Wook; Chen, Yen-Sen
1986-01-01
An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
NASA Technical Reports Server (NTRS)
Jongen, T.; Machiels, L.; Gatski, T. B.
1997-01-01
Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.
Southern Ocean eddy phenomenology
NASA Astrophysics Data System (ADS)
Frenger, I.; Münnich, M.; Gruber, N.; Knutti, R.
2015-11-01
Mesoscale eddies are ubiquitous features in the Southern Ocean, yet their phenomenology is not well quantified. To tackle this task, we use satellite observations of sea level anomalies and sea surface temperature (SST) as well as in situ temperature and salinity measurements from profiling floats. Over the period 1997-2010, we identified over a million mesoscale eddy instances and were able to track about 105 of them over 1 month or more. The Antarctic Circumpolar Current (ACC), the boundary current systems, and the regions where they interact are hot spots of eddy presence, representing also the birth places and graveyards of most eddies. These hot spots contrast strongly to areas shallower than about 2000 m, where mesoscale eddies are essentially absent, likely due to topographical steering. Anticyclones tend to dominate the southern subtropical gyres, and cyclones the northern flank of the ACC. Major causes of regional polarity dominance are larger formation numbers and lifespans, with a contribution of differential propagation pathways of long-lived eddies. Areas of dominance of one polarity are generally congruent with the same polarity being longer-lived, bigger, of larger amplitude, and more intense. Eddies extend down to at least 2000 m. In the ACC, eddies show near surface temperature and salinity maxima, whereas eddies in the subtropical areas generally have deeper anomaly maxima, presumably inherited from their origin in the boundary currents. The temperature and salinity signatures of the average eddy suggest that their tracer anomalies are a result of both trapping in the eddy core and stirring.
NASA Astrophysics Data System (ADS)
Anderson, Laurence A.; McGillicuddy, Dennis J.; Maltrud, Mathew E.; Lima, Ivan D.; Doney, Scott C.
2011-09-01
Two eddy-resolving (0.1°) physical-biological simulations of the North Atlantic Ocean are compared, one with the surface momentum flux computed only from wind velocities and the other using the difference between air and ocean velocity vectors. This difference in forcing has a significant impact on the intensities and relative number of different types of mesoscale eddies in the Sargasso Sea. Eddy/wind interaction significantly reduces eddy intensities and increases the number of mode-water eddies and "thinnies" relative to regular cyclones and anticyclones; it also modifies upward isopycnal displacements at the base of the euphotic zone, increasing them in the centers of mode water eddies and at the edges of cyclones, and decreasing them in the centers of cyclones. These physical changes increase phytoplankton growth rates and biomass in mode-water eddies, bringing the biological simulation into better agreement with field data. These results indicate the importance of including the eddy/wind interaction in simulations of the physics and biology of eddies in the subtropical North Atlantic. However, eddy intensities in the simulation with eddy/wind interaction are lower than observed, which suggests a decrease in horizontal viscosity or an increase in horizontal grid resolution will be necessary to regain the observed level of eddy activity.
NASA Technical Reports Server (NTRS)
Ruge, J. W.; Stueben, K.
1987-01-01
The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.
Explicit algebraic reynolds stress models for anisotropic wall-bounded flows
NASA Astrophysics Data System (ADS)
Menter, F. R.; Garbaruk, A. V.; Egorov, Y.
2012-01-01
In the present paper, two variants of Explicit Algebraic Reynolds Stress Model (EARSM) are presented and applied to a number of test cases. Both formulations start from the Wallin Johansson (WJ) EARSM stress-strain relationship. The goal of the first step was to combine the EARSM with the ω-equation-based Baseline (BSL) model, to avoid freestream sensitivities and ambiguities in comparison with the Shear Stress Transport (SST) model. This could be achieved by a slight change in the A1 constant. In addition, the standard eddy-viscosity formulation is used in the diffusion terms of the k- and the ω-equations. Secondly, a simplified version of the stress-strain relationship was developed. It is based on a linear form of the implicit algebraic model. It is not clear at the time if this formulation possess significant advantages against the WJ stress-strain model. For the current cases, both variants produced essentially identical results. Several test cases have been computed. The main interest in the simulations was on corner flow separation.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
Stationary mesoscale eddies, upgradient eddy fluxes, and the anisotropy of eddy diffusivity
NASA Astrophysics Data System (ADS)
Lu, Jianhua; Wang, Fuchang; Liu, Hailong; Lin, Pengfei
2016-01-01
The mesoscale eddies of which parameterization is needed in coarse-resolution ocean models include not only the transient eddies akin to baroclinic instability but also the stationary eddies associated with topography. By applying a modified Lorenz-type decomposition to the eddy-permitting Southern Ocean State Estimate, we show that the stationary mesoscale eddies contribute a significant part to the total eddy kinetic energy, eddy enstrophy, and the total eddy-induced isopycnal thickness and potential vorticity fluxes. We find that beneath middepth (about 1000 m) the upgradient eddy fluxes, or so-called "negative" eddy diffusivities, are mainly attributed to the stationary mesoscale eddies, whereas the remaining transient eddy diffusivity is positive, for which the Gent and McWilliams (1990) parameterization scheme applies well. A quantitative method of measuring the anisotropy of eddy diffusivity is presented. The effect of stationary mesoscale eddies is one of major sources responsible for the anisotropy of eddy diffusivity. We suggest that an independent parameterization scheme for stationary mesoscale eddies may be needed for coarse-resolution ocean models, although the transient eddies remain the predominant part of mesoscale eddies in the oceans.
NASA Astrophysics Data System (ADS)
Pichevin, Thierry; Nof, Doron
1996-09-01
A new nonlinear mechanism for the generation of "Meddies" by a cape is proposed. The essence of the new process is that the flow-force associated with any steady current that curves back on itself around a cape cannot be balanced without generating and shedding eddies. The process is modeled as follows. A westward flowing density current advances along a zonal wall and turns eastward after reaching the edge of the wall (i.e. the Cape of St Vincent). Integration of the steady (and inviscid) momentum equation along the wall gives the long-shore flow-force and shows that, no matter what the details of the turning process are, such a scenario is impossible. It corresponds to an unbalanced flow-force and, therefore, cannot exist. Namely, in an analogy to a rocket, the zonal longshore current forces the entire system to the west. A flow field that can compensate for such a force is westward drifting eddies that push the system to the east. In a similar fashion to the backward push associated with a firing cannon, the westward moving eddies (bullets) balance the integrated momentum of the flow around the cape. Nonlinear solutions are constructed analytically using an approach that enables one to compute the eddies' size and generation frequency without solving for the incredibly complicated details of the generation process itself. The method takes advantage of the fact that, after each eddy is generated, the system returns to its original structure. It is based on the integration of the momentum equation (for periodic flows) over a control volume and a perturbation expansion in ɛ, the ratio between the eddies' westward drift and the parent current speed. It is found that, because of the relatively small size of the Mediterranean eddies, β is not a sufficiently strong mechanism to remove the eddies (from the Cape of St Vincent) at the observed frequency. It is, therefore, concluded that westward advection must also take place. Specifically, it is found that an advection
Drikakis, D.; Margolin, L. G.; Smolarkiewicz, P. K.
2001-01-01
Recently several papers have appeared in the CFD literature, proposing an idealized instability problem as a benchmark for discriminating among numerical algorithms for two-dimensional Navier-Stokes flows. The problem is a double shear layer simulated at coarse resolution and with a prescribed interface perturbation. A variety of second-order accurate schemes have been tested, with all results falling into one of two solution patterns - one pattern with two eddies and the other with three eddies. In the literature, there is no fast-and-firm rule to predict the results of any particular algorithm. However it is asserted that the two-eddy solution is correct. Our own research has led to two conclusions. First, the appearance of the third eddy is tied up with small details of the truncation error; we illustrate this point by prescribing small changes that lead to reversal of the appearance/disappearance of the third eddy in several schemes. Second, we discuss the realizability of the two solutions and suggest that the three-eddy solution is the more physical. Overall, we conclude that this problem is a poor choice of benchmark to discriminate among numerical algorithms.
Numerical algebraic geometry and algebraic kinematics
NASA Astrophysics Data System (ADS)
Wampler, Charles W.; Sommese, Andrew J.
In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.
ERIC Educational Resources Information Center
Robertson, C. T.
1973-01-01
Discusses theories underlying the phenomena of solution viscosities, involving the Jones and Dole equation, B-coefficient determination, and flickering cluster model. Indicates that viscosity measurements provide a basis for the study of the structural effects of ions in aqueous solutions and are applicable in teaching high school chemistry. (CC)
Viscosity measuring using microcantilevers
Oden, Patrick Ian
2001-01-01
A method for the measurement of the viscosity of a fluid uses a micromachined cantilever mounted on a moveable base. As the base is rastered while in contact with the fluid, the deflection of the cantilever is measured and the viscosity determined by comparison with standards.
Viscosity of pure hydrocarbons
Knapstad, B.; Skjolsvik, P.A.; Oye, H.A.
1989-01-01
Accurate viscosity measurements have been performed on eight pure hydrocarbons at atmospheric pressure in the temperature range 20-150/sup 0/C, or up to approximately 20/sup 0/C below the boiling point of the hydrocarbon, by use of an absolute oscillating viscometer. The hydrocarbons are cyclohexane and benzene and the n-alkanes of hexane, heptane, octane, decane, dodecane, and tetradecane. The viscosities are described with a modified Arrhenius equation, and the deviation in fit is 0.12% or less. The accuracy is estimated to be 0.33-0.56%. The lowest viscosities are assumed to have the highest deviation. Literature data reported by Dymond and Young normally fit our viscosities within our estimated accuracy. Other literature viscosities tend to be higher than our results, especially for the n-alkanes.
Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models
NASA Astrophysics Data System (ADS)
Degrazia, G. A.; Rizza, U.; Puhales, F. S.; Welter, G. S.; Acevedo, O. C.; Maldaner, S.
2012-02-01
A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical diffusion theory is proposed. This viscosity is described in terms of a velocity variance and a time scale, both associated to the inertial subrange. This new subfilter viscosity contains a cutoff wavenumber kc, presenting an identical form (differing by a constant) to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described in terms of a sharp division between large and small wavenumbers of a turbulent flow and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics of different orders, generated from atmospheric boundary layer simulations employing both Taylor and Heisenberg subfilter viscosities have been compared with observations and results provided by other simulations. The comparison shows that the LES model utilizing the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in different vertical regions of a planetary convective boundary layer (CBL).
Quantization of Algebraic Reduction
Sniatycki, Jeodrzej
2007-11-14
For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.
Homogeneous and inhomogeneous eddies
Pavia, E.G.
1994-12-31
This work deals with mesoscale warm oceanic eddies; i.e., self-contained bodies of water which transport heat, among other things, for several months and for several hundreds of kilometers. This heat transport is believed to play an important role in the atmospheric and oceanic conditions of the region where it is being transported. Here the author examines the difference in evolution between eddies modeled as blobs of homogeneous water and eddies in which density varies in the horizontal. Preliminary results suggest that instability is enhanced by inhomogeneities, which would imply that traditional modeling studies, based on homogeneous vortices have underestimated the rate of heat-release from oceanic eddies to the surroundings. The approach is modeling in the simplest form; i.e., one single active layer. Although previous studies have shown the drastic effect on stability brought by two or more dynamically-relevant homogeneous layers, the author believes the single-layer eddy-model has not been investigated thoroughly.
On explicit algebraic stress models for complex turbulent flows
NASA Technical Reports Server (NTRS)
Gatski, T. B.; Speziale, C. G.
1992-01-01
Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
NASA Technical Reports Server (NTRS)
Ellis, R. C.; Fink, R. A.; Rich, R. W.
1989-01-01
A high torque capacity eddy current damper used as a rate limiting device for a large solar array deployment mechanism is discussed. The eddy current damper eliminates the problems associated with the outgassing or leaking of damping fluids. It also provides performance advantages such as damping torque rates, which are truly linear with respect to input speed, continuous 360 degree operation in both directions of rotation, wide operating temperature range, and the capability of convenient adjustment of damping rates by the user without disassembly or special tools.
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
ERIC Educational Resources Information Center
Schaefer, Claire
1989-01-01
Presents a lesson that introduces students in grades K-three to sources of design inspiration in contemporary urban settings. Using Don Eddy's painting of a jewelry store window display, asks students to describe and analyze the interplay of shape, pattern, and color. Suggests studio activities, including an activity in which students build a…
NASA Technical Reports Server (NTRS)
2002-01-01
This true-color satellite image shows a large phytoplankton bloom, several hundred square kilometers in size, in the Indian Ocean off the west coast of Tasmania. In this scene, the rich concentration of microscopic marine plants gives the water a lighter, more turquoise appearance which helps to highlight the current patterns there. Notice the eddies, or vortices in the water, that can be seen in several places. It is possible that these eddies were formed by converging ocean currents flowing around Tasmania, or by fresh river runoff from the island, or both. Often, eddies in the sea serve as a means for stirring the water, thus providing nutrients that help support phytoplankton blooms, which in turn provide nutrition for other organisms. Effectively, these eddies help feed the sea (click to read an article on this topic). This image was acquired November 7, 2000, by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) flying aboard the Orbview-2 satellite. Tasmania is located off Australia's southeastern coast. Image courtesy SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE
Estimation of turbulence dissipation rate by Large eddy PIV method in an agitated vessel
NASA Astrophysics Data System (ADS)
Kysela, Bohuš; Jašíková, Darina; Konfršt, Jiří; Šulc, Radek; Ditl, Pavel
2015-05-01
The distribution of turbulent kinetic energy dissipation rate is important for design of mixing apparatuses in chemical industry. Generally used experimental methods of velocity measurements for measurement in complex geometries of an agitated vessel disallow measurement in resolution of small scales close to turbulence dissipation ones. Therefore, Particle image velocity (PIV) measurement method improved by large eddy Ply approach was used. Large eddy PIV method is based on modeling of smallest eddies by a sub grid scale (SGS) model. This method is similar to numerical calculations using Large Eddy Simulation (LES) and the same SGS models are used. In this work the basic Smagorinsky model was employed and compared with power law approximation. Time resolved PIV data were processed by Large Eddy PIV approach and the obtained results of turbulent kinetic dissipation rate were compared in selected points for several operating conditions (impeller speed, operating liquid viscosity).
Nuclear viscosity and viscosity to entropy ratio
NASA Astrophysics Data System (ADS)
Fu, Dani; Mekjian, Aram
2010-11-01
Both a classical and a quantum mechanical evaluation of the shear viscosity of hadronic matter is developed and compared. The classical evaluation involves the scattering angle produced by a potential while a quantum description is based on phase shifts from this potential. A hard sphere potential and an attractive square well potential are considered. The classical evaluation of the scattering angle can be cast into a form that has the structure of Snell's refraction law for an attractive potential. The limit of a large index of refraction gives the hard sphere result. The high wave number limit of the quantum result for a hard sphere has a scaling law associated with it. This scaling law is similar to a result which gives a factor of two increase of the hard sphere geometric scattering cross section. This increase is associated with diffraction of the wave around the sphere. The quantum mechanical evaluation is discussed in the unitary limit of infinite scattering length. In the limit of large scattering length the effective range to quantum thermal wavelength appears as a limiting scale. The viscosity to entropy density ratio is developed. Results are compared with the string theory limit for this ratio involving Planck's constant.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
NASA Astrophysics Data System (ADS)
Alves, I. P.; Degrazia, G. A.; Buske, D.; Vilhena, M. T.; Moraes, O. L. L.; Acevedo, O. C.
2012-12-01
In this study an integral and an algebraic formulation for the eddy diffusivities in a shear driven planetary boundary layer are derived for pollutant dispersion applications. The expressions depend on the turbulence properties and on the distance from the source. They are based on the turbulent kinetic energy spectra, Taylor’s statistical diffusion theory and measured turbulent characteristics during intense wind events. The good agreement between the algebraic and the integral formulation for the eddy diffusivities corroborate the hypothesis that using an algebraic formulation as a surrogate for the eddy diffusivities in the neutral planetary boundary layer is valid. As a consequence, the vertical eddy diffusivity provided by the algebraic formulation and its asymptotic limit for large time (diffusion time much larger than the Lagrangian integral time scale), were introduced into an analytical air pollution model and validated against data from the classic Prairie Grass project. A statistical analysis, employing specific indices shows that the results are in good agreement with the observations. Furthermore, this study suggests that the inclusion of the memory effect, which is important in regions near to a continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. Therefore, the major finding of this paper is the necessity of including the downwind distance-dependent eddy diffusivity for low continuous point sources in air quality modeling studies.
Rubin, David M.; McDonald, Richard R.
1995-01-01
Recirculating flow in lateral separation eddies is typically weaker than main stem flow and provides an effective environment for trapping sediment. Observations of recirculating flow and sedimentary structures demonstrate that eddies pulsate in size and in flow velocity even when main stem flow is steady. Time series measurements of flow velocity and location of the reattachment point indicate that these pulsations are nonperiodic. Nonperiodic flow in the lee of a channel margin constriction is grossly different from the periodic flow in the lee of a cylinder that is isolated in a flow. Our experiments demonstrate that placing a flow-parallel plate adjacent to a cylinder is sufficient to cause the leeside flow to change from a periodic sequence of vortices to a nonperiodically pulsating lateral separation eddy, even if flow conditions are otherwise unchanged. Two processes cause the leeside flow to become nonperiodic when the plate is added. First, vortices that are shed from the cylinder deform and become irregular as they impact the plate or interfere with remnants of other vortices near the reattachment point. Second, these deformed vortices and other flow structures are recirculated in the lateral separation eddy, thereby influencing the future state (pressure and momentum distribution) of the recirculating flow. The vortex deformation process was confirmed experimentally by documenting spatial differences in leeside flow; vortex shedding that is evident near the separation point is undetectable near the reattachment point. Nonlinear forecasting techniques were used in an attempt to distinguish among several possible kinds of nonperiodic flows. The computational techniques were unable to demonstrate that any of the nonperiodic flows result from low-dimensional nonlinear processes.
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
Viscosity of colloidal suspensions
Cohen, E.G.D.; Schepper, I.M. de
1995-12-31
Simple expressions are given for the effective Newtonian viscosity as a function of concentration as well as for the effective visco-elastic response as a function of concentration and imposed frequency, of monodisperse neutral colloidal suspensions over the entire fluid range. The basic physical mechanisms underlying these formulae are discussed. The agreement with existing experiments is very good.
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
Eddy Flow during Magma Emplacement: The Basemelt Sill, Antarctica
NASA Astrophysics Data System (ADS)
Petford, N.; Mirhadizadeh, S.
2014-12-01
The McMurdo Dry Valleys magmatic system, Antarctica, forms part of the Ferrar dolerite Large Igneous Province. Comprising a vertical stack of interconnected sills, the complex provides a world-class example of pervasive lateral magma flow on a continental scale. The lowermost intrusion (Basement Sill) offers detailed sections through the now frozen particle macrostructure of a congested magma slurry1. Image-based numerical modelling where the intrusion geometry defines its own unique finite element mesh allows simulations of the flow regime to be made that incorporate realistic magma particle size and flow geometries obtained directly from field measurements. One testable outcome relates to the origin of rhythmic layering where analytical results imply the sheared suspension intersects the phase space for particle Reynolds and Peclet number flow characteristic of macroscopic structures formation2. Another relates to potentially novel crystal-liquid segregation due to the formation of eddies locally at undulating contacts at the floor and roof of the intrusion. The eddies are transient and mechanical in origin, unrelated to well-known fluid dynamical effects around obstacles where flow is turbulent. Numerical particle tracing reveals that these low Re number eddies can both trap (remove) and eject particles back into the magma at a later time according to their mass density. This trapping mechanism has potential to develop local variations in structure (layering) and magma chemistry that may otherwise not occur where the contact between magma and country rock is linear. Simulations indicate that eddy formation is best developed where magma viscosity is in the range 1-102 Pa s. Higher viscosities (> 103 Pa s) tend to dampen the effect implying eddy development is most likely a transient feature. However, it is nice to think that something as simple as a bumpy contact could impart physical and by implication chemical diversity in igneous rocks. 1Marsh, D.B. (2004), A
A Realizable Reynolds Stress Algebraic Equation Model
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.
1993-01-01
The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Shear thirning will cause a normally viscous fluid -- such as pie filling or whipped cream -- to deform and flow more readily under high shear conditions. In shear thinning, a pocket of fluid will deform and move one edge forward, as depicted here.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
NASA Technical Reports Server (NTRS)
Workman, Gary L.; Wang, Morgan
1992-01-01
The recognition of materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques.
Are Eddy Covariance series stationary?
Technology Transfer Automated Retrieval System (TEKTRAN)
Spectral analysis via a discrete Fourier transform is used often to examine eddy covariance series for cycles (eddies) of interest. Generally the analysis is performed on hourly or half-hourly data sets collected at 10 or 20 Hz. Each original series is often assumed to be stationary. Also automated ...
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.
Impact of Parameterized Lee Wave Drag on the Energy Budget of an Eddying Global Ocean Model
NASA Astrophysics Data System (ADS)
Trossman, D. S.; Arbic, B. K.; Garner, S.; Goff, J. A.; Jayne, S. R.; Metzger, E.; Wallcraft, A.
2012-12-01
We examine the impact of a lee wave drag parameterization on an eddying global ocean model. The wave drag parameterization represents the the momentum transfer associated with the generation of lee waves arising from geostrophic flow impinging upon rough topography. It is included in the online model, thus ensuring that abyssal currents and stratification in the simulation are affected by the presence of the wave drag. The model utilized here is the nominally 1/12th degree Hybrid Coordinate Ocean Model (HYCOM) forced by winds and air-sea buoyancy fluxes. An energy budget including the parameterized wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity is diagnosed during the model runs and compared with the wind power input and buoyancy fluxes. Wave drag and vertical viscosity are the largest of the mechanical energy dissipation rate terms, each more than half of a terawatt when globally integrated. The sum of all four dissipative terms approximately balances the rate of energy put by the winds and buoyancy fluxes into the ocean. An ad hoc global enhancement of the bottom drag at each grid point by a constant factor cannot serve as a perfect substitute for wave drag, particularly where there is little wave drag. Eddy length scales at the surface, sea surface height variance, surface kinetic energy, and positions of intensified jets in the model are compared with those inferred from altimetric observations. Vertical profiles of kinetic energy from the model are compared with mooring observations to investigate whether the model is improved when wave drag is inserted.; The drag and viscosity terms in our energy budget [log_10(W m^-2)]: (a) quadratic bottom boundary layer drag, (b) parameterized internal lee wave drag, (c) vertical viscosity, and (d) "horizontal" viscosity. Shown is an average of inline estimates over one year of the spin-up phase with wave drag.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The sample cell at the heart of CVX-2 will sit inside a thermostat providing three layers of insulation. The cell itself comprises a copper body that conducts heat efficiently and smoothes out thermal variations that that would destroy the xenon's uniformity. Inside the cell, the oscillating screen viscometer element is supported between two pairs of electrodes that deflect the screen and then measure screen motion.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Because xenon near the critical point will collapse under its own weight, experiments on Earth (green line) are limited as they get closer (toward the left) to the critical point. CVX in the microgravity of space (red line) moved into unmeasured territory that scientists had not been able to reach.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2001 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure that is placed inside a pressure canister. A similar canister holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (not shown) of the National Institutes of Standards and Technology, Gaithersburg, MD. This is a detail view of MSFC 0100143.
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Hall Viscosity I: Linear Response Theory for Viscosity
NASA Astrophysics Data System (ADS)
Bradlyn, Barry; Goldstein, Moshe; Read, Nicholas
2012-02-01
In two dimensional systems with broken time-reversal symmetry, there can exist a non-dissipative viscosity coefficient [1,2,3]. This Hall viscosity is similar in nature to the non-dissipative Hall conductivity. In order to investigate this phenomenon further, we develop a linear response formalism for viscosity. We derive a Kubo formula for the frequency dependent viscosity tensor in the long wavelength limit. We compute the viscosity tensor for the free electron gas, integer quantum Hall systems, and two-dimensional paired superfluids. In the zero frequency limit, we show how the known results [3,4] for the Hall viscosity are recovered.[4pt] [1] J. Avron, R. Seiler, and P. Zograf, Phys. Rev. Lett. 75, 697 (1995).[0pt] [2] P. Levay, J. Math. Phys. 36, 2792 (1995).[0pt] [3] N. Read, Phys. Rev. B 79, 045308 (2009).[0pt] [4] N. Read and E. Rezayi, Phys. Rev. B 84, 085316 (2011).
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Mesolayer of attached eddies in turbulent channel flow
NASA Astrophysics Data System (ADS)
Hwang, Yongyun
2016-10-01
Recent experimental measurements have reported that the outer peak of the streamwise wave-number spectra of the streamwise velocity depends on the Reynolds number. Starting from this puzzling observation, here it is proposed that the wall-parallel velocity components of each of the energy-containing motions in the form of Towsnend's attached eddies exhibit an inner-scaling nature in the region close to the wall. Some compelling evidence on this proposition has been presented with a careful inspection of scaling of velocity spectra from direct numerical simulations, a linear analysis with an eddy viscosity, and the recently computed statistical structure of the self-similar energy-containing motions in the logarithmic region. This observation suggests that the viscous wall effect would not be negligible at least below the peak wall-normal location of each of the energy-containing motions in the logarithmic and outer regions, reminiscent of the concept of the mesolayer previously observed in the mean momentum balance. It is shown that this behavior emerges due to a minimal form of scale interaction, modeled by the eddy viscosity in the linear theory, and enables one to explain the Reynolds-number-dependent behavior of the outer peak as well as the near-wall penetration of the large-scale outer structures in a consistent manner. Incorporation of this viscous wall effect to Townsend's attached eddies, which were originally built with an inviscid approximation at the wall, also reveals that the self-similarity of the wall-parallel velocity components of the energy-containing motions would be theoretically broken in the region close to the wall.
Large-eddy simulation of the turbulent flow in the downstream region of a backward-facing step
NASA Astrophysics Data System (ADS)
Silveira Neto, A.; Grand, D.; Metais, O.; Lesieur, M.
1991-05-01
A numerical simulation of a complex turbulent shear flow using large-eddy simulation techniques is carried out. The filtered Navier-Stokes equations are solved with a finite-volume method. The subgrid model is a local adaptation to the physical space of isotropic spectral eddy-viscosity models. The statistics of the mean field are in good agreement with the experimental data available, corresponding to a low step. Calculations in a high-step case show that the eddy structure of the flow presents striking analogies with the plane shear layers, with large billows shed behind the step, and longitudinal hairpin vortices strained between these billows.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
Viscosity of the earth's core.
NASA Technical Reports Server (NTRS)
Gans, R. F.
1972-01-01
Calculation of the viscosity of the core at the boundary of the inner and outer core. It is assumed that this boundary is a melting transition and the viscosity limits of the Andrade (1934,1952) hypothesis (3.7 to 18.5 cp) are adopted. The corresponding kinematic viscosities are such that the precessional system explored by Malkus (1968) would be unstable. Whether it would be sufficiently unstable to overcome a severely subadiabatic temperature gradient cannot be determined.
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of liquid xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Resembling a tiny bit of window screen, the oscillator at the heart of CVX-2 will vibrate between two pairs of paddle-like electrodes. The slight bend in the shape of the mesh has no effect on the data. What counts are the mesh's displacement in the xenon fluid and the rate at which the displacement dampens. The unit shown here is encased in a small test cell and capped with a sapphire windown to contain the xenon at high pressure.
Windmill driven eddy current heater
Birgel, W. J.; Hajec, C. S.
1983-12-20
A windmill electric heater converts wind energy to heat energy. A windmill drives a rotor of an eddy current heater. Magnetic fields are provided at an air gap between the rotor and a stator of the eddy current heater. Rotation of the rotor with respect to the stator causes eddy currents, and therefore heat, to be generated in the rotor. The heat generated in the rotor is drawn off for beneficial use such as in heating a house or other building. Excitation of the magnetic fields (and therefore the amount of heat generated) is controlled as a function of sensed parameters such as wind velocity, ambient temperature of the surroundings to be heated and temperature of the eddy current heater.
Eddy-Current Reference Standard
NASA Technical Reports Server (NTRS)
Ambrose, H. H., Jr.
1985-01-01
Magnetic properties of metallic reference standards duplicated and stabilized for eddy-current coil measurements over long times. Concept uses precisely machined notched samples of known annealed materials as reference standards.
An eddy closure for potential vorticity
Ringler, Todd D
2009-01-01
The Gent-McWilliams (GM) parameterization is extended to include a direct influence in the momentum equation. The extension is carried out in two stages; an analysis of the inviscid system is followed by an analysis of the viscous system. In the inviscid analysis the momentum equation is modified such that potential vorticity is conserved along particle trajectories following a transport velocity that includes the Bolus velocity in a manner exactly analogous to the continuity and tracer equations. In addition (and in contrast to traditional GM closures), the new formulation of the inviscid momentum equation results in a conservative exchange between potential and kinetic forms of energy. The inviscid form of the eddy closure conserves total energy to within an error proportional to the time derivative of the Bolus velocity. The hypothesis that the viscous term in the momentum equation should give rise to potential vorticity being diffused along isopycnals in a manner analogous to other tracers is examined in detail. While the form of the momentum closure that follows from a strict adherence to this hypothesis is not immediately interpretable within the constructs of traditional momentum closures, three approximations to this hypothesis results in a form of dissipation that is consistent with traditional Laplacian diffusion. The first two approximations are that relative vorticity, not potential vorticity, is diffused along isopyncals and that the flow is in approximate geostrophic balance. An additional approximation to the Jacobian term is required when the dissipation coefficient varies in space. More importantly, the critique of this hypothesis results in the conclusion that the viscosity parameter in the momentum equation should be identical to the tradition GM closure parameter {Kappa}. Overall, we deem the viscous form of the eddy closure for potential vorticity as a viable closure for use in ocean circulation models.
NONDESTRUCTIVE EDDY CURRENT TESTING
Renken, C.J. Jr.
1961-05-23
An eddy current testing device is described for measuring metal continuity independent of probe-to-sample spacing. An inductance would test probe is made a leg of a variable impedance bridge and the bridge is balanced with the probe away from the sample. An a-c signal is applied across the input terminals of the bridge circuit. As the probe is brought into proximity with the metal sample, the resulting impedance change in the probe gives an output signal from the bridge whose phase angle is proportional to the sample continuity and amplitude is proportional to the probe-tosample spacing. The output signal from the bridge is applied to a compensating network where, responsive to amplitude changes from the bridge output signal, a constant phased voltage output is maintained when the sample is continuous regardless of probe-to-sample spacing. A phase meter calibrated to read changes in resistivity of the metal sample measures the phase shift between the output of the compensating network and the original a-c signal applied to the bridge.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Effective Viscosity Coefficient of Nanosuspensions
NASA Astrophysics Data System (ADS)
Rudyak, V. Ya.; Belkin, A. A.; Egorov, V. V.
2008-12-01
Systematic calculations of the effective viscosity coefficient of nanosuspensions have been performed using the molecular dynamics method. It is established that the viscosity of a nanosuspension depends not only on the volume concentration of the nanoparticles but also on their mass and diameter. Differences from Einstein's relation are found even for nanosuspensions with a low particle concentration.
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
Volatiles Which Increase Magma Viscosity
NASA Astrophysics Data System (ADS)
Webb, S.
2015-12-01
The standard model of an erupting volcano is one in which the viscosity of a decompressing magma increases as the volatiles leave the melt structure to form bubbles. It has now been observed that the addition of the "volatiles" P, Cl and F result in an increase in silicate melt viscosity. This observation would mean that the viscosity of selected degassing magmas would decrease rather than increase. Here we look at P, Cl and F as three volatiles which increase viscosity through different structural mechanisms. In all three cases the volatiles increase the viscosity of peralkaline composition melts, but appear to always decrease the viscosity of peraluminous melts. Phosphorus causes the melt to unmix into a Na-P rich phase and a Na-poor silicate phase. Thus as the network modifying Na (or Ca) are removed to the phosphorus-rich melt, the matrix melt viscosity increases. With increasing amounts of added phosphorus (at network modifying Na ~ P) the addition of further phosphorus causes a decrease in viscosity. The addition of chlorine to Fe-free aluminosilicate melts results in an increase in viscosity. NMR data on these glass indicates that the chlorine sits in salt-like structures surrounded by Na and/or Ca. Such structures would remove network-modifying atoms from the melt structure and thus result in an increase in viscosity. The NMR spectra of fluorine-bearing glasses shows that F takes up at least 5 different structural positions in peralkaline composition melts. Three of these positions should result in a decrease in viscosity due to the removal of bridging oxygens. Two of the structural positons of F, however, should result in an increase in viscosity as they require the removal of network-modifying atoms from the melt structure (with one of the structures being that observed for Cl). This would imply that increasing amounts of F might result in an increase in viscosity. This proposed increase in viscosity with increasing F has now been experimentally confirmed.
NASA Technical Reports Server (NTRS)
Lytle, John K.; Harloff, Gary J.; Hsu, Andrew T.
1990-01-01
Previous calculations of jet-in-crossflow problems have been sensitive to the turbulence and artificial viscosity models and to the grid. Consequently, the eddy viscosity model in the PARC3D code was modified to consider the turbulent jet by switching from the Baldwin-Lomax (1978) model to an axisymmetric jet model. A modified artificial viscosity model has been utilized and evaluated in this study as well. The new model includes cell size scaling and a directional dependence in the coefficients. Computational results from PARC3D demonstrate the effects of the viscosity models on the pressure distribution fore and aft of the jet and the ability of the adaptive grid scheme to adjust to the three-dimensional gradients around the jet.
Conservative smoothing versus artificial viscosity
Guenther, C.; Hicks, D.L.; Swegle, J.W.
1994-08-01
This report was stimulated by some recent investigations of S.P.H. (Smoothed Particle Hydrodynamics method). Solid dynamics computations with S.P.H. show symptoms of instabilities which are not eliminated by artificial viscosities. Both analysis and experiment indicate that conservative smoothing eliminates the instabilities in S.P.H. computations which artificial viscosities cannot. Questions were raised as to whether conservative smoothing might smear solutions more than artificial viscosity. Conservative smoothing, properly used, can produce more accurate solutions than the von Neumann-Richtmyer-Landshoff artificial viscosity which has been the standard for many years. The authors illustrate this using the vNR scheme on a test problem with known exact solution involving a shock collision in an ideal gas. They show that the norms of the errors with conservative smoothing are significantly smaller than the norms of the errors with artificial viscosity.
Pseudo Algebraically Closed Extensions
NASA Astrophysics Data System (ADS)
Bary-Soroker, Lior
2009-07-01
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
Anomalous - viscosity current drive
Stix, Thomas H.; Ono, Masayuki
1988-01-01
An apparatus and method for maintaining a steady-state current in a toroidal magnetically confined plasma. An electric current is generated in an edge region at or near the outermost good magnetic surface of the toroidal plasma. The edge current is generated in a direction parallel to the flow of current in the main plasma and such that its current density is greater than the average density of the main plasma current. The current flow in the edge region is maintained in a direction parallel to the main current for a period of one or two of its characteristic decay times. Current from the edge region will penetrate radially into the plasma and augment the main plasma current through the mechanism of anomalous viscosity. In another aspect of the invention, current flow driven between a cathode and an anode is used to establish a start-up plasma current. The plasma-current channel is magnetically detached from the electrodes, leaving a plasma magnetically insulated from contact with any material obstructions including the cathode and anode.
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Scale-Similar Models for Large-Eddy Simulations
NASA Technical Reports Server (NTRS)
Sarghini, F.
1999-01-01
Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.
NASA Astrophysics Data System (ADS)
Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.
2016-02-01
A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper
ERIC Educational Resources Information Center
Benjamin, Carl; And Others
Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
ZBLAN Viscosity Instrumentation
NASA Technical Reports Server (NTRS)
Kaukler, William
2001-01-01
The past year's contribution from Dr. Kaukler's experimental effort consists of these 5 parts: a) Construction and proof-of-concept testing of a novel shearing plate viscometer designed to produce small shear rates and operate at elevated temperatures; b) Preparing nonlinear polymeric materials to serve as standards of nonlinear Theological behavior; c) Measurements and evaluation of above materials for nonlinear rheometric behavior at room temperature using commercial spinning cone and plate viscometers available in the lab; d) Preparing specimens from various forms of pitch for quantitative comparative testing in a Dynamic Mechanical Analyzer, Thermal Mechanical Analyzer; and Archeological Analyzer; e) Arranging to have sets of pitch specimens tested using the various instruments listed above, from different manufacturers, to form a baseline of the viscosity variation with temperature using the different test modes offered by these instruments by compiling the data collected from the various test results. Our focus in this project is the shear thinning behavior of ZBLAN glass over a wide range of temperature. Experimentally, there are no standard techniques to perform such measurements on glasses, particularly at elevated temperatures. Literature reviews to date have shown that shear thinning in certain glasses appears to occur, but no data is available for ZBLAN glass. The best techniques to find shear thinning behavior require the application of very low rates of shear. In addition, because the onset of the thinning behavior occurs at an unknown elevated temperature, the instruments used in this study must provide controlled low rates of shear and do so for temperatures approaching 600 C. In this regard, a novel shearing parallel plate viscometer was designed and a prototype built and tested.
Viscosity Measurement for Tellurium Melt
NASA Technical Reports Server (NTRS)
Lin, Bochuan; Li, Chao; Ban, Heng; Scripa, Rosalia N.; Su, Ching-Hua; Lehoczky, Sandor L.
2006-01-01
The viscosity of high temperature Te melt was measured using a new technique in which a rotating magnetic field was applied to the melt sealed in a suspended ampoule, and the torque exerted by rotating melt flow on the ampoule wall was measured. Governing equations for the coupled melt flow and ampoule torsional oscillation were solved, and the viscosity was extracted from the experimental data by numerical fitting. The computational result showed good agreement with experimental data. The melt velocity transient initiated by the rotating magnetic field reached a stable condition quickly, allowing the viscosity and electrical conductivity of the melt to be determined in a short period.
Critical Viscosity of Xenon investigators
NASA Technical Reports Server (NTRS)
2001-01-01
Dr. Dr. Robert F. Berg (right), principal investigator and Dr. Micheal R. Moldover (left), co-investigator, for the Critical Viscosity of Xenon (CVX/CVX-2) experiment. They are with the National Institutes of Standards and Technology, Gaithersburg, MD. The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. Although it does not easily combine with other chemicals, its viscosity at the critical point can be used as a model for a range of chemicals.
Fluid Merging Viscosity Measurement (FMVM)
NASA Technical Reports Server (NTRS)
2004-01-01
Astronaut Mike Fincke places droplets of honey onto the strings for the Fluid Merging Viscosity Measurement (FMVM) investigation onboard the International Space Station (ISS). The FMVM experiment measures the time it takes for two individual highly viscous fluid droplets to coalesce or merge into one droplet. Different fluids and droplet size combinations were tested in the series of experiments. By using the microgravity environment, researchers can measure the viscosity or 'thickness' of fluids without the influence of containers and gravity using this new technique. Understanding viscosity could help scientists understand industrially important materials such as paints, emulsions, polymer melts and even foams used to produce pharmaceutical, food, and cosmetic products.
Eddy current scanning at Fermilab
Boffo, C.; Bauer, P.; Foley, M.; Brinkmann, A.; Ozelis, J.; /Jefferson Lab
2005-07-01
In the framework of SRF cavity development, Fermilab is creating the infrastructure needed for the characterization of the material used in the cavity fabrication. An important step in the characterization of ''as received'' niobium sheets is the eddy current scanning. Eddy current scanning is a non-destructive technique first adopted and further developed by DESY with the purpose of checking the cavity material for sub-surface defects and inclusions. Fermilab has received and further upgraded a commercial eddy current scanner previously used for the SNS project. The upgrading process included developing new filtering software. This scanner is now used daily to scan the niobium sheets for the Fermilab third harmonic and transverse deflecting cavities. This paper gives a status report on the scanning results obtained so far, including a discussion of the typology of signals being detected. We also report on the efforts to calibrate this scanner, a work conducted in collaboration with DESY.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Viscosity Depressants for Coal Liquefaction
NASA Technical Reports Server (NTRS)
Kalfayan, S. H.
1983-01-01
Proposed process modification incorporates viscosity depressants to prevent coal from solidifying during liquefaction. Depressants reduce amount of heat needed to liquefy coal. Possible depressants are metallic soaps, such as stearate, and amides, such as stearamide and dimer acid amides.
Dynamic Model of Mesoscale Eddies
NASA Astrophysics Data System (ADS)
Dubovikov, Mikhail S.
2003-04-01
Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys.B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys.12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV
Expert system for analyzing eddy current measurements
Levy, Arthur J.; Oppenlander, Jane E.; Brudnoy, David M.; Englund, James M.; Loomis, Kent C.
1994-01-01
A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits DODGER to analyze eddy current data intelligently, and obviate operator uncertainty by analyzing the data in a uniform and consistent manner.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Eddy current thickness measurement apparatus
Rosen, Gary J.; Sinclair, Frank; Soskov, Alexander; Buff, James S.
2015-06-16
A sheet of a material is disposed in a melt of the material. The sheet is formed using a cooling plate in one instance. An exciting coil and sensing coil are positioned downstream of the cooling plate. The exciting coil and sensing coil use eddy currents to determine a thickness of the solid sheet on top of the melt.
Inexpensive Eddy-Current Standard
NASA Technical Reports Server (NTRS)
Berry, Robert F., Jr.
1985-01-01
Radial crack replicas serve as evaluation standards. Technique entails intimately joining two pieces of appropriate aluminum alloy stock and centering drilled hole through and along interface. Bore surface of hole presents two vertical stock interface lines 180 degrees apart. These lines serve as radial crack defect replicas during eddy-current technique setup and verification.
NASA Astrophysics Data System (ADS)
Carper, Matthew A.; Porté-Agel, Fernando
2008-04-01
The ability of subfilter-scale (SFS) models to reproduce the statistical properties of SFS stresses and energy transfers over heterogeneous surface roughness is key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. In this study, several SFS models are evaluated a priori using experimental data acquired downwind of a rough-to-smooth transition in a wind tunnel. The SFS models studied include the eddy-viscosity, similarity, non-linear and a mixed model consisting of a combination of the eddy-viscosity and non-linear models. The dynamic eddy-viscosity model is also evaluated. The experimental data consist of vertical and horizontal planes of high-spatial-resolution velocity fields measured using particle image velocimetry. These velocity fields are spatially filtered and used to calculate SFS stresses and SFS transfer rates of resolved kinetic energy. Coefficients for each SFS model are calculated by matching the measured and modelled SFS energy transfer rates. For the eddy-viscosity model, the Smagorinsky coefficient is also evaluated using a dynamic procedure. The model coefficients are found to be scale dependent when the filter scales are larger than the vertical measurement height and fall into the production subrange of the turbulence where the flow scales are anisotropic. Near the surface, the Smagorinsky coefficient is also found to decrease with distance downwind from the transition, in response to the increase in mean shear as the flow adjusts to the smooth surface. In a priori tests, the ability of each model to reproduce statistical properties of the SFS stress is assessed. While the eddy-viscosity model has low spatial correlation with the measured stress, it predicts mean stresses with the same accuracy as the other models. However, the deficiency of the eddy-viscosity model is apparent in the underestimation of the standard deviation of the SFS stresses and the inability to predict transfers of kinetic energy from
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
NASA Astrophysics Data System (ADS)
Borisov, Sergey; Nof, Doron
The question of how deep ocean eddies can cross the equator is addressed with the aid of analytical and numerical models. We focus on the possibility that deep ocean (lens-like) eddies can cross the equator via deep cross equatorial channels on the ocean floor. We first examine the behavior of solid balls (i.e., free particles) in a meridional parabolic channel on a plane. Such balls are subject to similar topographical forcing and inertial forces that a lens is subject to, except that pressure forces and friction are absent. We examine both single isolated balls and a "cloud" of (noninteractive) balls. In general, the balls' trajectories have a chaotic character; a fraction of the cloud crosses the equator and ends up in the northern hemisphere, and a fraction is left behind. More realistic numerical experiments (with a fully nonlinear reduced-gravity isopycnic model of the Bleck and Boudra type) show similar behavior. In all cases the equator acts as an "eddy smasher" in the sense that it breaks the lens into at least two parts, one crosses the equator and ends up in the northern hemisphere, and the other is left behind. Here, however, the system is not chaotic. Despite the obvious differences between clouds of balls and eddies, there is a remarkable similarity between the percentage of balls that penetrate into the opposite hemisphere and the percentage of eddies' mass that ends up in the other hemisphere. This suggests that the geometry of the channel and the presence of the equator determine how the fluid will be partitioned among the two hemispheres.
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.
Second-Order Algebraic Theories
NASA Astrophysics Data System (ADS)
Fiore, Marcelo; Mahmoud, Ola
Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
Large eddy simulations of laminar separation bubble
NASA Astrophysics Data System (ADS)
Cadieux, Francois
The flow over blades and airfoils at moderate angles of attack and Reynolds numbers ranging from ten thousand to a few hundred thousands undergoes separation due to the adverse pressure gradient generated by surface curvature. In many cases, the separated shear layer then transitions to turbulence and reattaches, closing off a recirculation region -- the laminar separation bubble. To avoid body-fitted mesh generation problems and numerical issues, an equivalent problem for flow over a flat plate is formulated by imposing boundary conditions that lead to a pressure distribution and Reynolds number that are similar to those on airfoils. Spalart & Strelet (2000) tested a number of Reynolds-averaged Navier-Stokes (RANS) turbulence models for a laminar separation bubble flow over a flat plate. Although results with the Spalart-Allmaras turbulence model were encouraging, none of the turbulence models tested reliably recovered time-averaged direct numerical simulation (DNS) results. The purpose of this work is to assess whether large eddy simulation (LES) can more accurately and reliably recover DNS results using drastically reduced resolution -- on the order of 1% of DNS resolution which is commonly achievable for LES of turbulent channel flows. LES of a laminar separation bubble flow over a flat plate are performed using a compressible sixth-order finite-difference code and two incompressible pseudo-spectral Navier-Stokes solvers at resolutions corresponding to approximately 3% and 1% of the chosen DNS benchmark by Spalart & Strelet (2000). The finite-difference solver is found to be dissipative due to the use of a stability-enhancing filter. Its numerical dissipation is quantified and found to be comparable to the average eddy viscosity of the dynamic Smagorinsky model, making it difficult to separate the effects of filtering versus those of explicit subgrid-scale modeling. The negligible numerical dissipation of the pseudo-spectral solvers allows an unambiguous
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Viscosities of aqueous blended amines
Hsu, C.H.; Li, M.H.
1997-07-01
Solutions of alkanolamines are an industrially important class of compounds used in the natural gas, oil refineries, petroleum chemical plants, and synthetic ammonia industries for the removal of acidic components like CO{sub 2} and H{sub 2}S from gas streams. The viscosities of aqueous mixtures of diethanolamine (DEA) + N-methyldiethanolamine (MDEA), DEA + 2-amino-2-methyl-1-propanol (AMP), and monoethanolamine (MEA) + 2-piperidineethanol (2-PE) were measured from 30 C to 80 C. A Redlich-Kister equation for the viscosity deviation was applied to represent the viscosity. On the basis of the available viscosity data for five ternary systems, MEA + MDEA + H{sub 2}O, MEA + AMP + H{sub 2}O, DEA + MDEA + H{sub 2}O, DEA + AMP + H{sub 2}O, and MEA + 2-PE + H{sub 2}O, a generalized set of binary parameters were determined. For the viscosity calculation of the systems tested, the overall average absolute percent deviation is about 1.0% for a total of 499 data points.
Transient eddies in the MACDA Mars reanalysis
NASA Astrophysics Data System (ADS)
Mooring, Todd A.; Wilson, R. John
2015-10-01
We present a survey of the transient eddy activity in the Mars Analysis Correction Data Assimilation (MACDA) reanalysis. The spatial structure and propagation characteristics of the eddies are emphasized. Band-pass-filtered variance and covariance fields are found to be zonally modulated, indicating a longitude dependence of the typical amplitudes of Martian transient eddies. Considerable repeatability of the eddy field spatial structures is found across Mars years, including a roughly wave number 3 pattern of low-level eddy meridional temperature transport (v'T'
2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
NASA Astrophysics Data System (ADS)
Ayupov, Shavkat; Kudaybergenov, Karimbergen
2016-03-01
The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.
Plethystic algebras and vector symmetric functions.
Rota, G C; Stein, J A
1994-01-01
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504
Algebra and Algebraic Thinking in School Math: 70th YB
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
Abstract Algebra to Secondary School Algebra: Building Bridges
ERIC Educational Resources Information Center
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
electromagnetics, eddy current, computer codes
2002-03-12
TORO Version 4 is designed for finite element analysis of steady, transient and time-harmonic, multi-dimensional, quasi-static problems in electromagnetics. The code allows simulation of electrostatic fields, steady current flows, magnetostatics and eddy current problems in plane or axisymmetric, two-dimensional geometries. TORO is easily coupled to heat conduction and solid mechanics codes to allow multi-physics simulations to be performed.
Mesoscale Eddy - Internal Wave Coupling and Closure of the Thermocline Circulation
NASA Astrophysics Data System (ADS)
Polzin, K. L.
2006-12-01
The standard dynamical paradigm for oceanic dynamics is to consider the stratified interior as an ideal fluid and place all dissipative processes in either the bottom boundary layer or associate them with eddy/mixed layer interactions. This conceptual framework is consistent with an absence of mean interior potential vorticity gradients. On the other hand, background potential vorticity gradients are clearly documented in hydrographic data, e.g. [1]. Moreover, current meter data [2] also document the presence of downgradient eddy fluxes of potential vorticity. Thus we arrive at an essential conundrum: what is the frictional or diabatic process that permits the material modification of potential vorticity within the stratified oceanic interior associated with the downgradient fluxes? It is clear that diabatic processes are far too weak. A case will be made here that a coupling between mesoscale eddies and the internal wavefield acts as a frictional process. The case to be presented will focus on the interpretation of observations. These include current meter array data obtained as part of the POLYMODE Local Dynamics Experiment (LDE). [3] found correlations between internal wave momentum fluxes (stresses) and eddy rate of strain estimates that they interpreted in terms of a horizontal viscosity ν_h=200-400 m2 s-1. A revised estimate of this horizontal viscosity (ν_h=50 m2 s-1) and a vertical viscosity (ν_v=3×10-3 m2 s-1) estimate will be presented. Viscosity coefficients of this magnitude indicate that transfers of energy, momentum and potential vorticity between internal waves and mesoscale eddies are a significant part of the eddy energy^{[4]} and eddy enstrophy (potential vorticity squared) budgets. Finally, an attempt will be made to relate such coupling coefficients to recent satellite altimetry based estimates of mesoscale eddy kinetic energy cascades^{[5]} (see also Scott et al., this session), which, according to a preliminary numerical study (Arbic et al
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.
A Programmed Course in Algebra.
ERIC Educational Resources Information Center
Mewborn, Ancel C.; Hively, Wells II
This programed textbook consists of short sections of text interspersed with questions designed to aid the student in understanding the material. The course is designed to increase the student's understanding of some of the basic ideas of algebra. Some general experience and manipulative skill with respect to high school algebra is assumed.…
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
Gamow functionals on operator algebras
NASA Astrophysics Data System (ADS)
Castagnino, M.; Gadella, M.; Betán, R. Id; Laura, R.
2001-11-01
We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
Elementary maps on nest algebras
NASA Astrophysics Data System (ADS)
Li, Pengtong
2006-08-01
Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
Plasma viscosity in spherical ICF implosion simulations
NASA Astrophysics Data System (ADS)
Vold, E.; Joglekar, A.; Ortega, M.; Moll, R.; Fenn, D.; Molvig, K.
2016-05-01
Inertial confinement fusion (ICF) hydrodynamic codes often ignore the effects of viscosity though recent research indicates plasma viscosity and mixing by classical transport processes may have a substantial impact on implosion dynamics. A Lagrangian hydrodynamic code in one-dimensional spherical geometry with plasma viscosity and mass transport, and including a three temperature model for ions, electrons, and radiation treated in a gray radiation diffusion approximation, is used to study differences between ICF implosions with and without plasma viscosity and to examine the role of artificial viscosity in a Lagrangian implosion simulation. It was found that plasma viscosity has substantial impacts on ICF shock dynamics characterized by shock burn timing, maximum burn temperatures, fuel compression, and time history of neutron production rates. Plasma viscosity reduces the need for artificial viscosity to maintain numerical stability in the Lagrangian formulation and this study suggests that artificial viscosity may provide an unphysical stability in implosion simulations.
Anomalous-viscosity current drive
Stix, T.H.; Ono, M.
1986-04-25
The present invention relates to a method and apparatus for maintaining a steady-state current for magnetically confining the plasma in a toroidal magnetic confinement device using anomalous viscosity current drive. A second aspect of this invention relates to an apparatus and method for the start-up of a magnetically confined toroidal plasma.
Large eddy simulation of turbulent channel flow: ILLIAC 4 calculation
NASA Technical Reports Server (NTRS)
Kim, J.; Moin, P.
1979-01-01
The three-dimensional time dependent equations of motion were numerically integrated for fully-developed turbulent channel flow. A large scale flow field was obtained directly from the solution of these equations, and small scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC 4 computer. The computed flow patterns show that the wall layer consists of coherent structures of low speed and high speed streaks alternating in the spanwise direction. These structures were absent in the regions away from the wall. Hot spots, small localized regions of very large turbulent shear stress, were frequently observed. The profiles of the pressure velocity-gradient correlations show a significant transfer of energy from the normal to the spanwise component of turbulent kinetic energy in the immediate neighborhood of the wall ('the splatting effect').
Models for silicate melt viscosity
NASA Astrophysics Data System (ADS)
Giordano, D.; Russell, K.; Moretti, R.; Mangiacapra, A.; Potuzak, M.; Romano, C.; Dingwell, D. B.
2004-12-01
The prediction of viscosity in silicate liquids, over the range of temperatures and compositions encountered in nature, remains one of the most challenging and elusive goals in Earth Sciences. Recent work has demonstrated that there are now sufficient experimental measurements of melt viscosity to create new viscosity models to replace previous Arrhenian models [1],[2] and extend the compositional range of more recent non-Arrhenian models [3]. Most recently, [4] have developed an empirical strategy for accurately predicting viscosities over a very wide range of anhydrous silicate melt compositions (e.g., rhyolite to basanite). Future models that improve upon this work, will probably extend the composition range of the model to consider, at least, H2O and other volatile components and may utilize a compositional basis that reflects melt structure. In preparation for the next generation model, we explore the attributes of the three most common equations that could be used to model the non-Arrhenian viscosity of multicomponent silicate melts. The equations for the non-Arrhenian temperature dependence of viscosity (η ) include: a) Vogel-Fulcher-Tammann (VFT): log η = A + B/(T - C) b) Adam and Gibbs (AG): log η = A + B/[T log (T/C)], and c) Avramov (Av): log η = A + [B/T]α We use an experimental database of approximately 900 high-quality viscosity measurements on silicate melts to test the ability of each equation to capture the experimental data. These equations have different merits [5]. VFT is purely empirical in nature. The AG model has a quasi-theoretical basis that links macroscopic transport properties directly to thermodynamic properties via the configurational entropy. Lastly, the model proposed by Avramov adopts a form designed to relate the fit parameter (α ) to the fragility of the melt. [1] Shaw, H.R., 1972. Am J Science, 272, 438-475. [2] Bottinga Y. and Weill, D., 1972. Am J Science, 272, 438-475. [3] Hess, K.U. and Dingwell, D.B, 1996, Am Min, 81
Capillary blood viscosity in microcirculation.
Cortinovis, A; Crippa, A; Cavalli, R; Corti, M; Cattaneo, L
2006-01-01
As known, at the arteriolar level there is the highest resistance to the flow due to the section and to the velocity with an average pressure fall of 50 mmHg (from 85 to 35 mmHg). This resistance is expressed in sec(-1) by the ratio W/2r. This ratio is very high with an average value of 332 sec(-1) and viscosity at this high shear-rate is negligible. At the capillary level the pressure fall is 11.5 mmHg but the vascular resistance W/2r is much lower, on average 32 sec(-1). We can say that if a resistance of 333 sec(-1) corresponds with a pressure fall of 50 mmHg, then a resistance of 32 sec(-1) should correspond with a pressure fall of 4.8 mmHg. The highest pressure fall is due to another kind of resistance which we can define as "Capillary Blood Viscosity" because it depends on the rheological and structural characteristics of the blood. Our instrument reproduces the structure of the capillary district in an experimental model and measures the General Blood Viscosity (GBV) and the Capillary Blood Viscosity (CBV) at the same shear-rate and in particular at the low shear-rate when in non-Newtonian fluids the highest increase in viscosity appears. Consequently, at the capillary, viscosity is dominant with respect to the other geometric and physical resistances. Moreover, the percentage ratio between the GBV and the CBV gives a physical measure of erythrocyte deformability. Knowing viscosity at shear-rate present in the circulatory system, we can obtain the size of RBCs aggregates in the different circulatory districts and their characteristics expressed like "aggregation bond". Changes in CBV are the only possibility in clinical practice to improve the circulatory flow in the capillary district because it is not sure that changes in the arteriolar section can improve the capillary flow or rather open arterio-venous anastomosis. Moreover, in the systemic circulation the aggregate size allows us to point out the phenomenon of cell adhesion because the presence of
Thermodynamics. [algebraic structure
NASA Technical Reports Server (NTRS)
Zeleznik, F. J.
1976-01-01
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
The effect of sweeteners on perceived viscosity.
Theunissen, M J; Kroeze, J H
1995-08-01
Two different sweeteners, sucrose and aspartame, were matched in perceived sweetness intensity. These solutions were thickened with carboxymethylcellulose to six different viscosity levels. Sucrose and aspartame appeared to decrease perceived viscosity of the solutions at a specific sweetener concentration, at all viscosity levels. However, in a second similar experiment with three viscosity levels and seven sucrose concentrations no effect of sucrose concentration on perceived viscosity was found. Reasons for these conflicting results are discussed. No definite conclusions about the effect of sweeteners on perceived viscosity can as yet be drawn.
Transient Eddies in the UCLA GCM
NASA Technical Reports Server (NTRS)
White, G. H.
1985-01-01
The simulation of transient eddies in the nine level UCLA general circulation model (GCM) was examined and compared to observations, with emphasis on the Northern Hemisphere winter. Qualitatively, the UCLA GCM reproduces many features of the observed circulation and the relationship between the time mean flow and transient eddies; however, the magnitudes of transient eddies in the UCLA GCM, particularly at frequencies lower than those associated with baroclinic instability, appear to be much less than those observed. The pattern of low level transient eddy heat fluxes were similar to observations and acted to dissipate the low level seasonal mean temperature field. The simulated transient eddy kinetic energy at 300 mb is given for eddies of all time scales shorter than a season.
Minimum-dissipation models for large-eddy simulation
NASA Astrophysics Data System (ADS)
Bae, Hyunji Jane; Rozema, Wybe; Moin, Parviz; Verstappen, Roel
2015-11-01
Minimum-dissipation eddy-viscosity models are a class of subgrid scale models for LES that give the minimum eddy dissipation required to dissipate the energy of subgrid scales. The QR minimum-dissipation model [Verstappen, J. Sci. Comp., 2011] gives good results in simulations of decaying grid turbulence carried out on an isotropic grid. In particular, due to the minimum dissipation property of the model, the predicted energy spectra are in very good agreement with the DNS results up to the cut-off wave number unlike other methods. However, its results on anisotropic grids are often unsatisfactory because the model does not properly incorporate the grid anisotropy. We propose the anisotropic minimum-dissipation (AMD) model [Rozema et al., submitted for publication, 2015], a minimum-dissipation model that generalizes the QR model to anisotropic grids. The AMD model is more cost effective than the dynamic Smagorinsky model, appropriately switches off in laminar and transitional flow on anisotropic grids, and its subgrid scale model is consistent with the theoretic subgrid tensor. Experiments show that the AMD model is as accurate as the dynamic Smagorinsky model and Vreman model in simulations of isotropic turbulence, temporal mixing layer, and turbulent channel flow. H. J. Bae acknowledges support from SGF. W. Rozema and R. Verstappen acknowledge sponsoring by NWO for the use of supercomputing facilities and the financial support to attend the CTR SP 2014.
Large eddy simulation of mechanical mixing in anaerobic digesters.
Wu, Binxin
2012-03-01
A comprehensive study of anaerobic digestion requires an advanced turbulence model technique to accurately predict mixing flow patterns because the digestion process that involves mass transfer between anaerobes and their substrates is primarily dependent on detailed information about the fine structure of turbulence in the digesters. This study presents a large eddy simulation (LES) of mechanical agitation of non-Newtonian fluids in anaerobic digesters, in which the sliding mesh method is used to characterize the impeller rotation. The three subgrid scale (SGS) models investigated are: (i) Smagorinsky-Lilly model, (ii) wall-adapting local eddy-viscosity model, and (iii) kinetic energy transport (KET) model. The simulation results show that the three SGS models produce very similar flow fields. A comparison of the simulated and measured axial velocities indicates that the LES profile shapes are in general agreement with the experimental data but they differ markedly in velocity magnitudes. A check of impeller power and flow numbers demonstrates that all the SGS models give excellent predictions, with the KET model performing the best. Moreover, the performance of six Reynolds-averaged Navier-Stokes turbulence models are assessed and compared with the LES results. PMID:22038563
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
Observations of Three Dimensional Surfzone Eddies
NASA Astrophysics Data System (ADS)
Arnold, J. L.; Henderson, S. M.; Solovitz, S.
2012-12-01
We present measurements of the vertical structure of surfzone eddies (frequencies 0.0005-0.01 Hz). From 16 Oct to 07 Nov 2011, an array of 12 Acoustic Doppler Profilers (ADPs) measured velocity profiles in 0-6 m water depth on a natural beach near Duck, North Carolina. We will analyze and describe vertical variations in eddy velocity. Vertical variability of eddy magnitude will be presented, as well as coherence and phase between near-surface and near-bed velocities. We aim to shed light on the causes and consequences of vertical eddy variability, which has recently been recognized in observations, but is not yet well understood.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Constraint algebra in bigravity
NASA Astrophysics Data System (ADS)
Soloviev, V. O.
2015-07-01
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Readiness and Preparation for Beginning Algebra.
ERIC Educational Resources Information Center
Rotman, Jack W.
Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
Two-parameter twisted quantum affine algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Zhang, Honglian
2016-09-01
We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.
Transient eddy current flow metering
NASA Astrophysics Data System (ADS)
Forbriger, J.; Stefani, F.
2015-10-01
Measuring local velocities or entire flow rates in liquid metals or semiconductor melts is a notorious problem in many industrial applications, including metal casting and silicon crystal growth. We present a new variant of an old technique which relies on the continuous tracking of a flow-advected transient eddy current that is induced by a pulsed external magnetic field. This calibration-free method is validated by applying it to the velocity of a spinning disk made of aluminum. First tests at a rig with a flow of liquid GaInSn are also presented.
Film cooling from inclined cylindrical holes using large eddy simulations
NASA Astrophysics Data System (ADS)
Peet, Yulia V.
2006-12-01
The goal of the present study is to investigate numerically the physics of the flow, which occurs during the film cooling from inclined cylindrical holes, Film cooling is a technique used in gas turbine industry to reduce heat fluxes to the turbine blade surface. Large Eddy Simulation (LES) is performed modeling a realistic film cooling configuration, which consists of a large stagnation-type reservoir, feeding an array of discrete cooling holes (film holes) flowing into a flat plate turbulent boundary layer. Special computational methodology is developed for this problem, involving coupled simulations using multiple computational codes. A fully compressible LES code is used in the area above the flat plate, while a low Mach number LES code is employed in the plenum and film holes. The motivation for using different codes comes from the essential difference in the nature of the flow in these different regions. Flowfield is analyzed inside the plenum, film hole and a crossflow region. Flow inside the plenum is stagnating, except for the region close to the exit, where it accelerates rapidly to turn into the hole. The sharp radius of turning at the trailing edge of the plenum pipe connection causes the flow to separate from the downstream wall of the film hole. After coolant injection occurs, a complex flowfield is formed consisting of coherent vortical structures responsible for bringing hot crossflow fluid in contact with the walls of either the film hole or the blade, thus reducing cooling protection. Mean velocity and turbulent statistics are compared to experimental measurements, yielding good agreement for the mean flowfield and satisfactory agreement for the turbulence quantities. LES results are used to assess the applicability of basic assumptions of conventional eddy viscosity turbulence models used with Reynolds-averaged (RANS) approach, namely the isotropy of an eddy viscosity and thermal diffusivity. It is shown here that these assumptions do not hold
Viscosity Index Improvers and Thickeners
NASA Astrophysics Data System (ADS)
Stambaugh, R. L.; Kinker, B. G.
The viscosity index of an oil or an oil formulation is an important physical parameter. Viscosity index improvers, VIIs, are comprised of five main classes of polymers: polymethylmethacrylates (PMAs), olefin copolymers (OCPs), hydrogenated poly(styrene-co-butadiene or isoprene) (HSD/SIP/HRIs), esterified polystyrene-co-maleic anhydride (SPEs) and a combination of PMA/OCP systems. The chemistry, manufacture, dispersancy and utility of each class are described. The comparative functions, properties, thickening ability, dispersancy and degradation of VIIs are discussed. Permanent and temporary shear thinning of VII-thickened formulations are described and compared. The end-use performance and choice of VI improvers is discussed in terms of low- and high-temperature viscosities, journal bearing oil film thickness, fuel economy, oil consumption, high-temperature pumping efficiency and deposit control. Discussion of future developments concludes that VI improvers will evolve to meet new challenges of increased thermal-oxidative degradation from increased engine operating temperatures, different base stocks of either synthetic base oils or vegetable oil-based, together with alcohol- or vegetable oil-based fuels. VI improvers must also evolve to deal with higher levels of fuel dilution and new types of sludge and also enhanced low-temperature requirements.
Density and viscosity of lipids under pressure
Technology Transfer Automated Retrieval System (TEKTRAN)
There is a lack of data for the viscosity of lipids under pressure. The current report is a part of the effort to fill this gap. The viscosity, density, and elastohydrodynamic film thicknesses of vegetable oil (HOSuO) were investigated. Pressure–viscosity coefficients (PVC) of HOSuO at different tem...
Improved Imaging With Laser-Induced Eddy Currents
NASA Technical Reports Server (NTRS)
Chern, Engmin J.
1993-01-01
System tests specimen of material nondestructively by laser-induced eddy-current imaging improved by changing method of processing of eddy-current signal. Changes in impedance of eddy-current coil measured in absolute instead of relative units.
Cartooning in Algebra and Calculus
ERIC Educational Resources Information Center
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
Eddy-Current Inspection of Ball Bearings
NASA Technical Reports Server (NTRS)
Bankston, B.
1985-01-01
Custom eddy-current probe locates surface anomalies. Low friction air cushion within cone allows ball to roll easily. Eddy current probe reliably detects surface and near-surface cracks, voids, and material anomalies in bearing balls or other spherical objects. Defects in ball surface detected by probe displayed on CRT and recorded on strip-chart recorder.
Observed deep energetic eddies by seamount wake
NASA Astrophysics Data System (ADS)
Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui
2015-11-01
Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport.
Observed deep energetic eddies by seamount wake
Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui
2015-01-01
Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport. PMID:26617343
Observed deep energetic eddies by seamount wake.
Chen, Gengxin; Wang, Dongxiao; Dong, Changming; Zu, Tingting; Xue, Huijie; Shu, Yeqiang; Chu, Xiaoqing; Qi, Yiquan; Chen, Hui
2015-01-01
Despite numerous surface eddies are observed in the ocean, deep eddies (a type of eddies which have no footprints at the sea surface) are much less reported in the literature due to the scarcity of their observation. In this letter, from recently collected current and temperature data by mooring arrays, a deep energetic and baroclinic eddy is detected in the northwestern South China Sea (SCS) with its intensity, size, polarity and structure being characterized. It remarkably deepens isotherm at deep layers by the amplitude of ~120 m and induces a maximal velocity amplitude about 0.18 m/s, which is far larger than the median velocity (0.02 m/s). The deep eddy is generated in a wake when a steering flow in the upper layer passes a seamount, induced by a surface cyclonic eddy. More observations suggest that the deep eddy should not be an episode in the area. Deep eddies significantly increase the velocity intensity and enhance the mixing in the deep ocean, also have potential implication for deep-sea sediments transport.
Exploring Eddy-Covariance Measurements Using a Spatial Approach: The Eddy Matrix
NASA Astrophysics Data System (ADS)
Engelmann, Christian; Bernhofer, Christian
2016-10-01
Taylor's frozen turbulence hypothesis states that "standard" eddy-covariance measurements of fluxes at a fixed location can replace a spatial ensemble of instantaneous values at multiple locations. For testing this hypothesis, a unique turbulence measurement set-up was used for two measurement campaigns over desert (Namibia) and grassland (Germany) in 2012. This "Eddy Matrix" combined nine ultrasonic anemometer-thermometers and 17 thermocouples in a 10 m × 10 m regular grid with 2.5-m grid distance. The instantaneous buoyancy flux derived from the spatial eddy covariance of the Eddy Matrix was highly variable in time (from -0.3 to 1 m K s^{-1}). However, the 10-min average reflected 83 % of the reference eddy-covariance flux with a good correlation. By introducing a combined eddy-covariance method (the spatial eddy covariance plus the additional flux of the temporal eddy covariance of the spatial mean values), the mean flux increases by 9 % relative to the eddy-covariance reference. Considering the typical underestimation of fluxes by the standard eddy-covariance method, this is seen as an improvement. Within the limits of the Eddy Matrix, Taylor's hypothesis is supported by the results.
On the effective viscosity of nanosuspensions
NASA Astrophysics Data System (ADS)
Rudyak, V. Ya.; Belkin, A. A.; Egorov, V. V.
2009-08-01
The effective viscosity of nanosuspensions is simulated using the molecular dynamics method. It is found that viscosity is controlled not only by the volume concentration of nanoparticles, by also by their mass and diameter. The viscosity of even strongly rarefied nanosuspensions (with a low concentration of nanoparticles) cannot be described by the Einstein relation. This means that the mechanism responsible for the increase in the viscosity of the medium is not of hydrodynamic origin. It is shown that the formation of viscosity of nanosuspensions is associated to a considerable extent with nonequilibrium microfluctuations of density and velocity of the carrier medium, which are induced by the motion of nanoparticles.
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
Sjaardema, G.; Gilkey, A.; Smith, M.; Forsythe, C.
2005-04-11
The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.
Wind changes above warm Agulhas Current eddies
NASA Astrophysics Data System (ADS)
Rouault, M.; Verley, P.; Backeberg, B.
2016-04-01
Sea surface temperature (SST) estimated from the Advanced Microwave Scanning Radiometer E onboard the Aqua satellite and altimetry-derived sea level anomalies are used south of the Agulhas Current to identify warm-core mesoscale eddies presenting a distinct SST perturbation greater than to 1 °C to the surrounding ocean. The analysis of twice daily instantaneous charts of equivalent stability-neutral wind speed estimates from the SeaWinds scatterometer onboard the QuikScat satellite collocated with SST for six identified eddies shows stronger wind speed above the warm eddies than the surrounding water in all wind directions, if averaged over the lifespan of the eddies, as was found in previous studies. However, only half of the cases showed higher wind speeds above the eddies at the instantaneous scale; 20 % of cases had incomplete data due to partial global coverage by the scatterometer for one path. For cases where the wind is stronger above warm eddies, there is no relationship between the increase in surface wind speed and the SST perturbation, but we do find a linear relationship between the decrease in wind speed from the centre to the border of the eddy downstream and the SST perturbation. SST perturbations range from 1 to 6 °C for a mean eddy SST of 15.9 °C and mean SST perturbation of 2.65 °C. The diameter of the eddies range from 100 to 250 km. Mean background wind speed is about 12 m s-1 (mostly southwesterly to northwesterly) and ranging mainly from 4 to 16 m s-1. The mean wind increase is about 15 %, which corresponds to 1.8 m s-1. A wind speed increase of 4 to 7 m s-1 above warm eddies is not uncommon. Cases where the wind did not increase above the eddies or did not decrease downstream had higher wind speeds and occurred during a cold front associated with intense cyclonic low-pressure systems, suggesting certain synoptic conditions need to be met to allow for the development of wind speed anomalies over warm-core ocean eddies. In many cases
Intense submesoscale upwelling in anticyclonic eddies
NASA Astrophysics Data System (ADS)
Brannigan, L.
2016-04-01
Observations from around the global ocean show that enhanced biological activity can be found in anticyclonic eddies. This may mean that upwelling of nutrient-rich water occurs within the eddy, but such upwelling is not captured by models that resolve mesoscale processes. High-resolution simulations presented here show intense submesoscale upwelling from the thermocline to the mixed layer in anticyclonic eddies. The properties of the upwelling are consistent with a process known as symmetric instability. A simple limiting nutrient experiment shows that this upwelling can drive much higher biological activity in anticyclonic eddies when there is a high nutrient concentration in the thermocline. An estimate for the magnitude of upwelling associated with symmetric instability in anticyclonic eddies in the Sargasso Sea shows that it may be of comparable magnitude to other processes, though further work is required to understand the full implications for basin-scale nutrient budgets.
Large Eddy Simulation of a Turbulent Jet
NASA Technical Reports Server (NTRS)
Webb, A. T.; Mansour, Nagi N.
2001-01-01
Here we present the results of a Large Eddy Simulation of a non-buoyant jet issuing from a circular orifice in a wall, and developing in neutral surroundings. The effects of the subgrid scales on the large eddies have been modeled with the dynamic large eddy simulation model applied to the fully 3D domain in spherical coordinates. The simulation captures the unsteady motions of the large-scales within the jet as well as the laminar motions in the entrainment region surrounding the jet. The computed time-averaged statistics (mean velocity, concentration, and turbulence parameters) compare well with laboratory data without invoking an empirical entrainment coefficient as employed by line integral models. The use of the large eddy simulation technique allows examination of unsteady and inhomogeneous features such as the evolution of eddies and the details of the entrainment process.
Orientation of eddy fluxes in geostrophic turbulence.
Nadiga, B T
2008-07-28
Given its importance in parametrizing eddies, we consider the orientation of eddy flux of potential vorticity (PV) in geostrophic turbulence. We take two different points of view, a classical ensemble- or time-average point of view and a second scale decomposition point of view. A net alignment of the eddy flux of PV with the appropriate mean gradient or the large-scale gradient of PV is required. However, we find this alignment to be very weak. A key finding of our study is that in the scale decomposition approach, there is a strong correlation between the eddy flux and a nonlinear combination of resolved gradients. This strong correlation is absent in the classical decomposition. This finding points to a new model to parametrize the effects of eddies in global ocean circulation.
Unified Ultrasonic/Eddy-Current Data Acquisition
NASA Technical Reports Server (NTRS)
Chern, E. James; Butler, David W.
1993-01-01
Imaging station for detecting cracks and flaws in solid materials developed combining both ultrasonic C-scan and eddy-current imaging. Incorporation of both techniques into one system eliminates duplication of computers and of mechanical scanners; unifies acquisition, processing, and storage of data; reduces setup time for repetitious ultrasonic and eddy-current scans; and increases efficiency of system. Same mechanical scanner used to maneuver either ultrasonic or eddy-current probe over specimen and acquire point-by-point data. For ultrasonic scanning, probe linked to ultrasonic pulser/receiver circuit card, while, for eddy-current imaging, probe linked to impedance-analyzer circuit card. Both ultrasonic and eddy-current imaging subsystems share same desktop-computer controller, containing dedicated plug-in circuit boards for each.
The nature and consequences of oceanic eddies
NASA Astrophysics Data System (ADS)
McWilliams, James C.
Mesoscale eddies are everywhere in the ocean. They provide important material and dynamical fluxes for the equilibrium balances of the general circulation and climate. Eddy effects are necessary ingredients for oceanic general circulation models, whether parameterized or, as is increasingly done, explicitly resolved in the simulations. The primary characteristics of eddies are summarized in this paper, and the principal roles of eddies in the dynamics of large-scale circulation are described. Those eddy roles are the following: maintenance of boundary and equatorial currents; lateral and vertical buoyancy fluxes, isopycnal form stress, and available potential energy conversion; Reynolds stress, kinetic energy conversion, and current rectification; material dispersion and mixing; energy cascades and dissipation routes; Lagrangian mean advection; surface-layer density restratification; ventilation and subduction; stratification control; frontogenesis; topographic form stress; biological pumping and quenching; and generation of intrinsic climate variability.
Eddy current analysis in fusion devices
Turner, L.R.
1988-06-01
In magnetic fusion devices, particularly tokamaks and reversed field pinch (RFP) experiments, time-varying magnetic fields are in intimate contact with electrically conducting components of the device. Induced currents, fields, forces, and torques result. This note reviews the analysis of eddy current effects in the following systems: Interaction of a tokamak plasma with the eddy currents in the first wall, blanket, and shield (FWBS) systems; Eddy currents in a complex but two-dimensional vacuum vessel, as in TFTR, JET, and JT-60; Eddy currents in the FWBS system of a tokamak reactor, such as NET, FER, or ITER; and Eddy currents in a RFP shell. The cited studies are chosen to be illustrative, rather than exhaustive. 42 refs.
Algebraic Systems and Pushdown Automata
NASA Astrophysics Data System (ADS)
Petre, Ion; Salomaa, Arto
We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.
Low Viscosity Zone and Mantle Dynamics
NASA Astrophysics Data System (ADS)
Stein, C.; Hansen, U.
2005-12-01
We use a three-dimensional mantle convection model to explore the influence of rheological properties on variations in viscosity and mantle dynamics. In particular the interaction of a temperature-, pressure- and stress-dependent viscosity has been studied. In temperature- and stress-dependent viscosity convection, a stagnant lid mode of convection arises if the viscosity is strongly dominated by temperature. This is linked to a strong viscosity drop over the top boundary layer with little further viscosity variations with depth. An almost constant viscosity-depth profile with only a maximum at mid-depth is obtained, if the system is strongly influenced by the stress dependence. This is coupled to a mobilised surface which takes part in the convective process. A low viscosity zone (LVZ) at shallow depths and a viscosity peak at mid-depth have been obtained for the balanced combination of the temperature and stress dependence of the viscosity. The appearance of both zones correlates with the appearance of plate-like motion. Small rigid surface pieces sink into the interior. But subduction is faster than the new creation of plates leading only to an occassional occurrence of the features. Additional pressure dependence of the viscosity helps to slow down subduction speed, so that plates and the LVZ exist over long times. Further the long-wavelength flow resulting in convection with depth-dependent properties leads to extended plates and a more global LVZ.
Superparamagnetic nanoparticle-based viscosity test
NASA Astrophysics Data System (ADS)
Wu, Kai; Liu, Jinming; Wang, Yi; Ye, Clark; Feng, Yinglong; Wang, Jian-Ping
2015-08-01
Hyperviscosity syndrome is triggered by high blood viscosity in the human body. This syndrome can result in retinopathy, vertigo, coma, and other unanticipated complications. Serum viscosity is one of the important factors affecting whole blood viscosity, which is regarded as an indicator of general health. In this letter, we propose and demonstrate a Brownian relaxation-based mixing frequency method to test human serum viscosity. This method uses excitatory and detection coils and Brownian relaxation-dominated superparamagnetic nanoparticles, which are sensitive to variables of the liquid environment such as viscosity and temperature. We collect the harmonic signals produced by magnetic nanoparticles and estimate the viscosity of unknown solutions by comparison to the calibration curves. An in vitro human serum viscosity test is performed in less than 1.5 min.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
Darlington, R
1999-12-01
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.
Algebraic Flux Correction II. Compressible Euler Equations
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias
Algebraic flux correction schemes of TVD and FCT type are extended to systems of hyperbolic conservation laws. The group finite element formulation is employed for the treatment of the compressible Euler equations. An efficient algorithm is proposed for the edge-by-edge matrix assembly. A generalization of Roe's approximate Riemann solver is derived by rendering all off-diagonal matrix blocks positive semi-definite. Another usable low-order method is constructed by adding scalar artificial viscosity proportional to the spectral radius of the cumulative Roe matrix. The limiting of antidiffusive fluxes is performed using a transformation to the characteristic variables or a suitable synchronization of correction factors for the conservative ones. The outer defect correction loop is equipped with a block-diagonal preconditioner so as to decouple the discretized Euler equations and solve them in a segregated fashion. As an alternative, a strongly coupled solution strategy (global BiCGSTAB method with a block-Gauß-Seidel preconditioner) is introduced for applications which call for the use of large time steps. Various algorithmic aspects including the implementation of characteristic boundary conditions are addressed. Simulation results are presented for inviscid flows in a wide range of Mach numbers.
Critical Viscosity of Xenon team
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure (at left) that is placed inside a pressure canister. A similar canister (right) holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (not shown) of the National Institutes of Standards and Technology, Gaithersburg, MD.
Critical Viscosity of Xenon team
NASA Technical Reports Server (NTRS)
2001-01-01
The Critical Viscosity of Xenon Experiment (CVX-2) on the STS-107 Research 1 mission in 2002 will measure the viscous behavior of xenon, a heavy inert gas used in flash lamps and ion rocket engines, at its critical point. The thermostat for CVX sits inside the white cylinder on a support structure (at left) that is placed inside a pressure canister. A similar canister (right) holds the electronics and control systems. The CVX-2 arrangement is identical. The principal investigator is Dr. Robert F. Berg (left) of the National Institutes of Standards and Technology, Gaithersburg, MD.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Conformable eddy current array delivery
NASA Astrophysics Data System (ADS)
Summan, Rahul; Pierce, Gareth; Macleod, Charles; Mineo, Carmelo; Riise, Jonathan; Morozov, Maxim; Dobie, Gordon; Bolton, Gary; Raude, Angélique; Dalpé, Colombe; Braumann, Johannes
2016-02-01
The external surface of stainless steel containers used for the interim storage of nuclear material may be subject to Atmospherically Induced Stress Corrosion Cracking (AISCC). The inspection of such containers poses a significant challenge due to the large quantities involved; therefore, automating the inspection process is of considerable interest. This paper reports upon a proof-of-concept project concerning the automated NDT of a set of test containers containing artificially generated AISCCs. An Eddy current array probe with a conformable padded surface from Eddyfi was used as the NDT sensor and end effector on a KUKA KR5 arc HW robot. A kinematically valid cylindrical raster scan path was designed using the KUKA|PRC path planning software. Custom software was then written to interface measurement acquisition from the Eddyfi hardware with the motion control of the robot. Preliminary results and analysis are presented from scanning two canisters.
Rotating concave eddy current probe
Roach, Dennis P.; Walkington, Phil; Rackow, Kirk A.; Hohman, Ed
2008-04-01
A rotating concave eddy current probe for detecting fatigue cracks hidden from view underneath the head of a raised head fastener, such as a buttonhead-type rivet, used to join together structural skins, such as aluminum aircraft skins. The probe has a recessed concave dimple in its bottom surface that closely conforms to the shape of the raised head. The concave dimple holds the probe in good alignment on top of the rivet while the probe is rotated around the rivet's centerline. One or more magnetic coils are rigidly embedded within the probe's cylindrical body, which is made of a non-conducting material. This design overcomes the inspection impediment associated with widely varying conductivity in fastened joints.
A simulation of the global ocean circulation with resolved eddies
NASA Astrophysics Data System (ADS)
Semtner, Albert J.; Chervin, Robert M.
1988-12-01
A multilevel primitive-equation model has been constructed for the purpose of simulating ocean circulation on modern supercomputing architectures. The model is designed to take advantage of faster clock speeds, increased numbers of processors, and enlarged memories of machines expected to be available over the next decade. The model allows global eddy-resolving simulations to be conducted in support of the World Ocean Circulation Experiment. Furthermore, global ocean modeling is essential for proper representation of the full range of oceanic and climatic phenomena. The first such global eddy-resolving ocean calculation is reported here. A 20-year integration of a global ocean model with ½° grid spacing and 20 vertical levels has been carried out with realistic geometry and annual mean wind forcing. The temperature and salinity are constrained to Levitus gridded data above 25-m depth and below 710-m depth (on time scales of 1 month and 3 years, respectively), but the values in the main thermocline are unconstrained for the last decade of the calculation. The final years of the simulation allow the spontaneous formation of waves and eddies through the use of scale-selective viscosity and diffusion. A quasi-equilibrium state shows many realistic features of ocean circulation, including unstable separating western boundary currents, the known anomalous northward heat transport in the South Atlantic, and a global compensation for the abyssal spread of North Atlantic Deep Water via a long chain of thermocline mass transport from the tropical Pacific, through the Indonesian archipelago, across the Indian Ocean, and around the southern tip of Africa. This chain of thermocline transport is perhaps the most striking result from the model, and eddies and waves are evident along the entire 20,000-km path of the flow. The modeled Gulf Stream separates somewhat north of Cape Hatteras, produces warm- and cold-core rings, and maintains its integrity as a meadering thermal front
BRST charges for finite nonlinear algebras
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.
2010-07-01
Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.
Some Remarks on Kite Pseudo Effect Algebras
NASA Astrophysics Data System (ADS)
Dvurečenskij, Anatolij; Holland, W. Charles
2014-05-01
Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ, ρ: I→ I. Using a clever construction on the ordinal sum of ( G +) I and ( G -) I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.
Poleward migration of eddy driven jets
NASA Astrophysics Data System (ADS)
Chemke, Rei; Kaspi, Yohai
2014-05-01
There are observational evidence for a poleward migration of temporal anomalies of zonal winds in the upper troposphere. We show that such poleward migration can be due to poleward migration of eddy-driven jets; In fact, any eddy driven baroclinic jet should propagate poleward over time due to the variation of baroclinicity across the jet due to the sphericity of the planet. We demonstrate this using a high resolution idealized GCM where we examine the eddy driven jets over a wide range of rotation rates (up to 24 times the rotation rate of Earth). Unlike Earth-like rotation rates, where the eddy driven jet and the subtropical jet usually merge, at higher rotation rates the eddy driven jets are clearly separated from the subtropical jet and migrate poleward, while the subtropical jets remain in a constant latitude over time. The poleward drift is caused because measures of baroclinicity, such as Eady growth rate and supercriticality have a poleward bias due to the variation of the Coriolis parameter across the jet. This results in a poleward biased eddy momentum flux convergence relative to the mean jet, which overtime deflects the jet poleward. This is demonstrated systematically over the series of numerical simulations we present. As the rotation rate increases, and more (narrower) jets emerge the migration rate becomes smaller due to less eddy momentum flux convergence over the narrower baroclinic zones. This mechanism is consistent with eddy life cycle studies, which show the effects of sphericity on eddy propagation. In addition, we suggest scaling for the meridional scale of the jets and their spacing as function of the planetary rotation rate and latitude.
Operator product expansion algebra
Holland, Jan; Hollands, Stefan
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Eddy current technique for predicting burst pressure
Petri, Mark C.; Kupperman, David S.; Morman, James A.; Reifman, Jaques; Wei, Thomas Y. C.
2003-01-01
A signal processing technique which correlates eddy current inspection data from a tube having a critical tubing defect with a range of predicted burst pressures for the tube is provided. The method can directly correlate the raw eddy current inspection data representing the critical tubing defect with the range of burst pressures using a regression technique, preferably an artificial neural network. Alternatively, the technique deconvolves the raw eddy current inspection data into a set of undistorted signals, each of which represents a separate defect of the tube. The undistorted defect signal which represents the critical tubing defect is related to a range of burst pressures utilizing a regression technique.
Eddy current inspection of graphite fiber components
NASA Technical Reports Server (NTRS)
Workman, G. L.; Bryson, C. C.
1990-01-01
The recognition of defects in materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques. The unique capabilities of E-probes and horseshoe probes for inspecting probes for inspecting graphite fiber materials were evaluated and appear to hold great promise once the technology development matures. The initial results are described of modeling eddy current interactions with certain flaws in graphite fiber samples.
Constructing a parasupersymmetric Virasoro algebra
NASA Astrophysics Data System (ADS)
Kuwata, S.
2011-03-01
We construct a para SUSY Virasoro algebra by generalizing the ordinary fermion in SUSY Virasoro algebra (Ramond or Neveu-Schwarz algebra) to the parafermion. First, we obtain a polynomial relation (PR) between different-mode parafermion fi's by generalizing the corresponding single-mode PR to such that is invariant under the unitary transformation of fi (Green's condition). Differently from a usual context, where the Green's condition is imposed only on the defining relation of fi (degree three with respect to fi and fi†), we impose it on any degree of PR. For the case of order-two parafermion (the simplest case of para SUSY), we calculate a PR between the parasupercharge G0, the bosonic hamiltonian LB0 and parafermionic one LF0, although it is difficult to obtain a PR between G0 and the total hamiltonian L0 (= LB0 + LF0). Finally, we construct a para SUSY Virasoro algebra by generalizing L0 to the Ln's such that form a Virasoro algebra.
Viscosity dictates metabolic activity of Vibrio ruber
Borić, Maja; Danevčič, Tjaša; Stopar, David
2012-01-01
Little is known about metabolic activity of bacteria, when viscosity of their environment changes. In this work, bacterial metabolic activity in media with viscosity ranging from 0.8 to 29.4 mPas was studied. Viscosities up to 2.4 mPas did not affect metabolic activity of Vibrio ruber. On the other hand, at 29.4 mPas respiration rate and total dehydrogenase activity increased 8 and 4-fold, respectively. The activity of glucose-6-phosphate dehydrogenase (GPD) increased up to 13-fold at higher viscosities. However, intensified metabolic activity did not result in faster growth rate. Increased viscosity delayed the onset as well as the duration of biosynthesis of prodigiosin. As an adaptation to viscous environment V. ruber increased metabolic flux through the pentose phosphate pathway and reduced synthesis of a secondary metabolite. In addition, V. ruber was able to modify the viscosity of its environment. PMID:22826705
Eddy Current Testing, RQA/M1-5330.17.
ERIC Educational Resources Information Center
National Aeronautics and Space Administration, Huntsville, AL. George C. Marshall Space Flight Center.
As one in the series of classroom training handbooks, prepared by the U.S. space program, instructional material is presented in this volume concerning familiarization and orientation on eddy current testing. The subject is presented under the following headings: Introduction, Eddy Current Principles, Eddy Current Equipment, Eddy Current Methods,…
Artificial Fluid Properties for Large-Eddy Simulation of Compressible Turbulent Mixing
Cook, A W
2007-01-08
An alternative methodology is described for Large-Eddy Simulation of flows involving shocks, turbulence and mixing. In lieu of filtering the governing equations, it is postulated that the large-scale behavior of an ''LES'' fluid, i.e., a fluid with artificial properties, will be similar to that of a real fluid, provided the artificial properties obey certain constraints. The artificial properties consist of modifications to the shear viscosity, bulk viscosity, thermal conductivity and species diffusivity of a fluid. The modified transport coefficients are designed to damp out high wavenumber modes, close to the resolution limit, without corrupting lower modes. Requisite behavior of the artificial properties is discussed and results are shown for a variety of test problems, each designed to exercise different aspects of the models. When combined with a 10th-order compact scheme, the overall method exhibits excellent resolution characteristics for turbulent mixing, while capturing shocks and material interfaces in crisp fashion.
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing
NASA Astrophysics Data System (ADS)
Cook, Andrew W.
2007-05-01
An alternative methodology is described for large-eddy simulation (LES) of flows involving shocks, turbulence, and mixing. In lieu of filtering the governing equations, it is postulated that the large-scale behavior of a LES fluid, i.e., a fluid with artificial properties, will be similar to that of a real fluid, provided the artificial properties obey certain constraints. The artificial properties consist of modifications to the shear viscosity, bulk viscosity, thermal conductivity, and species diffusivity of a fluid. The modified transport coefficients are designed to damp out high wavenumber modes, close to the resolution limit, without corrupting lower modes. Requisite behavior of the artificial properties is discussed and results are shown for a variety of test problems, each designed to exercise different aspects of the models. When combined with a tenth-order compact scheme, the overall method exhibits excellent resolution characteristics for turbulent mixing, while capturing shocks and material interfaces in a crisp fashion.
Burns, S.P.; Gianoulakis, S.E.
1995-07-01
A numerical solution for buoyant natural convection within a square enclosure containing a fluid with highly temperature dependent viscosity is presented. Although the fluid properties employed do not represent any real fluid, the large variation in the fluid viscosity with temperature is characteristic of turbulent flow modeling with eddy-viscosity concepts. Results are obtained using a primitive variable formulation and the resistor method. The results presented include velocity, temperature and pressure distributions within the enclosure as well as shear stress and heat flux distributions along the enclosure walls. Three mesh refinements were employed and uncertainty values are suggested for the final mesh refinement. These solutions are part of a contributed benchmark solution set for the subject problem.
A Metric Conceptual Space Algebra
NASA Astrophysics Data System (ADS)
Adams, Benjamin; Raubal, Martin
The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Holographic viscosity of fundamental matter.
Mateos, David; Myers, Robert C; Thomson, Rowan M
2007-03-01
A holographic dual of a finite-temperature SU(Nc) gauge theory with a small number of flavors Nf
Colored Quantum Algebra and Its Bethe State
NASA Astrophysics Data System (ADS)
Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun
2014-12-01
We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.
Generalized Galilean algebras and Newtonian gravity
NASA Astrophysics Data System (ADS)
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Motivating Activities that Lead to Algebra
ERIC Educational Resources Information Center
Menon, Ramakrishnan
2004-01-01
Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.
Large-eddy Advection in Evapotranspiration Estimates from an Array of Eddy Covariance Towers
NASA Astrophysics Data System (ADS)
Lin, X.; Evett, S. R.; Gowda, P. H.; Colaizzi, P. D.; Aiken, R.
2014-12-01
Evapotranspiration was continuously measured by an array of eddy covariance systems and large weighting lysimeter in a sorghum in Bushland, Texas in 2014. The advective divergence from both horizontal and vertical directions were measured through profile measurements above canopy. All storage terms were integrated from the depth of soil heat flux plate to the height of eddy covariance measurement. Therefore, a comparison between the eddy covariance system and large weighing lysimeter was conducted on hourly and daily basis. The results for the discrepancy between eddy covariance towers and the lysimeter will be discussed in terms of advection and storage contributions in time domain and frequency domain.
Thin film eddy current impulse deicer
NASA Technical Reports Server (NTRS)
Smith, Samuel O.; Zieve, Peter B.
1990-01-01
Two new styles of electrical impulse deicers has been developed and tested in NASA's Icing Research Tunnel. With the Eddy Current Repulsion Deicing Boot (EDB), a thin and flexible spiral coil is encapsulated between two thicknesses of elastomer. The coil, made by an industrial printed circuit board manufacturer, is bonded to the aluminum aircraft leading edge. A capacitor bank is discharged through the coil. Induced eddy currents repel the coil from the aluminum aircraft structure and shed accumulated ice. A second configuration, the Eddy Current Repulsion Deicing-Strip (EDS) uses an outer metal erosion strip fastened over the coil. Opposite flowing eddy currents repel the strip and create the impulse deicing force. The outer strip serves as a surface for the collection and shedding of ice and does not require any structural properties. The EDS is suitable for composite aircraft structures. Both systems successfully dispelled over 95 percent of the accumulated ice from airfoils over the range of the FAA icing envelope.
Process Specification for Eddy Current Inspection
NASA Technical Reports Server (NTRS)
Koshti, Ajay
2011-01-01
This process specification establishes the minimum requirements for eddy current inspection of flat surfaces, fastener holes, threaded fasteners and seamless and welded tubular products made from nonmagnetic alloys such as aluminum and stainless steel.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
The addition of algebraic turbulence modeling to program LAURA
NASA Astrophysics Data System (ADS)
Cheatwood, F. Mcneil; Thompson, R. A.
1993-04-01
The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is modified to allow the calculation of turbulent flows. This is accomplished using the Cebeci-Smith and Baldwin-Lomax eddy-viscosity models in conjunction with the thin-layer Navier-Stokes options of the program. Turbulent calculations can be performed for both perfect-gas and equilibrium flows. However, a requirement of the models is that the flow be attached. It is seen that for slender bodies, adequate resolution of the boundary-layer gradients may require more cells in the normal direction than a laminar solution, even when grid stretching is employed. Results for axisymmetric and three-dimensional flows are presented. Comparison with experimental data and other numerical results reveal generally good agreement, except in the regions of detached flow.
Discrimination in a General Algebraic Setting.
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Discrimination in a General Algebraic Setting
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421
Characteristic Numbers of Matrix Lie Algebras
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Fan, En-Gui
2008-04-01
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.
Spatial-Operator Algebra For Robotic Manipulators
NASA Technical Reports Server (NTRS)
Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.
1991-01-01
Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.
Twining characters and orbit Lie algebras
Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph
1996-12-05
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
Eddy currents in a conducting sphere
NASA Technical Reports Server (NTRS)
Bergman, John; Hestenes, David
1986-01-01
This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal current in a circular loop. Analytical expressions for the eddy currents are derived as a power series in the vectorial displacement of the center of the sphere from the axis of the loop. These are used for first order calculations of the power dissipated in the sphere and the force and torque exerted on the sphere by the electromagnetic field of the loop.
Automated eddy current analysis of materials
NASA Technical Reports Server (NTRS)
Workman, Gary L.
1991-01-01
The use of eddy current techniques for characterizing flaws in graphite-based filament-wound cylindrical structures is described. A major emphasis was also placed upon incorporating artificial intelligence techniques into the signal analysis portion of the inspection process. Developing an eddy current scanning system using a commercial robot for inspecting graphite structures (and others) was a goal in the overall concept and is essential for the final implementation for the expert systems interpretation. Manual scans, as performed in the preliminary work here, do not provide sufficiently reproducible eddy current signatures to be easily built into a real time expert system. The expert systems approach to eddy current signal analysis requires that a suitable knowledge base exist in which correct decisions as to the nature of a flaw can be performed. A robotic workcell using eddy current transducers for the inspection of carbon filament materials with improved sensitivity was developed. Improved coupling efficiencies achieved with the E-probes and horseshoe probes are exceptional for graphite fibers. The eddy current supervisory system and expert system was partially developed on a MacIvory system. Continued utilization of finite element models for predetermining eddy current signals was shown to be useful in this work, both for understanding how electromagnetic fields interact with graphite fibers, and also for use in determining how to develop the knowledge base. Sufficient data was taken to indicate that the E-probe and the horseshoe probe can be useful eddy current transducers for inspecting graphite fiber components. The lacking component at this time is a large enough probe to have sensitivity in both the far and near field of a thick graphite epoxy component.
An extended structure-based model based on a stochastic eddy-axis evolution equation
NASA Technical Reports Server (NTRS)
Kassinos, S. C.; Reynolds, W. C.
1995-01-01
We have proposed and implemented an extension of the structure-based model for weak deformations. It was shown that the extended model will correctly reduce to the form of standard k-e models for the case of equilibrium under weak mean strain. The realizability of the extended model is guaranteed by the method of its construction. The predictions of the proposed model were very good for rotating homogeneous shear flows and for irrotational axisymmetric contraction, but were seriously deficient in the case of plane strain and axisymmetric expansion. We have concluded that the problem behind these difficulties lies in the algebraic constitutive equation relating the Reynolds stresses to the structure parameters rather than in the slow model developed here. In its present form, this equation assumes that under irrotational strain the principal axes of the Reynolds stresses remain locked onto those of the eddy-axis tensor. This is correct in the RDT limit, but inappropriate under weaker mean strains, when the non-linear eddy-eddy interactions tend to misalign the two sets of principal axes and create some non-zero theta and gamma.
The nonlinear evolution of tearing mode with electron viscosity in electron magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Cai, Huishan; Dou, Xiankang; Li, Ding
2010-03-01
The general time evolution of tearing mode due to electron viscosity μe from linear to nonlinear phase in the framework of electron magnetohydrodynamics (EMHD) is derived by quasilinear theory. Tearing mode grows exponentially in the linear phase and slows to an algebraic growth behavior Ψ1∝(μet)2/3 (Ψ1 is the magnetic flux) in the nonlinear phase. These two phases are separated by a transition during which the growth behavior is much different from that in the linear and nonlinear phases. It behaves as Ψ1∝μe5/8t1/2 approximately.
Mesoscale eddies transport deep-sea sediments
Zhang, Yanwei; Liu, Zhifei; Zhao, Yulong; Wang, Wenguang; Li, Jianru; Xu, Jingping
2014-01-01
Mesoscale eddies, which contribute to long-distance water mass transport and biogeochemical budget in the upper ocean, have recently been taken into assessment of the deep-sea hydrodynamic variability. However, how such eddies influence sediment movement in the deepwater environment has not been explored. Here for the first time we observed deep-sea sediment transport processes driven by mesoscale eddies in the northern South China Sea via a full-water column mooring system located at 2100 m water depth. Two southwestward propagating, deep-reaching anticyclonic eddies passed by the study site during January to March 2012 and November 2012 to January 2013, respectively. Our multiple moored instruments recorded simultaneous or lagging enhancement of suspended sediment concentration with full-water column velocity and temperature anomalies. We interpret these suspended sediments to have been trapped and transported from the southwest of Taiwan by the mesoscale eddies. The net near-bottom southwestward sediment transport by the two events is estimated up to one million tons. Our study highlights the significance of surface-generated mesoscale eddies on the deepwater sedimentary dynamic process. PMID:25089558
Eddies off the Queen Charlotte Islands
NASA Technical Reports Server (NTRS)
2002-01-01
The bright red, green, and turquoise patches to the west of British Columbia's Queen Charlotte Islands and Alaska's Alexander Archipelago highlight the presence of biological activity in the ocean. These colors indicate high concentrations of chlorophyll, the primary pigment found in phytoplankton. Notice that there are a number of eddies visible in the Pacific Ocean in this pseudo-color scene. The eddies are formed by strong outflow currents from rivers along North America's west coast that are rich in nutrients from the springtime snowmelt running off the mountains. This nutrient-rich water helps stimulate the phytoplankton blooms within the eddies. (For more details, read Tracking Eddies that Feed the Sea.) To the west of the eddies in the water, another type of eddy-this one in the atmosphere-forms the clouds into the counterclockwise spiral characteristic of a low pressure system in the Northern Hemisphere. (Click on the image above to see it at full resolution; or click to see the scene in true-color.) The snow-covered mountains of British Columbia are visible in the upper righthand corner of the image. This scene was constructed using SeaWiFS data collected on June 13, 2002. SeaWiFS image courtesy the SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE
Mesoscale eddies transport deep-sea sediments.
Zhang, Yanwei; Liu, Zhifei; Zhao, Yulong; Wang, Wenguang; Li, Jianru; Xu, Jingping
2014-01-01
Mesoscale eddies, which contribute to long-distance water mass transport and biogeochemical budget in the upper ocean, have recently been taken into assessment of the deep-sea hydrodynamic variability. However, how such eddies influence sediment movement in the deepwater environment has not been explored. Here for the first time we observed deep-sea sediment transport processes driven by mesoscale eddies in the northern South China Sea via a full-water column mooring system located at 2100 m water depth. Two southwestward propagating, deep-reaching anticyclonic eddies passed by the study site during January to March 2012 and November 2012 to January 2013, respectively. Our multiple moored instruments recorded simultaneous or lagging enhancement of suspended sediment concentration with full-water column velocity and temperature anomalies. We interpret these suspended sediments to have been trapped and transported from the southwest of Taiwan by the mesoscale eddies. The net near-bottom southwestward sediment transport by the two events is estimated up to one million tons. Our study highlights the significance of surface-generated mesoscale eddies on the deepwater sedimentary dynamic process.
An Empirical Viscosity Model for Coal Slags
Matyas, Josef; Cooley, Scott K.; Sundaram, S. K.; Rodriguez, Carmen P.; Edmondson, Autumn B.; Arrigoni, Benjamin M.
2008-10-25
Slags of low viscosity readily penetrate the refractory lining in slagging gasifiers, causing rapid and severe corrosion called spalling. In addition, a low-viscosity slag that flows down the gasifier wall forms a relatively thin layer of slag on the refractory surface, allowing the corrosive gases in the gasifier to participate in the chemical reactions between the refractory and the slag. In contrast, a slag viscosity of <25 Pa•s at 1400°C is necessary to minimize the possibility of plugging the slag tap. There is a need to predict and optimize slag viscosity so slagging gasifiers can operate continuously at temperatures ranging from 1300 to 1650°C. The approach adopted in this work was to statistically design and prepare simulated slags, measure the viscosity as a function of temperature, and develop a model to predict slag viscosity based on slag composition and temperature. Statistical design software was used to select compositions from a candidate set of all possible vertices that will optimally represent the composition space for 10 main components. A total of 21 slag compositions were generated, including 5 actual coal slag compositions. The Arrhenius equation was applied to measured viscosity versus temperature data of tested slags, and the Arrhenius coefficients (A and B in ln(vis) = A + B/T) were expressed as linear functions of the slag composition. The viscosity model was validated using 1) data splitting approach, and 2) viscosity/temperature data of selected slag compositions from the literature that were formulated and melted at Pacific Northwest National Laboratory. The capability of the model to predict the viscosity of coal slags was compared with the model developed by Browning et al. because this model can predict the viscosity of slags from coal ash better than the most commonly used empirical models found in the literature.
Improved engine wall models for Large Eddy Simulation (LES)
NASA Astrophysics Data System (ADS)
Plengsaard, Chalearmpol
Improved wall models for Large Eddy Simulation (LES) are presented in this research. The classical Werner-Wengle (WW) wall shear stress model is used along with near-wall sub-grid scale viscosity. A sub-grid scale turbulent kinetic energy is employed in a model for the eddy viscosity. To gain better heat flux results, a modified classical variable-density wall heat transfer model is also used. Because no experimental wall shear stress results are available in engines, the fully turbulent developed flow in a square duct is chosen to validate the new wall models. The model constants in the new wall models are set to 0.01 and 0.8, respectively and are kept constant throughout the investigation. The resulting time- and spatially-averaged velocity and temperature wall functions from the new wall models match well with the law-of-the-wall experimental data at Re = 50,000. In order to study the effect of hot air impinging walls, jet impingement on a flat plate is also tested with the new wall models. The jet Reynolds number is equal to 21,000 and a fixed jet-to-plate spacing of H/D = 2.0. As predicted by the new wall models, the time-averaged skin friction coefficient agrees well with experimental data, while the computed Nusselt number agrees fairly well when r/D > 2.0. Additionally, the model is validated using experimental data from a Caterpillar engine operated with conventional diesel combustion. Sixteen different operating engine conditions are simulated. The majority of the predicted heat flux results from each thermocouple location follow similar trends when compared with experimental data. The magnitude of peak heat fluxes as predicted by the new wall models is in the range of typical measured values in diesel combustion, while most heat flux results from previous LES wall models are over-predicted. The new wall models generate more accurate predictions and agree better with experimental data.
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
Unifying the Algebra for All Movement
ERIC Educational Resources Information Center
Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.
2015-01-01
There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…
Build an Early Foundation for Algebra Success
ERIC Educational Resources Information Center
Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela
2016-01-01
Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…
Difficulties in Initial Algebra Learning in Indonesia
ERIC Educational Resources Information Center
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-01-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…
A Balancing Act: Making Sense of Algebra
ERIC Educational Resources Information Center
Gavin, M. Katherine; Sheffield, Linda Jensen
2015-01-01
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
Algebra? A Gate! A Barrier! A Mystery!
ERIC Educational Resources Information Center
Mathematics Educatio Dialogues, 2000
2000-01-01
This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…
Computer Algebra Systems, Pedagogy, and Epistemology
ERIC Educational Resources Information Center
Bosse, Michael J.; Nandakumar, N. R.
2004-01-01
The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…
Teaching Strategies to Improve Algebra Learning
ERIC Educational Resources Information Center
Zbiek, Rose Mary; Larson, Matthew R.
2015-01-01
Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…
Assessment of dynamic closure for premixed combustion large eddy simulation
NASA Astrophysics Data System (ADS)
Langella, Ivan; Swaminathan, Nedunchezhian; Gao, Yuan; Chakraborty, Nilanjan
2015-09-01
Turbulent piloted Bunsen flames of stoichiometric methane-air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.
Algebraic and Combinatorial Properties of Common RNA Pseudoknot Classes with Applications
Weinberg, Frank
2012-01-01
Abstract Predicting RNA structures with pseudoknots in general is an NP-complete problem. Accordingly, several authors have suggested subclasses that provide polynomial time prediction algorithms by allowing (respectively, disallowing) certain structural motives. In this article, we introduce a unifying algebraic view on most of these classes. That way it becomes possible to find linear time recognition algorithms that decide whether or not a given structure is member of a class (we offer these algorithms as a web service to the scientific community). Furthermore, by presenting a general translation scheme of our algebraic descriptions into multiple context-free grammars, and proving a new correspondence of multiple context-free grammars and generating functions, it becomes possible to derive the precise asymptotic size of all the classes, solving some open problems such as enumerating the Rivas & Eddy class of pseudoknots. PMID:23057823
Algebraic and combinatorial properties of common RNA pseudoknot classes with applications.
Nebel, Markus E; Weinberg, Frank
2012-10-01
Predicting RNA structures with pseudoknots in general is an NP-complete problem. Accordingly, several authors have suggested subclasses that provide polynomial time prediction algorithms by allowing (respectively, disallowing) certain structural motives. In this article, we introduce a unifying algebraic view on most of these classes. That way it becomes possible to find linear time recognition algorithms that decide whether or not a given structure is member of a class (we offer these algorithms as a web service to the scientific community). Furthermore, by presenting a general translation scheme of our algebraic descriptions into multiple context-free grammars, and proving a new correspondence of multiple context-free grammars and generating functions, it becomes possible to derive the precise asymptotic size of all the classes, solving some open problems such as enumerating the Rivas & Eddy class of pseudoknots.
Surface dilatational viscosity of Langmuir monolayers
NASA Astrophysics Data System (ADS)
Lopez, Juan; Vogel, Michael; Hirsa, Amir
2003-11-01
With increased interest in microfluidic systems, interfacial phenomena is receiving more attention. As the length scales of fluid problems decrease, the surface to volume ratio increases and the coupling between interfacial flow and bulk flow becomes increasingly dominated by effects due to intrinsic surface viscosities (shear and dilatational), in comparison to elastic effects (due to surface tension gradients). The surface shear viscosity is well-characterized, as cm-scale laboratory experiments are able to isolate its effects from other interfacial processes (e.g., in the deep-channel viscometer). The same is not true for the dilatational viscosity, because it acts in the direction of surface tension gradients. Their relative strength scale with the capillary number, and for cm-scale laboratory flows, surface tension effects tend to dominate. In microfluidic scale flows, the scaling favors viscosity. We have devised an experimental apparatus which is capable of isolating and enhancing the effects of dilatational viscosity at the cm scales by driving the interface harmonically in time, while keeping the interface flat. In this talk, we shall present both the theory for how this works as well as experimental measurements of surface velocity from which we deduce the dilatational viscosity of several monolayers on the air-water interface over a substantial range of surface concentrations. Anomalous behavior over some range of concentration, which superficially indicates negative viscosity, maybe explained in terms of compositional effects due to large spatial and temporal variations in concentration and corresponding viscosity.
Low shear viscosity due to Anderson localization
Giannakis, Ioannis; Hou Defu; Ren Haicang; Li Jiarong
2008-01-15
We study the Anderson localization effect on the shear viscosity in a system with random medium by Kubo formula. We show that this effect can suppress nonperturbatively the shear viscosity and other transport coefficients. The possible relevancy of such a suppression to the near perfect fluid behavior of the quark-gluon plasma created in heavy-ion collisions is discussed.
Reducing blood viscosity with magnetic fields
NASA Astrophysics Data System (ADS)
Tao, R.; Huang, K.
2011-07-01
Blood viscosity is a major factor in heart disease. When blood viscosity increases, it damages blood vessels and increases the risk of heart attacks. Currently, the only method of treatment is to take drugs such as aspirin, which has, however, several unwanted side effects. Here we report our finding that blood viscosity can be reduced with magnetic fields of 1 T or above in the blood flow direction. One magnetic field pulse of 1.3 T lasting ˜1 min can reduce the blood viscosity by 20%-30%. After the exposure, in the absence of magnetic field, the blood viscosity slowly moves up, but takes a couple of hours to return to the original value. The process is repeatable. Reapplying the magnetic field reduces the blood viscosity again. By selecting the magnetic field strength and duration, we can keep the blood viscosity within the normal range. In addition, such viscosity reduction does not affect the red blood cells’ normal function. This technology has much potential for physical therapy.
Measuring the Shear Viscosity at RHIC
Gavin, Sean; Abdel-Aziz, Mohamed
2006-11-17
Measurements of transverse momentum fluctuations can be used to determine the shear viscosity. We use current data to estimate the viscosity-to-entropy ratio in the range from 0.08 to 0.3, and discuss how future measurements can reduce this uncertainty.
Brief introduction to viscosity in hadron physics
Dobado, Antonio; Llanes-Estrada, Felipe J.; Torres-Rincon, Juan M.
2010-12-28
We introduce the concept of viscosity (both shear and bulk) in the context of hadron physics and in particular the meson gas, highlighting the current theoretical efforts to connect possible measurements of the viscosities to underlying physics such as a phase transition or the trace anomaly.
NASA Astrophysics Data System (ADS)
Yang, Di; Chen, Bicheng; Chamecki, Marcelo; Meneveau, Charles
2015-07-01
Once oil plumes such as those originating from underwater blowouts reach the ocean mixed layer (OML), their near-surface dispersion is influenced heavily by wind and wave-generated Langmuir turbulence. In this study, the complex oil spill dispersion process is modeled using large-eddy simulation (LES). The mean plume dispersion is characterized by performing statistical analysis of the resulting fields from the LES data. Although the instantaneous oil concentration exhibits high intermittency with complex spatial patterns such as Langmuir-induced striations, it is found that the time-averaged oil distribution can still be described quite well by smooth Gaussian-type plumes. LES results show that the competition between droplet rise velocity and vertical turbulent diffusion due to Langmuir turbulence is crucial in determining both the dilution rate and overall direction of transport of oil plumes in the OML. The smoothness of the mean plume makes it feasible to aim at modeling the oil dispersion using Reynolds-averaged type formulations, such as the K-profile parameterization (KPP) with sufficient vertical resolution to capture vertical profiles in the OML. Using LES data, we evaluate the eddy viscosity and eddy diffusivity following the KPP framework. We assess the performance of previous KPP models for pure shear turbulence and Langmuir turbulence by comparing them with the LES data. Based on the assessment a modified KPP model is proposed, which shows improved overall agreement with the LES results for both the eddy viscosity and the eddy diffusivity of the oil dispersion under a variety of flow conditions and droplet sizes.
Entropy algebras and Birkhoff factorization
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Tedeschi, Nicolas
2015-11-01
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.
Algebraic Activities Aid Discovery Lessons
ERIC Educational Resources Information Center
Wallace-Gomez, Patricia
2013-01-01
After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…
ERIC Educational Resources Information Center
Bosse, Michael J.; Ries, Heather; Chandler, Kayla
2012-01-01
Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…
Dimension independence in exterior algebra.
Hawrylycz, M
1995-01-01
The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520
Exploring Algebraic Misconceptions with Technology
ERIC Educational Resources Information Center
Sakow, Matthew; Karaman, Ruveyda
2015-01-01
Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…
ERIC Educational Resources Information Center
Oishi, Lindsay
2011-01-01
"Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…
Weaving Geometry and Algebra Together
ERIC Educational Resources Information Center
Cetner, Michelle
2015-01-01
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Algebra from Chips and Chopsticks
ERIC Educational Resources Information Center
Yun, Jeong Oak; Flores, Alfinio
2012-01-01
Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Algebra for All. Research Brief
ERIC Educational Resources Information Center
Bleyaert, Barbara
2009-01-01
The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless national…
Kinds of Knowledge in Algebra.
ERIC Educational Resources Information Center
Lewis, Clayton
Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…
Adventures in Flipping College Algebra
ERIC Educational Resources Information Center
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
ERIC Educational Resources Information Center
Deakin, Michael A. B.
1974-01-01
Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)
Elementary Algebra Connections to Precalculus
ERIC Educational Resources Information Center
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Math for All Learners: Algebra.
ERIC Educational Resources Information Center
Meader, Pam; Storer, Judy
This book consists of a series of activities aimed at providing a problem solving, hands-on approach so that students can experience concepts in algebra. Topics include ratio and proportion, patterns and formulas, integers, polynomials, linear equations, graphs, and probability. The activities come in the form of reproducible blackline masters…
Inequalities, Assessment and Computer Algebra
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…
Algebra, Home Mortgages, and Recessions
ERIC Educational Resources Information Center
Mariner, Jean A. Miller; Miller, Richard A.
2009-01-01
The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
NASA Astrophysics Data System (ADS)
Kuipers, J.
2012-06-01
New features of the symbolic algebra package Form 4 are discussed. Most importantly, these features include polynomial factorization and polynomial gcd computation. Examples of their use are shown. One of them is an exact version of Mincer which gives answers in terms of rational polynomials and 5 master integrals.
Effects of bulk viscosity at freezeout
Monnai, Akihiko; Hirano, Tetsufumi
2009-11-15
We investigate particle spectra and elliptic flow coefficients in relativistic heavy-ion collisions by taking into account the distortion of phase space distributions by bulk viscosity at freezeout. We first calculate the distortion of phase space distributions in a multicomponent system with Grad's 14-moment method. We find some subtle issues when macroscopic variables are matched with microscopic momentum distributions in a multicomponent system, and we develop a consistent procedure to uniquely determine the corrections to the phase space distributions. Next, we calculate particle spectra by using the Cooper-Frye formula to see the effect of the bulk viscosity. Despite the relative smallness of the bulk viscosity, we find that it is likely to have a visible effect on particle spectra and elliptic flow coefficients. This indicates the importance of taking into account bulk viscosity together with shear viscosity to constrain the transport coefficients with better accuracy from comparison with experimental data.
Viscosity of Common Seed and Vegetable Oils
NASA Astrophysics Data System (ADS)
Wes Fountain, C.; Jennings, Jeanne; McKie, Cheryl K.; Oakman, Patrice; Fetterolf, Monty L.
1997-02-01
Viscosity experiments using Ostwald-type gravity flow viscometers are not new to the physical chemistry laboratory. Several physical chemistry laboratory texts (1 - 3) contain at least one experiment studying polymer solutions or other well-defined systems. Several recently published articles (4 - 8) indicated the continued interest in using viscosity measurements in the teaching lab to illustrate molecular interpretation of bulk phenomena. Most of these discussions and teaching experiments are designed around an extensive theory of viscous flow and models of molecular shape that allow a full data interpretation to be attempted. This approach to viscosity experiments may not be appropriate for all teaching situations (e.g., high schools, general chemistry labs, and nonmajor physical chemistry labs). A viscosity experiment is presented here that is designed around common seed and vegetable oils. With the importance of viscosity to foodstuffs (9) and the importance of fatty acids to nutrition (10), an experiment using these common, recognizable oils has broad appeal.
Plasma viscosity elevations with simulated weightlessness
NASA Technical Reports Server (NTRS)
Martin, D. G.; Convertino, V. A.; Goldwater, D.; Ferguson, E. W.; Schoomaker, E. B.
1986-01-01
A hypothesis correlating an increase in blood viscosity during bed rest to a decrease in aerobic capacity during simulated weightlessness is tested. Eight human subjects were studied on the sixth day of bed rest during two consecutive 10-d bed rest periods separated by a 14-d recovery interval designed to simulate the flight-layover schedule of Shuttle astronauts. Plasma viscosity and volume were measured, together with maximal aerobic capacity (VO2max). An increase in hematocrit, plasma protein, and fibrinogen concentrations was found, contributing to an elevation in plasma viscosity. VO2max decreased significantly in the first, but not the second bed rest cycle, and though many individuals exhibited a decrease in plasma volume and aerobic capacity coupled with elevated plasma viscosity, correlations between these variables were lacking. It is concluded that the decrease in VO2max observed following simulated weightlessness cannot be attributed to alterations in muscle blood flow resulting from increased blood viscosity.
Influence of Molecular Coherence on Surface Viscosity
2015-01-01
Adding small fractions of cholesterol decreases the interfacial viscosity of dipalmitoylphosphatidylcholine (DPPC) monolayers by an order of magnitude per wt %. Grazing incidence X-ray diffraction shows that cholesterol at these small fractions does not mix ideally with DPPC but rather induces nanophase separated structures of an ordered, primarily DPPC phase bordered by a line-active, disordered, mixed DPPC-cholesterol phase. We propose that the free area in the classic Cohen and Turnbull model of viscosity is inversely proportional to the number of molecules in the coherence area, or product of the two coherence lengths. Cholesterol significantly reduces the coherence area of the crystals as well as the interfacial viscosity. Using this free area collapses the surface viscosity data for all surface pressures and cholesterol fractions to a universal logarithmic relation. The extent of molecular coherence appears to be a fundamental factor in determining surface viscosity in ordered monolayers. PMID:24991992
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.
Formal scattering theory by an algebraic approach
NASA Astrophysics Data System (ADS)
Alhassid, Y.; Levine, R. D.
1985-02-01
Formal scattering theory is recast in a Lie-algebraic form. The central result is an algebraic Lippmann-Schwinger equation for the wave operator from which an algebraic form of the Born series (containing only linked terms) is obtained. When a finite Lie algebra is sufficient, The Mo/ller wave operator, on the energy shell, can be solved for explicitly as an element of the corresponding group. The method is illustrated for the separable potential whose relevant algebra is found to be U(1,1).
Hardman-Mountford, Nick J.; Greenwood, Jim; Richardson, Anthony J.; Feng, Ming; Matear, Richard J.
2016-01-01
Mesoscale eddies are ubiquitous features of ocean circulation that modulate the supply of nutrients to the upper sunlit ocean, influencing the rates of carbon fixation and export. The popular eddy-pumping paradigm implies that nutrient fluxes are enhanced in cyclonic eddies because of upwelling inside the eddy, leading to higher phytoplankton production. We show that this view does not hold for a substantial portion of eddies within oceanic subtropical gyres, the largest ecosystems in the ocean. Using space-based measurements and a global biogeochemical model, we demonstrate that during winter when subtropical eddies are most productive, there is increased chlorophyll in anticyclones compared with cyclones in all subtropical gyres (by 3.6 to 16.7% for the five basins). The model suggests that this is a consequence of the modulation of winter mixing by eddies. These results establish a new paradigm for anticyclonic eddies in subtropical gyres and could have important implications for the biological carbon pump and the global carbon cycle. PMID:27386549
Dufois, François; Hardman-Mountford, Nick J; Greenwood, Jim; Richardson, Anthony J; Feng, Ming; Matear, Richard J
2016-05-01
Mesoscale eddies are ubiquitous features of ocean circulation that modulate the supply of nutrients to the upper sunlit ocean, influencing the rates of carbon fixation and export. The popular eddy-pumping paradigm implies that nutrient fluxes are enhanced in cyclonic eddies because of upwelling inside the eddy, leading to higher phytoplankton production. We show that this view does not hold for a substantial portion of eddies within oceanic subtropical gyres, the largest ecosystems in the ocean. Using space-based measurements and a global biogeochemical model, we demonstrate that during winter when subtropical eddies are most productive, there is increased chlorophyll in anticyclones compared with cyclones in all subtropical gyres (by 3.6 to 16.7% for the five basins). The model suggests that this is a consequence of the modulation of winter mixing by eddies. These results establish a new paradigm for anticyclonic eddies in subtropical gyres and could have important implications for the biological carbon pump and the global carbon cycle. PMID:27386549
A daily global mesoscale ocean eddy dataset from satellite altimetry.
Faghmous, James H; Frenger, Ivy; Yao, Yuanshun; Warmka, Robert; Lindell, Aron; Kumar, Vipin
2015-01-01
Mesoscale ocean eddies are ubiquitous coherent rotating structures of water with radial scales on the order of 100 kilometers. Eddies play a key role in the transport and mixing of momentum and tracers across the World Ocean. We present a global daily mesoscale ocean eddy dataset that contains ~45 million mesoscale features and 3.3 million eddy trajectories that persist at least two days as identified in the AVISO dataset over a period of 1993-2014. This dataset, along with the open-source eddy identification software, extract eddies with any parameters (minimum size, lifetime, etc.), to study global eddy properties and dynamics, and to empirically estimate the impact eddies have on mass or heat transport. Furthermore, our open-source software may be used to identify mesoscale features in model simulations and compare them to observed features. Finally, this dataset can be used to study the interaction between mesoscale ocean eddies and other components of the Earth System.
The statistical behaviour of attached eddies
NASA Astrophysics Data System (ADS)
Woodcock, J. D.; Marusic, I.
2015-01-01
Townsend's attached eddy hypothesis forms the basis of an established model of the logarithmic layer in wall-bounded turbulent flows in which this inertially dominated region is characterised by a hierarchy of geometrically self-similar eddying motions that scale with their distance to the wall. The hypothesis has gained considerable support from high Reynolds number measurements of the second-order moments of the fluctuating velocities. Recently, Meneveau and Marusic ["Generalized logarithmic law for high-order moments in turbulent boundary layers," J. Fluid Mech. 719, R1 (2013)] presented experimental evidence that all even-ordered moments of the streamwise velocity will exhibit a logarithmic dependence on the distance from the wall. They demonstrated that this was consistent with the attached eddy hypothesis, so long as the velocity distribution is assumed to be Gaussian (which allows the use of the central limit theorem). In this paper, we derive this result from the attached eddy model without assuming a Gaussian velocity distribution, and find that such logarithmic behaviours are valid in the large Reynolds number limit. We also revisit the physical and mathematical basis of the attached eddy hypothesis, in order to increase rigour and minimise the assumptions required to apply the hypothesis. To this end, we have extended the proof of Campbell's theorem to apply to the velocity field corresponding to a forest of variously sized eddies that are randomly placed on the wall. This enables us to derive all moments of the velocity in the logarithmic region, including cross-correlations between different components of the velocity. By contrast, previous studies of the attached eddy hypothesis have considered only the mean velocity and its second order moments. From this, we obtain qualitatively correct skewnesses and flatnesses for the spanwise and wall-normal fluctuations. The issue of the Reynolds number dependence of von Kármán's constant is also addressed.
Eruptive viscosity and volcano morphology
NASA Technical Reports Server (NTRS)
Posin, Seth B.; Greeley, Ronald
1988-01-01
Terrestrial central volcanoes formed predominantly from lava flows were classified as shields, stratovolcanoes, and domes. Shield volcanoes tend to be large in areal extent, have convex slopes, and are characterized by their resemblance to inverted hellenic war shields. Stratovolcanoes have concave slopes, whereas domes are smaller and have gentle convex slopes near the vent that increase near the perimeter. In addition to these differences in morphology, several other variations were observed. The most important is composition: shield volcanoes tend to be basaltic, stratovolcanoes tend to be andesitic, and domes tend to be dacitic. However, important exceptions include Fuji, Pico, Mayon, Izalco, and Fuego which have stratovolcano morphologies but are composed of basaltic lavas. Similarly, Ribkwo is a Kenyan shield volcano composed of trachyte and Suswa and Kilombe are shields composed of phonolite. These exceptions indicate that eruptive conditions, rather than composition, may be the primary factors that determine volcano morphology. The objective of this study is to determine the relationships, if any, between eruptive conditions (viscosity, erupted volume, and effusion rate) and effusive volcano morphology. Moreover, it is the goal of this study to incorporate these relationships into a model to predict the eruptive conditions of extraterrestrial (Martian) volcanoes based on their morphology.
Eddies in the Red Sea: A statistical and dynamical study
NASA Astrophysics Data System (ADS)
Zhan, Peng; Subramanian, Aneesh C.; Yao, Fengchao; Hoteit, Ibrahim
2014-06-01
Sea level anomaly (SLA) data spanning 1992-2012 were analyzed to study the statistical properties of eddies in the Red Sea. An algorithm that identifies winding angles was employed to detect 4998 eddies propagating along 938 unique eddy tracks. Statistics suggest that eddies are generated across the entire Red Sea but that they are prevalent in certain regions. A high number of eddies is found in the central basin between 18°N and 24°N. More than 87% of the detected eddies have a radius ranging from 50 to 135 km. Both the intensity and relative vorticity scale of these eddies decrease as the eddy radii increase. The averaged eddy lifespan is approximately 6 weeks. AEs and cyclonic eddies (CEs) have different deformation features, and those with stronger intensities are less deformed and more circular. Analysis of long-lived eddies suggests that they are likely to appear in the central basin with AEs tending to move northward. In addition, their eddy kinetic energy (EKE) increases gradually throughout their lifespans. The annual cycles of CEs and AEs differ, although both exhibit significant seasonal cycles of intensity with the winter and summer peaks appearing in February and August, respectively. The seasonal cycle of EKE is negatively correlated with stratification but positively correlated with vertical shear of horizontal velocity and eddy growth rate, suggesting that the generation of baroclinic instability is responsible for the activities of eddies in the Red Sea.
Viscosities of the Gay-Berne Nematic Liquid Crystal
NASA Astrophysics Data System (ADS)
Smondyrev, A. M.; Loriot, George B.; Pelcovits, Robert A.
1995-09-01
We present molecular dynamics simulation measurements of the viscosities of the Gay-Berne phenomenological model of liquid crystals in the nematic and isotropic phases. The temperature dependence of the rotational and shear viscosities, including the nonmonotonic behavior of one shear viscosity, are in good agreement with experimental data. The bulk viscosities are significantly larger than the shear viscosities, again in agreement with experiment.
Temporal Large-Eddy Simulation
NASA Technical Reports Server (NTRS)
Pruett, C. D.; Thomas, B. C.
2004-01-01
In 1999, Stolz and Adams unveiled a subgrid-scale model for LES based upon approximately inverting (defiltering) the spatial grid-filter operator and termed .the approximate deconvolution model (ADM). Subsequently, the utility and accuracy of the ADM were demonstrated in a posteriori analyses of flows as diverse as incompressible plane-channel flow and supersonic compression-ramp flow. In a prelude to the current paper, a parameterized temporal ADM (TADM) was developed and demonstrated in both a priori and a posteriori analyses for forced, viscous Burger's flow. The development of a time-filtered variant of the ADM was motivated-primarily by the desire for a unifying theoretical and computational context to encompass direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaged Navier-Stokes simulation (RANS). The resultant methodology was termed temporal LES (TLES). To permit exploration of the parameter space, however, previous analyses of the TADM were restricted to Burger's flow, and it has remained to demonstrate the TADM and TLES methodology for three-dimensional flow. For several reasons, plane-channel flow presents an ideal test case for the TADM. Among these reasons, channel flow is anisotropic, yet it lends itself to highly efficient and accurate spectral numerical methods. Moreover, channel-flow has been investigated extensively by DNS, and a highly accurate data base of Moser et.al. exists. In the present paper, we develop a fully anisotropic TADM model and demonstrate its utility in simulating incompressible plane-channel flow at nominal values of Re(sub tau) = 180 and Re(sub tau) = 590 by the TLES method. The TADM model is shown to perform nearly as well as the ADM at equivalent resolution, thereby establishing TLES as a viable alternative to LES. Moreover, as the current model is suboptimal is some respects, there is considerable room to improve TLES.
An improved dynamic non-equilibrium wall-model for large eddy simulation
NASA Astrophysics Data System (ADS)
Park, George Ilhwan; Moin, Parviz
2014-01-01
A non-equilibrium wall-model based on unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations has been implemented in an unstructured mesh environment. The method is similar to that of the wall-model for structured mesh described by Wang and Moin [Phys. Fluids 14, 2043-2051 (2002)], but is supplemented by a new dynamic eddy viscosity/conductivity model that corrects the effect of the resolved Reynolds stress (resolved turbulent heat flux) on the skin friction (wall heat flux). This correction is crucial in predicting the correct level of the skin friction. Unlike earlier models, this eddy viscosity/conductivity model does not have a stress-matching procedure or a tunable free parameter, and it shows consistent performance over a wide range of Reynolds numbers. The wall-model is validated against canonical (attached) transitional and fully turbulent flows at moderate to very high Reynolds numbers: a turbulent channel flow at Reτ = 2000, an H-type transitional boundary layer up to Reθ = 3300, and a high Reynolds number boundary layer at Reθ = 31 000. Application to a separated flow over a NACA4412 airfoil operating close to maximum lift is also considered to test the performance of the wall-model in complex non-equilibrium flows.
An improved dynamic non-equilibrium wall-model for large eddy simulation
NASA Astrophysics Data System (ADS)
Park, George Ilhwan; Moin, Parviz
2013-11-01
A non-equilibrium wall-model based on unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations has been implemented in an unstructured mesh environment. The method is similar to that of the wall-model described by Wang and Moin [Phys. Fluids 14, 2043-2051, (2002)], but is supplemented by a new dynamic eddy viscosity/conductivity model that corrects the effect of the resolved Reynolds stress (resolved turbulent heat flux) on the skin friction (wall heat flux). This correction is crucial for accurate prediction of the skin friction and wall heat flux. Unlike earlier models, this eddy viscosity/conductivity model does not have a stress-matching procedure or a tunable free parameter, and it shows consistent performance over a wide range of Reynolds numbers. The wall-model is validated against canonical (attached) transitional and fully turbulent flows at moderate to very high Reynolds number: a turbulent channel flow at Reτ = 2000, an H-type transitional boundary layer up to Reθ = 3300, and a high Reynolds number boundary layer at Reθ = 31000. An application to the flow over NACA4412 airfoil is ongoing and hopefully will be presented. This work was supported by the Winston and Fu-Mei Stanford Graduate Fellowship, NASA Aeronautics Scholarship Program, and NASA under the Subsonic Fixed-Wing Program and the Boeing Company.
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-15
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
Atomic effect algebras with compression bases
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-15
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model
NASA Astrophysics Data System (ADS)
Chou, Yi-Ju; Fringer, Oliver B.
2008-11-01
Transport of suspended sediment in high Reynolds number channel flows [Re=O(600 000)] is simulated using large-eddy simulation along with a dynamic-mixed model (DMM). Because the modeled sediment concentration is low and the bulk Stokes' number (Stb) is small during the simulation, the sediment concentration is calculated through the use of the Eulerian approach. In order to employ the DMM for the suspended sediment, we formulate a generalized bottom boundary condition in a finite-volume formulation that accounts for sediment flux from the bed without requiring specific details of the underlying turbulence model. This enables the use of the pickup function without requiring any assumptions about the behavior of the eddy viscosity. Using our new boundary condition, simulations indicate that the resolved component of the vertical flux is one order of magnitude greater than the resolved subfilter-scale flux, which is in turn one order of magnitude greater than the eddy-diffusive flux. Analysis of the behavior of the suspended sediment above the bed indicates the existence of three basic time scales that arise due to varying degrees of competition between the upward turbulent flux and downward settling flux. Instantaneous sediment concentration and velocity fields indicate that streamwise vortices account for a bulk of the resolved flux of sediment from the bed.
Oil droplet plume evolution in Langmuir turbulence: a Large Eddy Simulation study
NASA Astrophysics Data System (ADS)
Yang, Di; Chen, Bicheng; Chamecki, Marcelo; Meneveau, Charles
2014-11-01
When the oil plumes from deep water blowouts reach the ocean mixed layer (OML), their fates on the sea surface are highly affected by the interactions with wind and wave-generated Langmuir turbulence in the OML. In this study, we use large eddy simulations (LES) to quantify the complex oil dispersion phenomena. We find that although the instantaneous surface oil slick patterns are very complex, the time-averaged surface oil plume can be parameterized as a Gaussian-type plume. The centerline of the surface plume is inclined clockwise (in the Northern Hemisphere) with respect to the wind and wave direction due to Ekman transport. The initial width of the mean surface plume and the inclination angle increase as the droplet size decreases. The surface plume width grows downstream, with a growth rate that varies non-monotonically with oil droplet size. Using LES data, we evaluate the eddy viscosity and eddy diffusivity following the K-profile parameterization (KPP) framework. We also evaluate stress-strain misalignments caused by Stokes drift and evaluate means of parameterizing these effects. Improvements to the KPP model will be discussed. This study is supported by a Gulf of Mexico Research Initiative research grant.
An eddy tracking algorithm based on dynamical systems theory
NASA Astrophysics Data System (ADS)
Conti, Daniel; Orfila, Alejandro; Mason, Evan; Sayol, Juan Manuel; Simarro, Gonzalo; Balle, Salvador
2016-11-01
This work introduces a new method for ocean eddy detection that applies concepts from stationary dynamical systems theory. The method is composed of three steps: first, the centers of eddies are obtained from fixed points and their linear stability analysis; second, the size of the eddies is estimated from the vorticity between the eddy center and its neighboring fixed points, and, third, a tracking algorithm connects the different time frames. The tracking algorithm has been designed to avoid mismatching connections between eddies at different frames. Eddies are detected for the period between 1992 and 2012 using geostrophic velocities derived from AVISO altimetry and a new database is provided for the global ocean.
Large eddy simulations of compressible turbulent flows
NASA Technical Reports Server (NTRS)
Porter-Locklear, Freda
1995-01-01
An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.
Vertical eddy heat fluxes from model simulations
NASA Technical Reports Server (NTRS)
Stone, Peter H.; Yao, Mao-Sung
1991-01-01
Vertical eddy fluxes of heat are calculated from simulations with a variety of climate models, ranging from three-dimensional GCMs to a one-dimensional radiative-convective model. The models' total eddy flux in the lower troposphere is found to agree well with Hantel's analysis from observations, but in the mid and upper troposphere the models' values are systematically 30 percent to 50 percent smaller than Hantel's. The models nevertheless give very good results for the global temperature profile, and the reason for the discrepancy is unclear. The model results show that the manner in which the vertical eddy flux is carried is very sensitive to the parameterization of moist convection. When a moist adiabatic adjustment scheme with a critical value for the relative humidity of 100 percent is used, the vertical transports by large-scale eddies and small-scale convection on a global basis are equal: but when a penetrative convection scheme is used, the large-scale flux on a global basis is only about one-fifth to one-fourth the small-scale flux. Comparison of the model results with observations indicates that the results with the latter scheme are more realistic. However, even in this case, in mid and high latitudes the large and small-scale vertical eddy fluxes of heat are comparable in magnitude above the planetary boundary layer.
Automated eddy current analysis of materials
NASA Technical Reports Server (NTRS)
Workman, Gary L.
1990-01-01
This research effort focused on the use of eddy current techniques for characterizing flaws in graphite-based filament-wound cylindrical structures. A major emphasis was on incorporating artificial intelligence techniques into the signal analysis portion of the inspection process. Developing an eddy current scanning system using a commercial robot for inspecting graphite structures (and others) has been a goal in the overall concept and is essential for the final implementation for expert system interpretation. Manual scans, as performed in the preliminary work here, do not provide sufficiently reproducible eddy current signatures to be easily built into a real time expert system. The expert systems approach to eddy current signal analysis requires that a suitable knowledge base exist in which correct decisions as to the nature of the flaw can be performed. In eddy current or any other expert systems used to analyze signals in real time in a production environment, it is important to simplify computational procedures as much as possible. For that reason, we have chosen to use the measured resistance and reactance values for the preliminary aspects of this work. A simple computation, such as phase angle of the signal, is certainly within the real time processing capability of the computer system. In the work described here, there is a balance between physical measurements and finite element calculations of those measurements. The goal is to evolve into the most cost effective procedures for maintaining the correctness of the knowledge base.
Stratospheric eddy diffusion coefficients from tracer data
NASA Technical Reports Server (NTRS)
Massie, S. T.; Hunten, D. M.
1981-01-01
Global distributions of nitrous oxide, methane, ozone, and carbon 14 are used to estimate four sets of stratospheric eddy diffusion coefficients. A photochemical equilibrium model calculates O(3P), O(1D), H, HO2, OH, H2O2, NO, and NO2 densities, as a function of altitude, latitude, and time. The calculated O(1D), OH, and observed Cl densities are used to obtain the eddy profiles associated with the methane and nitrous oxide distributions, for altitudes between 10 and 40 km. Application of a constant flux condition to the seasonally averaged ozone data yields eddy values below 20 km. Time-dependent carbon 14 calculations produce eddy coefficients between 13 and 27 km. A composite profile is obtained by comparing the four sets of coefficients. Further, carbon 14 computations are used to test these profiles as well as those recommended in reports issued by the National Academy of Sciences in 1976 and 1979. The composite eddy profile produces the best agreement.
Viscosity measurement techniques in Dissipative Particle Dynamics
NASA Astrophysics Data System (ADS)
Boromand, Arman; Jamali, Safa; Maia, Joao M.
2015-11-01
In this study two main groups of viscosity measurement techniques are used to measure the viscosity of a simple fluid using Dissipative Particle Dynamics, DPD. In the first method, a microscopic definition of the pressure tensor is used in equilibrium and out of equilibrium to measure the zero-shear viscosity and shear viscosity, respectively. In the second method, a periodic Poiseuille flow and start-up transient shear flow is used and the shear viscosity is obtained from the velocity profiles by a numerical fitting procedure. Using the standard Lees-Edward boundary condition for DPD will result in incorrect velocity profiles at high values of the dissipative parameter. Although this issue was partially addressed in Chatterjee (2007), in this work we present further modifications (Lagrangian approach) to the original LE boundary condition (Eulerian approach) that will fix the deviation from the desired shear rate at high values of the dissipative parameter and decrease the noise to signal ratios in stress measurement while increases the accessible low shear rate window. Also, the thermostat effect of the dissipative and random forces is coupled to the dynamic response of the system and affects the transport properties like the viscosity and diffusion coefficient. We investigated thoroughly the dependency of viscosity measured by both Eulerian and Lagrangian methodologies, as well as numerical fitting procedures and found that all the methods are in quantitative agreement.
Linear algebra algorithms for divisors on an algebraic curve
NASA Astrophysics Data System (ADS)
Khuri-Makdisi, Kamal
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and matrices of size $O(g^2)\\times O(g)$. When the base field $k$ is finite, or if $C$ has a rational point over $k$, these give algorithms for working on the Jacobian of $C$ that require $O(g^4)$ field operations, arising from the Gaussian elimination. Our point of view is strongly geometric, and our representation of points on the Jacobian is fairly simple to work with; in particular, none of our algorithms involves arithmetic with polynomials. We note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in Hess' 1999 Ph.D. thesis, which works with function fields as extensions of $k[x]$. However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and Smart), and $C_{ab}$ curves (Harasawa and Suzuki); in all those cases, one can attain a complexity of $O(g^2)$.
Viscosity studies of water based magnetite nanofluids
NASA Astrophysics Data System (ADS)
Anu, K.; Hemalatha, J.
2016-05-01
Magnetite nanofluids of various concentrations have been synthesized through co-precipitation method. The structural and topographical studies made with the X-Ray Diffractometer and Atomic Force Microscope are presented in this paper. The density and viscosity studies for the ferrofluids of various concentrations have been made at room temperature. The experimental viscosities are compared with theoretical values obtained from Einstein, Batchelor and Wang models. An attempt to modify the Rosensweig model is made and the modified Rosensweig equation is reported. In addition, new empirical correlation is also proposed for predicting viscosity of ferrofluid at various concentrations.
Viscosity of high-temperature iodine
NASA Technical Reports Server (NTRS)
Kang, Steve H.; Kunc, Joseph A.
1991-01-01
The viscosity coefficient of iodine in the temperature range 500 - 3000 K is calculated. Because of the low dissociation energy of the I2 molecules, the dissociation degree of the gas increases quickly with temperature, and I + I2 and I + I collisions must be taken into account in calculation of viscosity at temperatures greater than 1000 deg. Several possible channels for atom-atom interaction are considered, and the resulting collision integrals are averaged over all the important channels. It is also shown that the rigid-sphere model is inaccurate in predictions of the viscosity.
Viscoseal performance with rarefied-gas sealant
NASA Technical Reports Server (NTRS)
Milligan, M. W.
1973-01-01
A fundamental study of viscoseals having a rarefied gas as the sealant was conducted. Both experimental and analytical investigations are reported. Three different analytical models were formulated and are described in detail. An experimental investigation was conducted on multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. Comparisons are presented between actual viscoseal performance and the theoretical predictions for both sealing coefficient and net leakage parameters as functions of the degree of gas rarefication. Recommendations are presented for the use of the analytical models.
Viscoseal performance with rarefied-gas sealant
NASA Technical Reports Server (NTRS)
Milligan, M. W.
1971-01-01
A fundamental study of viscoseals having a rarefied gas as the sealant has been conducted. Both experimental and analytical investigations are reported. Three different analytical models have been formulated and are described in detail. An experimental investigation has been conducted on multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. Comparisons are presented between actual viscoseal performance and the theoretical predictions for both sealing coefficient and net leakage parameters as functions of the degree of gas rarefication. Recommendations are presented for the use of the analytical models.
Shear viscosity from effective couplings of gravitons
Cai Ronggen; Nie Zhangyu; Sun Yawen
2008-12-15
We calculate the shear viscosity of field theories with gravity duals using Kubo formula by calculating the Green function of dual transverse gravitons and confirm that the value of the shear viscosity is fully determined by the effective coupling of transverse gravitons on the horizon. We calculate the effective coupling of transverse gravitons for Einstein and Gauss-Bonnet gravities coupled with matter fields, respectively. Then we apply the resulting formula to the case of AdS Gauss-Bonnet gravity with F{sup 4} term corrections of Maxwell field and discuss the effect of F{sup 4} terms on the ratio of the shear viscosity to entropy density.
Bulk viscosity of superfluid hyperon stars
Gusakov, Mikhail E.; Kantor, Elena M.
2008-10-15
We calculate the bulk viscosity due to nonequilibrium weak processes in superfluid nucleon-hyperon matter of neutron stars. For that, the dissipative relativistic hydrodynamics, formulated eariler [M. E. Gusakov, Phys. Rev. D 76, 083001 (2007).] for superfluid mixtures, is extended to the case when both nucleons and hyperons are superfluid. It is demonstrated that in the most general case (when neutrons, protons, {lambda}, and {sigma}{sup -} hyperons are superfluid), nonequilibrium weak processes generate 16 bulk viscosity coefficients, with only three of them being independent. In addition, we correct an inaccuracy in a widely used formula for the bulk viscosity of nonsuperfluid nucleon-hyperon matter.
Blood viscosity: influence of erythrocyte aggregation.
Chien, S; Usami, S; Dellenback, R J; Gregersen, M I; Nanninga, L B; Guest, M M
1967-08-18
The addition of purified canine or bovine fibrinogen to suspensions of canine erythocytes in Ringer solution caused an increase in viscosity and the formation of aggregates of erythocytes. Both of these effects became increasingly pronounced as the fibrinogen concentration was raised, and they approached plateaus with 1 gram of fibrinogen per 100 milliliters. An increase in shear rate (or shear stress) reduced both the effect on viscosity and the aggregate size. The data suggest that fibrinogen causes an increase in blood viscosity and a departure from Newtonian behavior by interacting with erythrocytes to form cell aggregates which can be dispersed by shear stress. PMID:17842794
Shear viscosity in the postquasistatic approximation
Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W.
2010-05-15
We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.
Lu Egang; Moore, Guy D.
2011-04-15
We compute the bulk viscosity of a gas of pions at temperatures below the QCD crossover temperature, for the physical value of m{sub {pi}}, to lowest order in chiral perturbation theory. Bulk viscosity is controlled by number-changing processes which become exponentially slow at low temperatures when the pions become exponentially dilute, leading to an exponentially large bulk viscosity {zeta}{approx}(F{sub 0}{sup 8}/m{sub {pi}}{sup 5})exp(2m{sub {pi}}/T), where F{sub 0}{approx_equal}93 MeV is the pion decay constant.
Drag reduction by a linear viscosity profile.
De Angelis, Elisabetta; Casciola, Carlo M; L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil
2004-11-01
Drag reduction by polymers in turbulent flows raises an apparent contradiction: the stretching of the polymers must increase the viscosity, so why is the drag reduced? A recent theory proposed that drag reduction, in agreement with experiments, is consistent with the effective viscosity growing linearly with the distance from the wall. With this self-consistent solution the reduction in the Reynolds stress overwhelms the increase in viscous drag. In this Rapid Communication we show, using direct numerical simulations, that a linear viscosity profile indeed reduces the drag in agreement with the theory and in close correspondence with direct simulations of the FENE-P model at the same flow conditions.
Eddy analysis in the Eastern China Sea using altimetry data
NASA Astrophysics Data System (ADS)
Qin, Dandi; Wang, Jianhong; Liu, Yu; Dong, Changming
2015-12-01
Statistical characteristics of mesoscale eddies in the Eastern China Sea (ECS) are analyzed using altimetry sea surface height anomaly (SSHA) data from 1993 to 2010. A velocity geometry-based automated eddy detection scheme is employed to detect eddies from the SSHA data to generate an eddy data set. About 1,096 eddies (one lifetime of eddies is counted as one eddy) with a lifetime longer than or equal to 4 weeks are identified in this region. The average lifetime and radius of eddies are 7 weeks and 55 km, respectively, and there is no significant difference between cyclonic eddies (CEs) and anticyclonic eddies (AEs) in this respect. Eddies' lifetimes are generally longer in deep water than in shallow water. Most eddies propagate northeastward along the Kuroshio (advected by the Kuroshio), with more CEs generated on its western side and AEs on its eastern side. The variation of the Kuroshio transport is one of the major mechanisms for eddy genesis, however the generation of AEs on the eastern side of the Kuroshio (to the open ocean) is also subject to other factors, such as the wind stress curl due to the presence of the Ryukyu Islands and the disturbance from the open ocean.
Turbulent fluxes by "Conditional Eddy Sampling"
NASA Astrophysics Data System (ADS)
Siebicke, Lukas
2015-04-01
Turbulent flux measurements are key to understanding ecosystem scale energy and matter exchange, including atmospheric trace gases. While the eddy covariance approach has evolved as an invaluable tool to quantify fluxes of e.g. CO2 and H2O continuously, it is limited to very few atmospheric constituents for which sufficiently fast analyzers exist. High instrument cost, lack of field-readiness or high power consumption (e.g. many recent laser-based systems requiring strong vacuum) further impair application to other tracers. Alternative micrometeorological approaches such as conditional sampling might overcome major limitations. Although the idea of eddy accumulation has already been proposed by Desjardin in 1972 (Desjardin, 1977), at the time it could not be realized for trace gases. Major simplifications by Businger and Oncley (1990) lead to it's widespread application as 'Relaxed Eddy Accumulation' (REA). However, those simplifications (flux gradient similarity with constant flow rate sampling irrespective of vertical wind velocity and introduction of a deadband around zero vertical wind velocity) have degraded eddy accumulation to an indirect method, introducing issues of scalar similarity and often lack of suitable scalar flux proxies. Here we present a real implementation of a true eddy accumulation system according to the original concept. Key to our approach, which we call 'Conditional Eddy Sampling' (CES), is the mathematical formulation of conditional sampling in it's true form of a direct eddy flux measurement paired with a performant real implementation. Dedicated hardware controlled by near-real-time software allows full signal recovery at 10 or 20 Hz, very fast valve switching, instant vertical wind velocity proportional flow rate control, virtually no deadband and adaptive power management. Demonstrated system performance often exceeds requirements for flux measurements by orders of magnitude. The system's exceptionally low power consumption is ideal
Solitonlike solutions in loop current eddies
NASA Technical Reports Server (NTRS)
Nakamoto, Shoichiro
1989-01-01
The application of the nonlinear quasi-geostrophic equations to an isolated eddy in the western continental slope region in the Gulf of Mexico is examined for a two-layer ocean model with bottom topography. In the linear limit, solutions are topographic nondispersive waves. Form-preserving solutions, or solitons, have been found. The solution is shown to be a limiting form for a nonlinear dispersive system propagating northward along the topographic waveguide in the western continental slope region in the Gulf of Mexico. Using satellite-tracked drifter data, a linear relationship is found between the amplitude of the deduced stream function of the eddy and its observed translational velocity over the continental slope, which supports the hypothesis that some mesoscale eddies interacting with the continental slope behave as solitons.
Alternative algebraic approaches in quantum chemistry
Mezey, Paul G.
2015-01-22
Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.
The algebras of large N matrix mechanics
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
2003-06-03
The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran code is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.
2003-06-03
The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
Introduction to Image Algebra Ada
NASA Astrophysics Data System (ADS)
Wilson, Joseph N.
1991-07-01
Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.
Eddy current heating in magnetic refrigerators
NASA Technical Reports Server (NTRS)
Kittel, Peter
1990-01-01
Eddy current heating can be a significant source of parasitic heating in low temperature magnetic refrigerators. To study this problem a technique to approximate the heating due to eddy currents has been developed. A formula is presented for estimating the heating within a variety of shapes commonly found in magnetic refrigerators. These shapes include circular, square, and rectangular rods; cylindrical and split cylindrical shells; wire loops; and 'coil foil. One set of components evaluated are different types of thermal radiation shields. This comparison shows that a simple split shield is almost as effective (only 23 percent more heating) as using a shield, with the same axial thermal conductivity, made of 'coil foil'.
Casimir Interaction from Magnetically Coupled Eddy Currents
Intravaia, Francesco; Henkel, Carsten
2009-09-25
We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasistatic magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.
Eddy Correlation Flux Measurement System (ECOR) Handbook
Cook, DR
2011-01-31
The eddy correlation (ECOR) flux measurement system provides in situ, half-hour measurements of the surface turbulent fluxes of momentum, sensible heat, latent heat, and carbon dioxide (CO2) (and methane at one Southern Great Plains extended facility (SGP EF) and the North Slope of Alaska Central Facility (NSA CF). The fluxes are obtained with the eddy covariance technique, which involves correlation of the vertical wind component with the horizontal wind component, the air temperature, the water vapor density, and the CO2 concentration.
Measurement of DWPF glass viscosity - Final Report
Harbour, J.R.
2000-02-17
This report details the results of a scoping study funded by the Defense Waste Processing Facility (DWPF) for the measurement of melt viscosities for simulated glasses representative of Macrobatch 2 (Tank 42/51 feed).
Second coefficient of viscosity in air
NASA Technical Reports Server (NTRS)
Ash, Robert L.; Zuckerwar, Allan J.; Zheng, Zhonquan
1991-01-01
Acoustic attenuation measurements in air were analyzed in order to estimate the second coefficient of viscosity. Data over a temperature range of 11 C to 50 C and at relative humidities between 6 percent and 91 percent were used. This analysis showed that the second coefficient of viscosity varied between 1900 and 20,000 times larger than the dynamic or first coefficient of viscosity over the temperature and humidity range of the data. In addition, the data showed that the molecular relaxation effects, which are responsible for the magnitude of the second coefficient of viscosity, place severe limits on the use of time-independent, thermodynamic equations of state. Compressible flows containing large streamwise velocity gradients, like shock waves, which cause significant changes in particle properties to occur during time intervals shorter than hundredths of seconds, must be modeled using dynamic equations of state. The dynamic model approach is described briefly.
Viscosity of Sheared Helical filament Suspensions
NASA Astrophysics Data System (ADS)
Sartucci, Matthew; Urbach, Jeff; Blair, Dan; Schwenger, Walter
The viscosity of suspensions can be dramatically affected by high aspect ratio particles. Understanding these systems provides insight into key biological functions and can be manipulated for many technological applications. In this talk, the viscosity as a function of shear rate of suspensions of helical filaments is compared to that of suspensions of straight rod-like filaments. Our goal is to determine the impact of filament geometry on low volume fraction colloidal suspensions in order to identify strategies for altering viscosity with minimal volume fraction. In this research, the detached flagella of the bacteria Salmonella Typhimurium are used as a model system of helical filaments and compared to mutated straight flagella of the Salmonella. We compare rheological measurements of the suspension viscosity in response to shear flow and use a combination of the rheology and fluorescence microscopy to identify the microstructural changes responsible for the observed rheological response.
Quartz resonator fluid density and viscosity monitor
Martin, Stephen J.; Wiczer, James J.; Cernosek, Richard W.; Frye, Gregory C.; Gebert, Charles T.; Casaus, Leonard; Mitchell, Mary A.
1998-01-01
A pair of thickness-shear mode resonators, one smooth and one with a textured surface, allows fluid density and viscosity to be independently resolved. A textured surface, either randomly rough or regularly patterned, leads to trapping of liquid at the device surface. The synchronous motion of this trapped liquid with the oscillating device surface allows the device to weigh the liquid; this leads to an additional response that depends on liquid density. This additional response enables a pair of devices, one smooth and one textured, to independently resolve liquid density and viscosity; the difference in responses determines the density while the smooth device determines the density-viscosity product, and thus, the pair determines both density and viscosity.
Blood viscosity: influence of erythrocyte deformation.
Chien, S; Usami, S; Dellenback, R J; Gregersen, M I
1967-08-18
Suspensions of canine and human erythocytes hardened with acetaldehyde differ from the suspensions of normal erythrocytes with respect to their rheological behavior. Normal erythrocytes can be packed by centrifugation so that the sediment volume is nearly 100 percent cells, but the hardened erythrocytes (RBC's) can be packed only to approximately 60 percent cells. At the same cell percentage the viscosity of the hardened RBC suspension is higher than that of the suspension of normal erythocytes. An increase in shear stress deforms the normal erythocytes and lowers the suspension viscosity, but has no influence on the viscosity of the hardened cell suspension. In blood with high cell percentages, the shear deformation of normal RBC's plays an important role in reducing viscosity and facilitating flow at high shear stresses. PMID:17842793
Visualization and analysis of eddies in a global ocean simulation
Williams, Sean J; Hecht, Matthew W; Petersen, Mark; Strelitz, Richard; Maltrud, Mathew E; Ahrens, James P; Hlawitschka, Mario; Hamann, Bernd
2010-10-15
Eddies at a scale of approximately one hundred kilometers have been shown to be surprisingly important to understanding large-scale transport of heat and nutrients in the ocean. Due to difficulties in observing the ocean directly, the behavior of eddies below the surface is not very well understood. To fill this gap, we employ a high-resolution simulation of the ocean developed at Los Alamos National Laboratory. Using large-scale parallel visualization and analysis tools, we produce three-dimensional images of ocean eddies, and also generate a census of eddy distribution and shape averaged over multiple simulation time steps, resulting in a world map of eddy characteristics. As expected from observational studies, our census reveals a higher concentration of eddies at the mid-latitudes than the equator. Our analysis further shows that mid-latitude eddies are thicker, within a range of 1000-2000m, while equatorial eddies are less than 100m thick.
Viscosity distribution in the mantle convection models
NASA Astrophysics Data System (ADS)
Trubitsyn, V. P.
2016-09-01
Viscosity is a fundamental property of the mantle which determines the global geodynamical processes. According to the microscopic theory of defects and laboratory experiments, viscosity exponentially depends on temperature and pressure, with activation energy and activation volume being the parameters. The existing laboratory measurements are conducted with much higher strain rates than in the mantle and have significant uncertainty. The data on postglacial rebound only allow the depth distributions of viscosity to be reconstructed. Therefore, spatial distributions (along the depth and lateral) are as of now determined from the models of mantle convection which are calculated by the numerical solution of the convection equations, together with the viscosity dependences on pressure and temperature ( PT-dependences). The PT-dependences of viscosity which are presently used in the numerical modeling of convection give a large scatter in the estimates for the lower mantle, which reaches several orders of magnitude. In this paper, it is shown that it is possible to achieve agreement between the calculated depth distributions of viscosity throughout the entire mantle and the postglacial rebound data. For this purpose, the values of the volume and energy of activation for the upper mantle can be taken from the laboratory experiments, and for the lower mantle, the activation volume should be reduced twice at the 660-km phase transition boundary. Next, the reduction in viscosity by an order of magnitude revealed at the depths below 2000 km by the postglacial rebound data can be accounted for by the presence of heavy hot material at the mantle bottom in the LLSVP zones. The models of viscosity spatial distribution throughout the entire mantle with the lithospheric plates are presented.
Shear viscosity in SU(2) lattice gluodynamics
NASA Astrophysics Data System (ADS)
Braguta, V. V.; Kotov, A. Yu
2015-05-01
The calculation of the gluon plasma viscosity has been performed by lattice simulations in the SU(2) gluodynamics at T/Tc = 1.2 on the supercomputers. The evaluation is based on the Kubo formula that relates viscosity to the spectral function of the correlation functions of the energy-momentum tensor. For the extraction of the spectral function from the Euclidean correlator the linear method is applied.
Algebra: A Challenge at the Crossroads of Policy and Practice
ERIC Educational Resources Information Center
Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.
2011-01-01
The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…
A Simple BODIPY-Based Viscosity Probe for Imaging of Cellular Viscosity in Live Cells.
Su, Dongdong; Teoh, Chai Lean; Gao, Nengyue; Xu, Qing-Hua; Chang, Young-Tae
2016-01-01
Intracellular viscosity is a fundamental physical parameter that indicates the functioning of cells. In this work, we developed a simple boron-dipyrromethene (BODIPY)-based probe, BTV, for cellular mitochondria viscosity imaging by coupling a simple BODIPY rotor with a mitochondria-targeting unit. The BTV exhibited a significant fluorescence intensity enhancement of more than 100-fold as the solvent viscosity increased. Also, the probe showed a direct linear relationship between the fluorescence lifetime and the media viscosity, which makes it possible to trace the change of the medium viscosity. Furthermore, it was demonstrated that BTV could achieve practical applicability in the monitoring of mitochondrial viscosity changes in live cells through fluorescence lifetime imaging microscopy (FLIM).
A Simple BODIPY-Based Viscosity Probe for Imaging of Cellular Viscosity in Live Cells
Su, Dongdong; Teoh, Chai Lean; Gao, Nengyue; Xu, Qing-Hua; Chang, Young-Tae
2016-01-01
Intracellular viscosity is a fundamental physical parameter that indicates the functioning of cells. In this work, we developed a simple boron-dipyrromethene (BODIPY)-based probe, BTV, for cellular mitochondria viscosity imaging by coupling a simple BODIPY rotor with a mitochondria-targeting unit. The BTV exhibited a significant fluorescence intensity enhancement of more than 100-fold as the solvent viscosity increased. Also, the probe showed a direct linear relationship between the fluorescence lifetime and the media viscosity, which makes it possible to trace the change of the medium viscosity. Furthermore, it was demonstrated that BTV could achieve practical applicability in the monitoring of mitochondrial viscosity changes in live cells through fluorescence lifetime imaging microscopy (FLIM). PMID:27589762
A Simple BODIPY-Based Viscosity Probe for Imaging of Cellular Viscosity in Live Cells.
Su, Dongdong; Teoh, Chai Lean; Gao, Nengyue; Xu, Qing-Hua; Chang, Young-Tae
2016-01-01
Intracellular viscosity is a fundamental physical parameter that indicates the functioning of cells. In this work, we developed a simple boron-dipyrromethene (BODIPY)-based probe, BTV, for cellular mitochondria viscosity imaging by coupling a simple BODIPY rotor with a mitochondria-targeting unit. The BTV exhibited a significant fluorescence intensity enhancement of more than 100-fold as the solvent viscosity increased. Also, the probe showed a direct linear relationship between the fluorescence lifetime and the media viscosity, which makes it possible to trace the change of the medium viscosity. Furthermore, it was demonstrated that BTV could achieve practical applicability in the monitoring of mitochondrial viscosity changes in live cells through fluorescence lifetime imaging microscopy (FLIM). PMID:27589762
Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050
Kumjian-Pask algebras of desourcification
NASA Astrophysics Data System (ADS)
Rosjanuardi, Rizky; Yusnitha, Isnie
2016-02-01
Kumjian-Pask algebra which was introduced by Pino, Clark, an Huef and Raeburn [1] in 2013, gives a purely algebraic version of a k-graph algebra. Rosjanuardi [2] gave necessary and sufficient condition of finitely dimensional complex Kumjian-Pask algebra of row-finite k-graph without sources. We will improve the previous results which allows us to deal with sources. We will consider Kumjian-Pask algebra for locally convex row-finite k-graph which was introduced by Clark, Flynn and an Huef [3], and use the desourcification of the graph to get conditions which characterise when the complex Kumjian-Pask algebra of locally convex row-finite k-graph is finite dimensional.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
NASA Astrophysics Data System (ADS)
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Gulf Stream eddies - Recent observations in the western Sargasso Sea.
NASA Technical Reports Server (NTRS)
Richardson, P. L.; Knauss, J. A.; Strong, A. E.
1973-01-01
A cyclonic Gulf Stream eddy was observed in the western Sargasso Sea by satellite infrared measurements and later confirmed by ship measurements. Fourteen months of observations indicate that the eddy moved southwestward at an average rate of 1 mile per day. The evidence suggests that the eddy was absorbed by the Gulf Stream off Florida.
The influence of eddy currents on magnetic actuator performance
NASA Technical Reports Server (NTRS)
Zmood, R. B.; Anand, D. K.; Kirk, J. A.
1987-01-01
The present investigation of the effects of eddy currents on EM actuators' transient performance notes that a transfer function representation encompassing a first-order model of the eddy current influence can be useful in control system analysis. The method can be extended to represent the higher-order effects of eddy currents for actuators that cannot be represented by semiinfinite planes.
Eddy-Current Inspection Of Graphite-Fiber Composites
NASA Technical Reports Server (NTRS)
Workman, G. L.; Bryson, C. C.
1993-01-01
NASA technical memorandum describes initial research on, and proposed development of, automated system for nondestructive eddy-current inspection of parts made of graphite-fiber/epoxy-matrix composite materials. Sensors in system E-shaped or U-shaped eddy-current probes like those described in "Eddy-Current Probes For Inspecting Graphite-Fiber Composites" (MFS-26129).
An expert system for analyzing eddy current measurements
Levy, A.J.; Oppenlander, J.E.; Brudnoy, D.M.; Englund, J.M.; Loomis, K.C.
1991-12-31
A method and apparatus (called DODGER) analyzes eddy current data for heat exchanger tubes or any other metallic object. DODGER uses an expert system to analyze eddy current data by reasoning with uncertainty and pattern recognition. The expert system permits, DODGER to analyze eddy current data intelligently, an obviate operator uncertainty by analyzing the data in a uniform and consistent manner.
NASA Astrophysics Data System (ADS)
Lampitella, P.; Colombo, E.; Inzoli, F.
2014-04-01
The paper presents a consistent large eddy simulation (LES) framework which is particularly suited for implicitly filtered LES with unstructured finite volume (FV) codes. From the analysis of the subgrid-scale (SGS) stress tensor arising in this new LES formulation, a novel form of scale-similar SGS model is proposed and combined with a classical eddy viscosity term. The constants in the resulting mixed model are then computed trough a new, cheaper, dynamic procedure based on a consistent redefinition of the Germano identity within the new LES framework. The dynamic mixed model is implemented in a commercial, unstructured, finite volume solver and numerical tests are performed on the turbulent pipe flow at Reτ = 320-1142, showing the flexibility and improvements of the approach over classical modeling strategies. Some limitations of the proposed implementation are also highlighted.
NASA Technical Reports Server (NTRS)
Senocak, I.; Ackerman, A. S.; Kirkpatrick, M. P.; Stevens, D. E.; Mansour, N. N.
2004-01-01
Large-eddy simulation (LES) is a widely used technique in armospheric modeling research. In LES, large, unsteady, three dimensional structures are resolved and small structures that are not resolved on the computational grid are modeled. A filtering operation is applied to distinguish between resolved and unresolved scales. We present two near-surface models that have found use in atmospheric modeling. We also suggest a simpler eddy viscosity model that adopts Prandtl's mixing length model (Prandtl 1925) in the vicinity of the surface and blends with the dynamic Smagotinsky model (Germano et al, 1991) away from the surface. We evaluate the performance of these surface models by simulating a neutraly stratified atmospheric boundary layer.
Multicloning and Multibroadcasting in Operator Algebras
NASA Astrophysics Data System (ADS)
Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej
2015-12-01
We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.
On Realization of Generalized Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan
2012-12-01
A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G(H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G(H) possesses an order determining set of generalized states.
NASA Astrophysics Data System (ADS)
Chajda, Ivan
2014-10-01
Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11-21, 2007) showing that they can be considered as structures essentially weaker than semilattices but still with certain involutions in sections. The aim of this paper is to involve a similar approach for BCI-algebras.
Difficulties in initial algebra learning in Indonesia
NASA Astrophysics Data System (ADS)
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-12-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.
Literal algebra for satellite dynamics. [perturbation analysis
NASA Technical Reports Server (NTRS)
Gaposchkin, E. M.
1975-01-01
A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.
Entanglement and algebraic independence in fermion systems
NASA Astrophysics Data System (ADS)
Benatti, Fabio; Floreanini, Roberto
2014-04-01
In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence.
Comparison of characteristics of hydrographic structures in Aleutian eddies
NASA Astrophysics Data System (ADS)
Saito, R.; Yasuda, I.; Komatsu, K.; Ishiyama, H.; Ueno, H.; Onishi, H.; Setou, T.; Shimizu, M.
2014-12-01
Mesoscale anticylonic eddies formed in the Alaskan Stream region south of the Aleutian Islands between the 180° meridian and about 170°E are called Aleutian eddies. Many of these eddies propagate in the southwestward direction, and often reach western subarctic gyre. The objective of present study is to compare hydrographic structures of three Aleutian eddies with distinctive propagation paths and evaluate potential impacts of physical environment along the paths on those eddies. We observed three eddies during the summers of 2010 and 2012, in which two of the eddies (A and C) were observed west of 172°E and one (B) east of 172°E. In each eddy, a subsurface cold dichothermal water (3.0-4.0°C) was observed to be located above a subsurface warm mesothermal water (4.0-4.5°C), and the two waters were separated by 26.5-26.6σθ isopycnals. The minimum temperature in the dichothermal water at ~26.4σθ was lower in the eddies A and C (2.8-2.9°C) than in the eddy B (3.2°C). This difference could be ascribed to eddy history of wintertime cooling and influence of warm Alaskan Stream. The Aleutian eddies were originated from the Alaskan Stream, and propagated westward after isolation from the Alaskan Stream. Winter cooling could make the dichothermal water cooler for eddies which were isolated for longer time. This is the case for the eddy A. The particle tracking experiments using the 1/10° eddy resolving ocean model called FRA-ROMS (Fisheries Research Agency of Japan) demonstrated that the water within the eddy was mostly originated from cold water around the propagation path in the early spring, suggesting continuous cooling of dichothermal water after the winter-time cooling. The eddy B stayed near the Alaskan Stream which could provide warm water to the eddy, to make less cold dichothermal water. The particle tacking experiments using FRA-ROMS confirmed that the water in the eddy was mainly originated from warm Alaskan Stream in the early spring, suggesting
The turbulent cascade of individual eddies
NASA Astrophysics Data System (ADS)
Huertas-Cerdeira, Cecilia; Lozano-Durán, Adrián; Jiménez, Javier
2014-11-01
The merging and splitting processes of Reynolds-stress carrying structures in the inertial range of scales are studied through their time-resolved evolution in channels at Reλ = 100 - 200 . Mergers and splits coexist during the whole life of the structures, and are responsible for a substantial part of their growth and decay. Each interaction involves two or more eddies and results in little overall volume loss or gain. Most of them involve a small eddy that merges with, or splits from, a significantly larger one. Accordingly, if merge and split indexes are respectively defined as the maximum number of times that a structure has merged from its birth or will split until its death, the mean eddy volume grows linearly with both indexes, suggesting an accretion process rather than a hierarchical fragmentation. However, a non-negligible number of interactions involve eddies of similar scale, with a second probability peak of the volume of the smaller parent or child at 0.3 times that of the resulting or preceding structure. Funded by the Multiflow project of the ERC.
Eddy current sensing of intermetallic composite consolidation
NASA Technical Reports Server (NTRS)
Dharmasena, Kumar P.; Wadley, Haydn N. G.
1991-01-01
A finite element method is used to explore the feasibility and optimization of a probe-type eddy current sensor for determining the thickness of plate specimens during a hot isostatic pressing cycle. The dependence of the sensor's impedance upon sample-sensor separation in the high frequency limit is calculated, and factors that maximize sensitivity to the final stages of densification are identified.
Investigations of eddy coherence in jet flows
NASA Technical Reports Server (NTRS)
Yule, A. J.
1980-01-01
In turbulent shear flow the term coherent structures refers to eddies which are both spatially coherent, i.e., large eddies, aand also temporally coherent, i.e., they retain their identities for times which are long compared with their time scales in fixed point measurements. In transitional flows, the existence of such structures is evident from flow visualizations. In many other flows, such structures are not so evident. The reasons for the existence of these two classes of flows are discussed and attention is focused upon the more difficult flows, where coherent structures are not so evident. Techniques by which the existence (or nonexistence) of such structures in these flows can be established from point measurements, are also discussed. A major problem is shown to be the need to discriminate between real losses in eddy coherence and apparent losses in coherence introduced by phase scrambling effects which 'smear' multipoint correlations. The analysis of multiprobe time dependent data in cold and reacting round turbulent jets is described and it is shown how evidence of strong eddy coherence can be extracted from data.
Large-Eddy Simulation and Multigrid Methods
Falgout,R D; Naegle,S; Wittum,G
2001-06-18
A method to simulate turbulent flows with Large-Eddy Simulation on unstructured grids is presented. Two kinds of dynamic models are used to model the unresolved scales of motion and are compared with each other on different grids. Thereby the behavior of the models is shown and additionally the feature of adaptive grid refinement is investigated. Furthermore the parallelization aspect is addressed.
Some C∗-algebras which are coronas of non-C∗-Banach algebras
NASA Astrophysics Data System (ADS)
Voiculescu, Dan-Virgil
2016-07-01
We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.
ERIC Educational Resources Information Center
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
NASA Astrophysics Data System (ADS)
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
ERIC Educational Resources Information Center
Ozgun-Koca, S. Ash
2010-01-01
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…
Methane fluxes above the Hainich forest by True Eddy Accumulation and Eddy Covariance
NASA Astrophysics Data System (ADS)
Siebicke, Lukas; Gentsch, Lydia; Knohl, Alexander
2016-04-01
Understanding the role of forests for the global methane cycle requires quantifying vegetation-atmosphere exchange of methane, however observations of turbulent methane fluxes remain scarce. Here we measured turbulent fluxes of methane (CH4) above a beech-dominated old-growth forest in the Hainich National Park, Germany, and validated three different measurement approaches: True Eddy Accumulation (TEA, closed-path laser spectroscopy), and eddy covariance (EC, open-path and closed-path laser spectroscopy, respectively). The Hainich flux tower is a long-term Fluxnet and ICOS site with turbulent fluxes and ecosystem observations spanning more than 15 years. The current study is likely the first application of True Eddy Accumulation (TEA) for the measurement of turbulent exchange of methane and one of the very few studies comparing open-path and closed-path eddy covariance (EC) setups side-by-side. We observed uptake of methane by the forest during the day (a methane sink with a maximum rate of 0.03 μmol m-2 s-1 at noon) and no or small fluxes of methane from the forest to the atmosphere at night (a methane source of typically less than 0.01 μmol m-2 s-1) based on continuous True Eddy Accumulation measurements in September 2015. First results comparing TEA to EC CO2 fluxes suggest that True Eddy Accumulation is a valid option for turbulent flux quantifications using slow response gas analysers (here CRDS laser spectroscopy, other potential techniques include mass spectroscopy). The TEA system was one order of magnitude more energy efficient compared to closed-path eddy covariance. The open-path eddy covariance setup required the least amount of user interaction but is often constrained by low signal-to-noise ratios obtained when measuring methane fluxes over forests. Closed-path eddy covariance showed good signal-to-noise ratios in the lab, however in the field it required significant amounts of user intervention in addition to a high power consumption. We conclude
NASA Astrophysics Data System (ADS)
Zhou, Fang; Ren, Hong-Li; Xu, Xiao-Feng; Zhou, You
2016-08-01
In the upper troposphere during winter, positive synoptic eddy (SE) feedback plays an indispensible role in maintaining the Pacific-North American (PNA) pattern that dominates climate variability on inter-annual timescales over the North Pacific and downstream regions. This study shows that the eddy forcing, induced by eddy-vorticity (EV) fluxes, is not only in-phase with, but also downstream to the PNA pattern in terms of its northeast Pacific lobe. We employ the eddy structure decomposition method to understand such an observed PNA-SEs feedback, and propose a kinematic mechanism that can depict dynamical processes associated with the eddy structure change and its induced positive eddy feedback relative to the PNA flow pattern. With this method, the winter-mean PNA-related SE structures are separated into climatological (basic) and anomalous SE structures, and these two parts can be used to represent the changes in SE structure in a statistical sense and then to calculate the EV fluxes in order to further elucidate the feedback mechanism. It is demonstrated that, on one hand, the winter-mean PNA flow tends to systematically deform the structures of SEs and induce anomalous EV fluxes, and these winter-mean EV fluxes primarily converge into the PNA cyclonic center, which, in return enhances the PNA flow. On the other hand, the PNA-related northeast Pacific flow is featured by a stronger zonal wind shear in the east than the west, which can induce larger zonal-slanting eddy structure change and then stronger meridional EV fluxes that converge to form downstream feedback. This kinematic mechanism may help to deeply understand the dynamical eddy feedback between the low-frequency PNA flow and high-frequency SEs.
On the similarity of variable viscosity flows
NASA Astrophysics Data System (ADS)
Voivenel, L.; Danaila, L.; Varea, E.; Renou, B.; Cazalens, M.
2016-08-01
Turbulent mixing is ubiquitous in both nature and industrial applications. Most of them concern different fluids, therefore with variable physical properties (density and/or viscosity). The focus here is on variable viscosity flows and mixing, involving density-matched fluids. The issue is whether or not these flows may be self-similar, or self-preserving. The importance of this question stands on the predictability of these flows; self-similar dynamical systems are easier tractable from an analytical viewpoint. More specifically, self-similar analysis is applied to the scale-by-scale energy transport equations, which represent the transport of energy at each scale and each point of the flow. Scale-by-scale energy budget equations are developed for inhomogeneous and anisotropic flows, in which the viscosity varies as a result of heterogeneous mixture or temperature variations. Additional terms are highlighted, accounting for the viscosity gradients, or fluctuations. These terms are present at both small and large scales, thus rectifying the common belief that viscosity is a small-scale quantity. Scale-by-scale energy budget equations are then adapted for the particular case of a round jet evolving in a more viscous host fluid. It is further shown that the condition of self-preservation is not necessarily satisfied in variable-viscosity jets. Indeed, the jet momentum conservation, as well as the constancy of the Reynolds number in the central region of the jet, cannot be satisfied simultaneously. This points to the necessity of considering less stringent conditions (with respect to classical, single-fluid jets) when analytically tackling these flows and reinforces the idea that viscosity variations must be accounted for when modelling these flows.
Viscosity of Xenon Examined in Microgravity
NASA Technical Reports Server (NTRS)
Zimmerli, Gregory A.; Berg, Robert F.; Moldover, Michael R.
1999-01-01
Why does water flow faster than honey? The short answer, that honey has a greater viscosity, merely rephrases the question. The fundamental answer is that viscosity originates in the interactions between a fluid s molecules. These interactions are so complicated that, except for low-density gases, the viscosity of a fluid cannot be accurately predicted. Progress in understanding viscosity has been made by studying moderately dense gases and, more recently, fluids near the critical point. Modern theories predict a universal behavior for all pure fluids near the liquid-vapor critical point, and they relate the increase in viscosity to spontaneous fluctuations in density near this point. The Critical Viscosity of Xenon (CVX) experiment tested these theories with unprecedented precision when it flew aboard the Space Shuttle Discovery (STS-85) in August 1997. Near the critical point, xenon is a billion times more compressible than water, yet it has about the same density. Because the fluid is so "soft," it collapses under its own weight when exposed to the force of Earth s gravity - much like a very soft spring. Because the CVX experiment is conducted in microgravity, it achieves a very uniform fluid density even very close to the critical point. At the heart of the CVX experiment is a novel viscometer built around a small nickel screen. An oscillating electric field forces the screen to oscillate between pairs of electrodes. Viscosity, which dampens the oscillations, can be calculated by measuring the screen motion and the force applied to the screen. So that the fluid s delicate state near the critical point will not be disrupted, the screen oscillations are set to be both slow and small.
Obituary: John Allen Eddy (1931-2009)
NASA Astrophysics Data System (ADS)
Gingerich, Owen
2011-12-01
Jack Eddy, who was born 25 March 1931 in Pawnee City in southeastern Nebraska, died after a long battle with cancer in Tucson, Arizona, on 10 June 2009. Best known for his work on the long-term instability of the sun, described in a landmark paper in Science titled "The Maunder Minimum," he also deserves recognition as one of the triumvirate who founded the Historical Astronomy Division of the AAS. His father ran a cooperative farm store where Jack worked as a teenager; his parents were of modest means and there were concerns whether he could afford college, but one of the state senators, also from Pawnee City, nominated him for the U.S. Naval Academy. A course in celestial navigation gave him a love of the sky. After graduation in 1953, he served four years on aircraft carriers in the Pacific during the Korean War and then as a navigator and operations officer on a destroyer in the Persian Gulf. In 1957, he left the Navy and entered graduate school at the University of Colorado in Boulder, where in 1962 he received a Ph.D. in astro-geophysics. His thesis, supervised by Gordon Newkirk, dealt with light scattering in the upper atmosphere, based on data from stratospheric balloon flights. He then worked as teacher and researcher at the High Altitude Observatory in Boulder. Always adventuresome and willing to explore new frontiers, on his own time Eddy examined an Amerindian stone circle in the Big Horn mountains of Wyoming, a so-called medicine wheel, concluding that there were alignments with both the solstitial sun and Aldebaran. His conjectures became a cover story on Science magazine in June of 1974. In 1971 Jack privately reproduced for his friends a small collection of his own hilarious cartoons titled "Job Opportunities for Out-of-work Astronomers," with an abstract beginning, "Contrary to popular belief, a PhD in Astronomy/Astrophysics need not be a drawback in locating work in this decade." For example, under merchandising, a used car salesman advertises
Cluster automorphism groups of cluster algebras with coefficients
NASA Astrophysics Data System (ADS)
Chang, Wen; Zhu, Bin
2016-10-01
We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e. the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.
The Structure of Parafermion Vertex Operator Algebras: General Case
NASA Astrophysics Data System (ADS)
Dong, Chongying; Wang, Qing
2010-11-01
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
Gene algebra from a genetic code algebraic structure.
Sanchez, R; Morgado, E; Grau, R
2005-10-01
By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z(64), +) of the integer module 64. On the Z(64)-algebra of the set of 64(N) codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z(64))(N)-->(Z(64))(N). Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z(64)-algebra will help us explain the quantitative relationships between genes.
Dirac matrices as elements of a superalgebraic matrix algebra
NASA Astrophysics Data System (ADS)
Monakhov, V. V.
2016-08-01
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix algebra exists in this algebra, the Clifford exten-sion of the Grassmann algebra is a generalization of the matrix algebra and contains superalgebraic operators expanding matrix algebra and produces supersymmetric transformations.
Automated Angular Momentum Recoupling Algebra
NASA Astrophysics Data System (ADS)
Williams, H. T.; Silbar, Richard R.
1992-04-01
We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.
Viscosity Measurement Using Drop Coalescence in Microgravity
NASA Technical Reports Server (NTRS)
Antar, Basil N.; Ethridge, Edwin C.; Maxwell, Daniel; Curreri, Peter A. (Technical Monitor)
2002-01-01
We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.
Predicting slag viscosity from coal ash composition
Laumb, J.; Benson, S.A.; Katrinak, K.A.; Schwalbe, R.; McCollor, D.P.
1999-07-01
Management of slag flow from cyclone-fired utility boilers requires accurate prediction of viscosity. Cyclones tend to build up slag when the cyclone combustion temperature is less than the temperature required to melt and tap the ash from the coal being fired. Cyclone-fired boilers designed for lignite are equipped with predry systems, which remove 6-9% of the moisture from the coal. Cyclones tend to slag when the as-received heating value of the fuel is less than 6350 Btu/lb and T250 (temperature where viscosity equals 250 poise) is greater than 2350 F. The T250 value, as well as the rest of the viscosity-temperature relationship, can be predicted using models based on coal ash composition. The focus of this work is to evaluate several models in terms of their agreement with measured viscosities. Viscosity measurements were made for ten samples, including nine lignite coals and one lignite-derived slag. Model performance is related to the SiO{sub 2}, CaO, and Fe{sub 2}O{sub 3} contents of the slag. The Sage and McIlroy and Kalmanovitch models worked best for high SiO{sub 2} and low Fe{sub 2}O{sub 3} fuels. The Senior model worked best when Fe{sub 2}O{sub 3} content was moderate to high.
Viscosity of confined inhomogeneous nonequilibrium fluids
NASA Astrophysics Data System (ADS)
Zhang, Junfang; Todd, B. D.; Travis, Karl P.
2004-12-01
We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.
Effect of viscosity on learned satiation.
Mars, M; Hogenkamp, P S; Gosses, A M; Stafleu, A; De Graaf, C
2009-08-01
A higher viscosity of a food leads to a longer orosensory stimulation. This may facilitate the learned association between sensory signals and metabolic consequences. In the current study we investigated the effect of viscosity on learned satiation. In two intervention groups a low viscosity (LV) yogurt (n=24) and a high viscosity (HV) yogurt (n=22) was offered ad libitum for breakfast. In a learning period of 4 weeks, subjects consumed ad libitum a novel flavoured high energy density (HED) yogurt (150 kcal/100 g) or low energy density (LED) yogurt (50 kcal/100 g), with 10 exposures to each yogurt on alternate days. Over the repeated exposures, an interaction effect of exposure timeenergyviscosity on intake was seen (F(1,771)=4.12; p=0.04). In the HV intervention group a borderline significant interaction between exposure and energy density was observed (F(1,369)=3.61; p=0.06); after 10 exposures, the LED yogurt resulted in a 46+/-16 g higher intake compared with the HED yogurt. In the LV group, no significant interaction between exposure and energy density was seen (F(1,401)=1.04; p=0.31); after 10 exposures intake difference between the LED and HED yogurts was only 1.5+/-15 g. These results suggest that a higher viscosity facilitates learned satiation.
Entropy viscosity method applied to Euler equations
Delchini, M. O.; Ragusa, J. C.; Berry, R. A.
2013-07-01
The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)
Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras
NASA Astrophysics Data System (ADS)
Ondrus, Matthew; Wiesner, Emilie
2016-07-01
This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.
Projected changes to Tasman Sea eddies in a future climate
NASA Astrophysics Data System (ADS)
Oliver, Eric C. J.; O'Kane, Terence J.; Holbrook, Neil J.
2015-11-01
The Tasman Sea is a hot spot of ocean warming, that is linked to the increased poleward influence of the East Australian Current (EAC) over recent decades. Specifically, the EAC produces mesoscale eddies which have significant impacts on the physical, chemical, and biological properties of the Tasman Sea. To effectively consider and explain potential eddy changes in the next 50 years, we use high-resolution dynamically downscaled climate change simulations to characterize the projected future marine climate and mesoscale eddies in the Tasman Sea through the 2060s. We assess changes in the marine climate and the eddy field using bulk statistics and by detecting and tracking individual eddies. We find that the eddy kinetic energy is projected to increase along southeast Australia. In addition, we find that eddies in the projected future climate are composed of a higher proportion of anticyclonic eddies in this region and that these eddies are longer lived and more stable. This amounts to nearly a doubling of eddy-related southward temperature transport in the upper 200 m of the Tasman Sea. These changes are concurrent with increases in baroclinic and barotropic instabilities focused around the EAC separation point. This poleward transport and increase in eddy activity would be expected to also increase the frequency of sudden warming events, including ocean temperature extremes, with potential impacts on marine fisheries, aquaculture, and biodiversity off Tasmania's east coast, through direct warming or competition/predation from invasive migrating species.
A True Eddy Accumulation - Eddy Covariance hybrid for measurements of turbulent trace gas fluxes
NASA Astrophysics Data System (ADS)
Siebicke, Lukas
2016-04-01
Eddy covariance (EC) is state-of-the-art in directly and continuously measuring turbulent fluxes of carbon dioxide and water vapor. However, low signal-to-noise ratios, high flow rates and missing or complex gas analyzers limit it's application to few scalars. True eddy accumulation, based on conditional sampling ideas by Desjardins in 1972, requires no fast response analyzers and is therefore potentially applicable to a wider range of scalars. Recently we showed possibly the first successful implementation of True Eddy Accumulation (TEA) measuring net ecosystem exchange of carbon dioxide of a grassland. However, most accumulation systems share the complexity of having to store discrete air samples in physical containers representing entire flux averaging intervals. The current study investigates merging principles of eddy accumulation and eddy covariance, which we here refer to as "true eddy accumulation in transient mode" (TEA-TM). This direct flux method TEA-TM combines true eddy accumulation with continuous sampling. The TEA-TM setup is simpler than discrete accumulation methods while avoiding the need for fast response gas analyzers and high flow rates required for EC. We implemented the proposed TEA-TM method and measured fluxes of carbon dioxide (CO2), methane (CH4) and water vapor (H2O) above a mixed beech forest at the Hainich Fluxnet and ICOS site, Germany, using a G2301 laser spectrometer (Picarro Inc., USA). We further simulated a TEA-TM sampling system using measured high frequency CO2 time series from an open-path gas analyzer. We operated TEA-TM side-by-side with open-, enclosed- and closed-path EC flux systems for CO2, H2O and CH4 (LI-7500, LI-7200, LI-6262, LI-7700, Licor, USA, and FGGA LGR, USA). First results show that TEA-TM CO2 fluxes were similar to EC fluxes. Remaining differences were similar to those between the three eddy covariance setups (open-, enclosed- and closed-path gas analyzers). Measured TEA-TM CO2 fluxes from our physical
Biogeochemical properties of eddies in the California Current System
NASA Astrophysics Data System (ADS)
Chenillat, Fanny; Franks, Peter J. S.; Combes, Vincent
2016-06-01
The California Current System (CCS) has intense mesoscale activity that modulates and exports biological production from the coastal upwelling system. To characterize and quantify the ability of mesoscale eddies to affect the local and regional planktonic ecosystem of the CCS, we analyzed a 10 year-long physical-biological model simulation, using eddy detection and tracking to isolate the dynamics of cyclonic and anticyclonic eddies. As they propagate westward across the shelf, cyclonic eddies efficiently transport coastal planktonic organisms and maintain locally elevated production for up to 1 year (800 km offshore). Anticyclonic eddies, on the other hand, have a limited impact on local production over their ~6 month lifetime as they propagate 400 km offshore. At any given time ~8% of the model domain was covered by eddy cores. Though the eddies cover a small area, they explain ~50 and 20% of the transport of nitrate and plankton, respectively.
Do East Australian Current anticyclonic eddies leave the Tasman Sea?
NASA Astrophysics Data System (ADS)
Pilo, Gabriela S.; Oke, Peter R.; Rykova, Tatiana; Coleman, Richard; Ridgway, Ken
2015-12-01
Using satellite altimetry and high-resolution model output we analyze the pathway of large, long-lived anticyclonic eddies that originate near the East Australian Current (EAC) separation point. We show that 25-30% of these eddies propagate southward, around Tasmania, leave the Tasman Sea, and decay in the Great Australian Bight. This pathway has not been previously documented owing to poor satellite sampling off eastern Tasmania. As eddies propagate southward, they often "stall" for several months at near-constant latitude. Along the pathway eddies become increasingly barotropic. Eddy intensity is primarily influenced by merging with other eddies and a gradual decay otherwise. Surface temperature anomaly associated with anticyclonic eddies changes as they propagate, while surface salinity anomaly tends to remain relatively unchanged as they propagate.
Abrous, A.; Emery, A.F.
1995-12-31
The steady-state, buoyancy-driven flow of an incompressible fluid with temperature dependent viscosity within a square enclosure is solved numerically and the results are presented. The benchmark problem`s geometrical and mathematical descriptions adopted herein are those specified by the AdHoc Committee of Computational Heat Transfer which is compiling different solutions for this benchmark problem in heat transfer analysis. The objective is to compare solutions computed with several different algorithmic approaches for a problem having a large variation in fluid viscosity, characteristic of modeling turbulent flows with eddy diffusivity concepts. The results of the present analysis are submitted as a contribution to this comparison exercise that has for objective the assessment of the numerical accuracy of modeling the diffusion terms in the conservation equations with variable property.
Algebraic Thinking through Koch Snowflake Constructions
ERIC Educational Resources Information Center
Ghosh, Jonaki B.
2016-01-01
Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…
Investigating Algebraic Procedures Using Discussion and Writing
ERIC Educational Resources Information Center
Harper, Jonathan; Ford, Jeffrey
2012-01-01
This study reports on the implementation of an intermediate algebra curriculum centered on a framework of student-centered questions designed to investigate algebraic procedures. Instructional activities were designed to build discourse in the small-group discussion meetings of the course. Students were assigned writing prompts to emphasize the…
Practicing Algebraic Skills: A Conceptual Approach
ERIC Educational Resources Information Center
Friedlander, Alex; Arcavi, Abraham
2012-01-01
Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…
Using Students' Interests as Algebraic Models
ERIC Educational Resources Information Center
Whaley, Kenneth A.
2012-01-01
Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…
THE RADICAL OF A JORDAN ALGEBRA
McCrimmon, Kevin
1969-01-01
In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Situated Learning in an Abstract Algebra Classroom
ERIC Educational Resources Information Center
Ticknor, Cindy S.
2012-01-01
Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content…
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Predicting Turkish Ninth Grade Students' Algebra Performance
ERIC Educational Resources Information Center
Erbas, Ayhan Kursat
2005-01-01
The prediction of students' achievement in algebra in eighth and ninth grades has become a research interest for practical issues of placement. A group of simple, easily accessible variables was used to predict student performance in algebra after completion of eighth grade. The three variables of school type, grade level, and previous year…
Success in Algebra among Community College Students
ERIC Educational Resources Information Center
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
Calif. Laws Shift Gears on Algebra, Textbooks
ERIC Educational Resources Information Center
Robelen, Erik W.
2012-01-01
New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…
How To Prepare Students for Algebra.
ERIC Educational Resources Information Center
Wu, H.
2001-01-01
Suggests that no matter how much algebraic thinking is introduced in the early grades, and no matter how worthwhile this might be, the failure rate in algebra will continue unless the teaching of fractions and decimals is radically revamped. The proper study of fractions provides a ramp that leads students gently from whole number arithmetic up to…
Using the Internet To Investigate Algebra.
ERIC Educational Resources Information Center
Sherwood, Walter
The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…
New directions in algebraic dynamical systems
NASA Astrophysics Data System (ADS)
Schmidt, Klaus; Verbitskiy, Evgeny
2011-02-01
The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.
Classical and quantum Kummer shape algebras
NASA Astrophysics Data System (ADS)
Odzijewicz, A.; Wawreniuk, E.
2016-07-01
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.
Fourier theory and C∗-algebras
NASA Astrophysics Data System (ADS)
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Teaching Algebra to Students with Learning Disabilities
ERIC Educational Resources Information Center
Impecoven-Lind, Linda S.; Foegen, Anne
2010-01-01
Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…
Arithmetic and Cognitive Contributions to Algebra
ERIC Educational Resources Information Center
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
Just Say Yes to Early Algebra!
ERIC Educational Resources Information Center
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy
2015-01-01
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
An Inquiry-Based Linear Algebra Class
ERIC Educational Resources Information Center
Wang, Haohao; Posey, Lisa
2011-01-01
Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Algebraic Geodesics on Three-Dimensional Quadrics
NASA Astrophysics Data System (ADS)
Kai, Yue
2015-12-01
By Hamilton-Jacobi method, we study the problem of algebraic geodesics on the third-order surface. By the implicit function theorem, we proved the existences of the real geodesics which are the intersections of two algebraic surfaces, and we also give some numerical examples.
ERIC Educational Resources Information Center
Rickard, Caroline
2008-01-01
Shortly after starting work for the University of Chichester in the School of Teacher Education, the author was planning a session relating to algebra and found herself inspired by an article in MT182: "Algebraic Infants" by Andrews and Sayers (2003). Based on the making of families of "Multilink" animals, Andrews and Sayers (2003) claim that…
Focus on Fractions to Scaffold Algebra
ERIC Educational Resources Information Center
Ooten, Cheryl Thomas
2013-01-01
Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…
A Technology-Intensive Approach to Algebra.
ERIC Educational Resources Information Center
Heid, M. Kathleen; Zbiek, Rose Mary
1995-01-01
Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)
Modern Algebra, Mathematics: 5293.36.
ERIC Educational Resources Information Center
Edwards, Raymond J.
This guidebook covers Boolean algebra, matrices, linear transformations of the plane, characteristic values, vectors, and algebraic structures. Overall course goals and performance objectives for each unit are specified; sequencing of units and various time schedules are suggested. A sample pretest and posttest are given, and an annotated list of…
Teaching Modeling and Axiomatization with Boolean Algebra.
ERIC Educational Resources Information Center
De Villiers, Michael D.
1987-01-01
Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)
Diffusion, Viscosity and Crystal Growth in Microgravity
NASA Technical Reports Server (NTRS)
Myerson, Allan S.
1996-01-01
The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.
Viscosity jump in Earth's mid-mantle.
Rudolph, Maxwell L; Lekić, Vedran; Lithgow-Bertelloni, Carolina
2015-12-11
The viscosity structure of Earth's deep mantle affects the thermal evolution of Earth, the ascent of mantle plumes, settling of subducted oceanic lithosphere, and the mixing of compositional heterogeneities in the mantle. Based on a reanalysis of the long-wavelength nonhydrostatic geoid, we infer viscous layering of the mantle using a method that allows us to avoid a priori assumptions about its variation with depth. We detect an increase in viscosity at 800- to 1200-kilometers depth, far greater than the depth of the mineral phase transformations that define the mantle transition zone. The viscosity increase is coincident in depth with regions where seismic tomography has imaged slab stagnation, plume deflection, and changes in large-scale structure and offers a simple explanation of these phenomena.
Polyfunctional dispersants for controlling viscosity of phyllosilicates
Chaiko, David J.
2006-07-25
This invention provides phyllosilicates and polyfunctional dispersants which can be manipulated to selectively control the viscosity of phyllosilicate slurries. The polyfunctional dispersants used in the present invention, which include at least three functional groups, increase the dispersion and exfoliation of phyllosilicates in polymers and, when used in conjunction with phyllosilicate slurries, significantly reduce the viscosity of slurries having high concentrations of phyllosilicates. The functional groups of the polyfunctional dispersants are capable of associating with multivalent metal cations and low molecular weight organic polymers, which can be manipulated to substantially increase or decrease the viscosity of the slurry in a concentration dependent manner. The polyfunctional dispersants of the present invention can also impart desirable properties on the phyllosilicate dispersions including corrosion inhibition and enhanced exfoliation of the phyllosilicate platelets.
Viscosity near Earth's solid inner core
Smylie
1999-04-16
Anomalous splitting of the two equatorial translational modes of oscillation of Earth's solid inner core is used to estimate the effective viscosity just outside its boundary. Superconducting gravimeter observations give periods of 3.5822 +/- 0.0012 (retrograde) and 4.0150 +/- 0.0010 (prograde) hours. With the use of Ekman layer theory to estimate viscous drag forces, an inferred single viscosity of 1.22 x 10(11) Pascal seconds gives calculated periods of 3.5839 and 4.0167 hours for the two modes, close to the observed values. The large effective viscosity is consistent with a fluid, solid-liquid mixture surrounding the inner core associated with the "compositional convection" that drives Earth's geodynamo. PMID:10205048
Viscosity of Fluids in Subduction Zones
NASA Astrophysics Data System (ADS)
Audétat, Andreas; Keppler, Hans
2004-01-01
The viscosities of aqueous fluids with 10 to 80 weight percent dissolved silicates have been measured at 600° to 950°C and 1.0 to 2.0 gigapascals by in situ observation of falling spheres in the diamond anvil cell. The viscosities at 800°C range from 10-4 to 100.5 pascal seconds. The combination of low viscosities with a favorable wetting angle makes silicate-rich fluid an efficient agent for material transport at low-volume fractions. Our results therefore suggest that there may be a direct relationship between the position of the volcanic front and the onset of complete miscibility between water and silicate melt in the subducting slab.
Viscosity of fluids in subduction zones.
Audétat, Andreas; Keppler, Hans
2004-01-23
The viscosities of aqueous fluids with 10 to 80 weight percent dissolved silicates have been measured at 600 degrees to 950 degrees C and 1.0 to 2.0 gigapascals by in situ observation of falling spheres in the diamond anvil cell. The viscosities at 800 degrees C range from 10(-4) to 10(0.5) pascal seconds. The combination of low viscosities with a favorable wetting angle makes silicate-rich fluid an efficient agent for material transport at low-volume fractions. Our results therefore suggest that there may be a direct relationship between the position of the volcanic front and the onset of complete miscibility between water and silicate melt in the subducting slab. PMID:14739456
MODEL IDENTIFICATION AND COMPUTER ALGEBRA
Bollen, Kenneth A.; Bauldry, Shawn
2011-01-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.
Towards a consistent eddy-covariance processing: an intercomparison of EddyPro and TK3
NASA Astrophysics Data System (ADS)
Fratini, G.; Mauder, M.
2014-07-01
A comparison of two popular eddy-covariance software packages is presented, namely, EddyPro and TK3. Two approximately 1-month long test data sets were processed, representing typical instrumental setups (i.e., CSAT3/LI-7500 above grassland and Solent R3/LI-6262 above a forest). The resulting fluxes and quality flags were compared. Achieving a satisfying agreement and understanding residual discrepancies required several iterations and interventions of different nature, spanning from simple software reconfiguration to actual code manipulations. In this paper, we document our comparison exercise and show that the two software packages can provide utterly satisfying agreement when properly configured. Our main aim, however, is to stress the complexity of performing a rigorous comparison of eddy-covariance software. We show that discriminating actual discrepancies in the results from inconsistencies in the software configuration requires deep knowledge of both software packages and of the eddy-covariance method. In some instances, it may be even beyond the possibility of the investigator who does not have access to and full knowledge of the source code. Being the developers of EddyPro and TK3, we could discuss the comparison at all levels of details and this proved necessary to achieve a full understanding. As a result, we suggest that researchers are more likely to get comparable results when using EddyPro (v5.1.1) and TK3 (v3.11) - at least with the setting presented in this paper - than they are when using any other pair of EC software which did not undergo a similar cross-validation. As a further consequence, we also suggest that, to the aim of assuring consistency and comparability of centralized flux databases, and for a confident use of eddy fluxes in synthesis studies on the regional, continental and global scale, researchers only rely on software that have been extensively validated in documented intercomparisons.
NASA Technical Reports Server (NTRS)
Young, Richard E.
1986-01-01
The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.
Generalized correlation for viscosity of binary eutectics
Sharma, S.K.; Wanchoo, R.K.; Gupta, R.; Jotshi, C.K.
1995-12-31
Heat and mass transfer plays an important role during phase transformation process involving phase change materials. These processes are greatly influenced by thermophysical properties of the material, such as, viscosity, density, thermal conductivity, etc. Viscosity is one of the prime factors which controls the crystal growth rate during crystallization/cooling process of the phase change material. It directs the movement of convection currents arising due to concentration gradient, near the interface of the growing crystal. Eutectics are the compounds having sharp transition temperatures corresponding to specific composition and do not suffer from phase segregation, a major problem in incongruent and semi-congruent melting salt hydrates. The viscometric behavior of the following five binary eutectics in the temperature range of 313--363 K has been studied: Mg(NO{sub 3}){sub 2}{center_dot}6H{sub 2}O-NH{sub 4}NO{sub 3}; MgNO{sub 3}{center_dot}6H{sub 2}O-MgCl{sub 2}{center_dot}6H{sub 2}O; CO(NH{sub 2}){sub 2}-NH{sub 4}NO{sub 3}; CO(NH{sub 2}){sub 2}-NH{sub 4}Br and CH{sub 3}CONH{sub 2}-NaBr. An empirical correlation between reduced viscosity and reduced temperature for molten binary eutectics showing Arrhenius behavior above their melting points has been reported. The correlation predicts the temperature dependence of the eutectic viscosity to within {+-}6. Consistency tests for viscosity data using reduced parameters have been reported. The empirical correlation developed from this study predicts very well, the viscosity of the molten eutectics and salt hydrates to within {+-}6% of the experimental values.
Viscosity Meaurement Technique for Metal Fuels
Ban, Heng; Kennedy, Rory
2015-02-09
Metallic fuels have exceptional transient behavior, excellent thermal conductivity, and a more straightforward reprocessing path, which does not separate out pure plutonium from the process stream. Fabrication of fuel containing minor actinides and rare earth (RE) elements for irradiation tests, for instance, U-20Pu-3Am-2Np-1.0RE-15Zr samples at the Idaho National Laboratory, is generally done by melt casting in an inert atmosphere. For the design of a casting system and further scale up development, computational modeling of the casting process is needed to provide information on melt flow and solidification for process optimization. Therefore, there is a need for melt viscosity data, the most important melt property that controls the melt flow. The goal of the project was to develop a measurement technique that uses fully sealed melt sample with no Americium vapor loss to determine the viscosity of metallic melts and at temperatures relevant to the casting process. The specific objectives of the project were to: develop mathematical models to establish the principle of the measurement method, design and build a viscosity measurement prototype system based on the established principle, and calibrate the system and quantify the uncertainty range. The result of the project indicates that the oscillation cup technique is applicable for melt viscosity measurement. Detailed mathematical models of innovative sample ampoule designs were developed to not only determine melt viscosity, but also melt density under certain designs. Measurement uncertainties were analyzed and quantified. The result of this project can be used as the initial step toward the eventual goal of establishing a viscosity measurement system for radioactive melts.
Slim accretion discs with different viscosity prescriptions
NASA Astrophysics Data System (ADS)
Szuszkiewicz, Ewa
1990-05-01
The variability of X-ray sources powered by accretion may be connected to thermal instabilities in the innermost parts of slim disks. The time-scales of variability predicted by the theory with the standard alpha-viscosity prescription agree with those observed in a wide range of sources. The amplitudes (3-4 orders of magnitude in luiminosity) are correctly predicted for X-ray transient sources, but in general are too big for quasars, Seyferts, galactic blackhole candidates and LMXBs. It is shown that a slight modification of the viscosity prescription can offer a much better agreement with observations.
Apparatus and method for measuring viscosity
Murphy, R.J. Jr.
1986-02-25
The present invention is directed to an apparatus and method for measuring the viscosity of a fluid. This apparatus and method is particularly useful for the measurement of the viscosity of a liquid in a harsh environment characterized by high temperature and the presence of corrosive or deleterious gases and vapors which adversely affect conventional ball or roller bearings. The apparatus and method of the present invention employ one or more flexural or torsional bearings to suspend a bob capable of limited angular motion within a rotatable sleeve suspended from a stationary frame. 7 figs.
Apparatus and method for measuring viscosity
Murphy, Jr., Robert J.
1986-01-01
The present invention is directed to an apparatus and method for measuring the viscosity of a fluid. This apparatus and method is particularly useful for the measurement of the viscosity of a liquid in a harsh environment characterized by high temperature and the presence of corrosive or deleterious gases and vapors which adversely affect conventional ball or roller bearings. The apparatus and method of the present invention employ one or more flexural or torsional bearings to suspend a bob capable of limited angular motion within a rotatable sleeve suspended from a stationary frame.
Viscosity of a nanoconfined liquid during compression
Khan, Shah H.; Kramkowski, Edward L.; Ochs, Peter J.; Wilson, David M.; Hoffmann, Peter M.
2014-01-13
The viscous behavior of liquids under nanoconfinement is not well understood. Using a small-amplitude atomic force microscope, we found bulk-like viscosity in a nanoconfined, weakly interacting liquid. A further decrease in viscosity was observed at confinement sizes of a just few molecular layers. Overlaid over the continuum viscous behavior, we measured non-continuum stiffness and damping oscillations. The average stiffness of the confined liquid was found to scale linearly with the size of the confining tip, while the damping scales with the radius of curvature of the tip end.
Shear viscosity coefficient of liquid lanthanides
Patel, H. P. Thakor, P. B. Prajapati, A. V.; Sonvane, Y. A.
2015-05-15
Present paper deals with the computation of shear viscosity coefficient (η) of liquid lanthanides. The effective pair potential v(r) is calculated through our newly constructed model potential. The Pair distribution function g(r) is calculated from PYHS reference system. To see the influence of local field correction function, Hartree (H), Tailor (T) and Sarkar et al (S) local field correction function are used. Present results are compared with available experimental as well as theoretical data. Lastly, we found that our newly constructed model potential successfully explains the shear viscosity coefficient (η) of liquid lanthanides.
Measuring Viscosities of Gases at Atmospheric Pressure
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Mall, Gerald H.; Hoshang, Chegini
1987-01-01
Variant of general capillary method for measuring viscosities of unknown gases based on use of thermal mass-flowmeter section for direct measurement of pressure drops. In technique, flowmeter serves dual role, providing data for determining volume flow rates and serving as well-characterized capillary-tube section for measurement of differential pressures across it. New method simple, sensitive, and adaptable for absolute or relative viscosity measurements of low-pressure gases. Suited for very complex hydrocarbon mixtures where limitations of classical theory and compositional errors make theoretical calculations less reliable.
Shear Viscosity in a Gluon Gas
Xu Zhe; Greiner, Carsten
2008-05-02
The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio {eta}/s for a gluon gas, which involves elastic gg{yields}gg perturbative QCD (PQCD) scatterings as well as inelastic gg{r_reversible}ggg PQCD bremsstrahlung. For {alpha}{sub s}=0.3 we find {eta}/s=0.13 and for {alpha}{sub s}=0.6, {eta}/s=0.076. The small {eta}/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.
Viscosity profile of the lower mantle
NASA Technical Reports Server (NTRS)
Ellsworth, K.; Schubert, G.; Sammis, C. G.
1985-01-01
The viscosity of the earth's mantle is an important factor in studies of mantle convection and other problems in geodynamics. The present investigation is concerned with a determination of the variation of effective viscosity across the lower mantle from models of the Gibb's free energy of activation G(asterisk) and the adiabatic temperature profile. The variation of G(asterisk) with depth is calculated using both an elastic strain energy model, in which G(asterisk) is related to the seismic velocities, and a model which assumes G(asterisk) is proportional to the melting temperature.
A Theory of Solvation Effects on Viscosity
NASA Astrophysics Data System (ADS)
Yamakita, Tomofumi; Yoshimori, Akira
2015-04-01
We formulate a theory for calculating the viscosity of a dilute solution, considering the solute-solvent interaction. We consider an inhomogeneous density distribution of solvent particles caused by the interaction, using the equilibrium solute-solvent radial distribution function. The theory is a microscopic extension of Einstein's viscosity formula. We formulate the theory by a perturbation expansion, assuming that a solvent particle is much smaller than a solute particle. From the perturbation theory, we obtain hydrodynamic equations with new boundary conditions on the surface of the solute. The theory is applied to a system with a simple radial distribution function.
Shock capturing by the spectral viscosity method
NASA Technical Reports Server (NTRS)
Tadmor, Eitan
1989-01-01
A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.
Shear viscosity of a unitary Fermi gas.
Wlazłowski, Gabriel; Magierski, Piotr; Drut, Joaquín E
2012-07-13
We present an ab initio determination of the shear viscosity η of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio η/s. The minimum of η/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being (η/s)min≈0.2ℏ/k(B), which is close the Kovtun-Son-Starinets universal value ℏ/(4πk(B)).
Shear viscosity in a gluon gas.
Xu, Zhe; Greiner, Carsten
2008-05-01
The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio eta/s for a gluon gas, which involves elastic gg-->gg perturbative QCD (PQCD) scatterings as well as inelastic gg<-->ggg PQCD bremsstrahlung. For alpha_{s}=0.3 we find eta/s=0.13 and for alpha_{s}=0.6, eta/s=0.076. The small eta/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.
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Generalization of n-ary Nambu algebras and beyond
Ataguema, H.; Makhlouf, A.; Silvestrov, S.
2009-08-15
The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.
Oceanic mass transport by mesoscale eddies.
Zhang, Zhengguang; Wang, Wei; Qiu, Bo
2014-07-18
Oceanic transports of heat, salt, fresh water, dissolved CO2, and other tracers regulate global climate change and the distribution of natural marine resources. The time-mean ocean circulation transports fluid as a conveyor belt, but fluid parcels can also be trapped and transported discretely by migrating mesoscale eddies. By combining available satellite altimetry and Argo profiling float data, we showed that the eddy-induced zonal mass transport can reach a total meridionally integrated value of up to 30 to 40 sverdrups (Sv) (1 Sv = 10(6) cubic meters per second), and it occurs mainly in subtropical regions, where the background flows are weak. This transport is comparable in magnitude to that of the large-scale wind- and thermohaline-driven circulation. PMID:25035491
Oceanic mass transport by mesoscale eddies.
Zhang, Zhengguang; Wang, Wei; Qiu, Bo
2014-07-18
Oceanic transports of heat, salt, fresh water, dissolved CO2, and other tracers regulate global climate change and the distribution of natural marine resources. The time-mean ocean circulation transports fluid as a conveyor belt, but fluid parcels can also be trapped and transported discretely by migrating mesoscale eddies. By combining available satellite altimetry and Argo profiling float data, we showed that the eddy-induced zonal mass transport can reach a total meridionally integrated value of up to 30 to 40 sverdrups (Sv) (1 Sv = 10(6) cubic meters per second), and it occurs mainly in subtropical regions, where the background flows are weak. This transport is comparable in magnitude to that of the large-scale wind- and thermohaline-driven circulation.
Contoured Surface Eddy Current Inspection System
Batzinger, Thomas James; Fulton, James Paul; Rose, Curtis Wayne; Perocchi, Lee Cranford
2003-04-08
Eddy current inspection of a contoured surface of a workpiece is performed by forming a backing piece of flexible, resiliently yieldable material with a contoured exterior surface conforming in shape to the workpiece contoured surface. The backing piece is preferably cast in place so as to conform to the workpiece contoured surface. A flexible eddy current array probe is attached to the contoured exterior surface of the backing piece such that the probe faces the contoured surface of the workpiece to be inspected when the backing piece is disposed adjacent to the workpiece. The backing piece is then expanded volumetrically by inserting at least one shim into a slot in the backing piece to provide sufficient contact pressure between the probe and the workpiece contoured surface to enable the inspection of the workpiece contoured surface to be performed.
Eddy current signal comparison for tube identification
Glass, S. W. E-mail: Ratko.Vojvodic@areva.com; Vojvodic, R. E-mail: Ratko.Vojvodic@areva.com
2015-03-31
Inspection of nuclear power plant steam generator tubes is required to justify continued safe plant operation. The steam generators consist of thousands of tubes with nominal diameters of 15 to 22mm, approximately 1mm wall thickness, and 20 to 30m in length. The tubes are inspected by passing an eddy current probe through the tubes from tube end to tube end. It is critical to know exactly which tube identification (row and column) is associated with each tube's data. This is controlled by a precision manipulator that provides the tube ID to the eddy current system. Historically there have been some instances where the manipulator incorrectly reported the tube ID. This can have serious consequences including lack of inspection of a tube, or if a pluggable indication is detected, the tube is likely to be mis-plugged thereby risking a primary to secondary leak.
Eddy current signal comparison for tube identification
NASA Astrophysics Data System (ADS)
Glass, S. W.; Vojvodic, R.
2015-03-01
Inspection of nuclear power plant steam generator tubes is required to justify continued safe plant operation. The steam generators consist of thousands of tubes with nominal diameters of 15 to 22mm, approximately 1mm wall thickness, and 20 to 30m in length. The tubes are inspected by passing an eddy current probe through the tubes from tube end to tube end. It is critical to know exactly which tube identification (row and column) is associated with each tube's data. This is controlled by a precision manipulator that provides the tube ID to the eddy current system. Historically there have been some instances where the manipulator incorrectly reported the tube ID. This can have serious consequences including lack of inspection of a tube, or if a pluggable indication is detected, the tube is likely to be mis-plugged thereby risking a primary to secondary leak.
INNOVATIVE EDDY CURRENT PROBE FOR MICRO DEFECTS
Santos, Telmo G.; Vilaca, Pedro; Quintino, Luisa; Santos, Jorge dos; Rosado, Luis
2010-02-22
This paper reports the development of an innovative eddy current (EC) probe, and its application to micro-defects on the root of the Friction Stir Welding (FSW). The new EC probe presents innovative concept issues, allowing 3D induced current in the material, and a lift-off independence. Validation experiments were performed on aluminium alloys processed by FSW. The results clearly show that the new EC probe is able to detect and sizing surface defects about 60 microns depth.
NASA Astrophysics Data System (ADS)
Schmitt, François G.
2007-09-01
Boussinesq's hypothesis is at the heart of eddy viscosity models, which are used in many different fields to model turbulent flows. In its present time formulation, this hypothesis corresponds to an alignment between the Reynolds stress and mean strain tensors. We begin with historical remarks on Boussinesq's results and recall that he introduced a local averaging twenty years before Reynolds, but using an approach that prevented him from discovering Reynolds' stress tensor. We then introduce an indicator that characterizes the validity of this hypothesis. For experimental and numerical databases, when the tensors are known, this can be used to directly estimate the validity of this hypothesis. We show, using several different databases, that this hypothesis is almost never verified. We address, in conclusion, the analogy with kinetic theory, and the reason why this analogy cannot be applied, in general, for turbulent flows. To cite this article: F.G. Schmitt, C. R. Mecanique 335 (2007).
Interface Exchange as an Indicator for Eddy Heat Transport
Petersen, Mark R.; Williams, Sean J.; Hecht, Matthew W.; Maltrud, Mathew E.; Hamann, Bernd; Patchett, John M.; Ahrens, James P.
2012-06-12
The ocean contains many large-scale, long-lived vortices, called mesoscale eddies, that are believed to have a role in the transport and redistribution of salt, heat, and nutrients throughout the ocean. Determining this role, however, has proven to be a challenge, since the mechanics of eddies are only partly understood; a standard definition for these ocean eddies does not exist and, therefore, scientifically meaningful, robust methods for eddy extraction, characterization, tracking and visualization remain a challenge. In order to shed light on the nature and potential roles of eddies, we have combined our previous research on eddy identification and tracking, and have used those approaches as the basis for analysis-driven computational experiments on the nature of eddies. Based on the resulting visualizations of eddy behavior, we have devised a new metric to characterize the transfer of water into and out of eddies across their boundary, and have developed visualization methods for this new metric to provide clues about the role eddies play in the global ocean and, potentially, climate change.
Eddy current inspection tool. [Patent application
Petrini, R.R.; Van Lue, D.F.
1980-10-29
A miniaturized inspection tool, for testing and inspection of metal objects in locations with difficult accessibility, which comprises eddy current sensing equipment with a probe coil, and associated coaxial coil cable, oil energizing means, and circuit means responsive to impedance changes in the coil as effected by induced eddy currents in a test object to produce a data output signal proportional to such changes. The coil and cable are slideably received in the utility channel of the flexible insertion tube of a fiberoptic scope. The scope is provided with light transmitting and receiving fiberoptics for viewing through the flexible tube, and articulation means for articulating the distal end of the tube and permitting close control of coil placement relative to a test object. The eddy current sensing equipment includes a tone generator for generating audible signals responsive to the data output signal. In one selected mode of operation, the tone generator responsive to the output signal above a selected level generates a constant single frequency tone for signalling detection of a discontinuity and, in a second selected mode, generates a tone whose frequency is proportional to the difference between the output signal and a predetermined selected threshold level.
Commensurability Effects in Viscosity of Nanoconfined Water.
Neek-Amal, Mehdi; Peeters, Francois M; Grigorieva, Irina V; Geim, Andre K
2016-03-22
The rate of water flow through hydrophobic nanocapillaries is greatly enhanced as compared to that expected from macroscopic hydrodynamics. This phenomenon is usually described in terms of a relatively large slip length, which is in turn defined by such microscopic properties as the friction between water and capillary surfaces and the viscosity of water. We show that the viscosity of water and, therefore, its flow rate are profoundly affected by the layered structure of confined water if the capillary size becomes less than 2 nm. To this end, we study the structure and dynamics of water confined between two parallel graphene layers using equilibrium molecular dynamics simulations. We find that the shear viscosity is not only greatly enhanced for subnanometer capillaries, but also exhibits large oscillations that originate from commensurability between the capillary size and the size of water molecules. Such oscillating behavior of viscosity and, consequently, the slip length should be taken into account in designing and studying graphene-based and similar membranes for desalination and filtration.
Viscosity Measurement using Drop Coalescence in Microgravity
NASA Technical Reports Server (NTRS)
Antar, Basil N.; Ethridge, Edwin; Maxwell, Daniel
1999-01-01
We present in here details of a new method, using drop coalescence, for application in microgravity environment for determining the viscosity of highly viscous undercooled liquids. The method has the advantage of eliminating heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Also, due to the rapidity of the measurement, homogeneous nucleation would be avoided. The technique relies on both a highly accurate solution to the Navier-Stokes equations as well as on data gathered from experiments conducted in near zero gravity environment. The liquid viscosity is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity of two coalescing drops. Results are presented from two validation experiments of the method which were conducted recently on board the NASA KC-135 aircraft. In these tests the viscosity of a highly viscous liquid, such as glycerine at different temperatures, was determined to reasonable accuracy using the liquid coalescence method. The experiments measured the free surface velocity of two glycerine drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The free surface velocity was then compared with the computed values obtained from different viscosity values. The results of these experiments were found to agree reasonably well with the calculated values.
Heat flux viscosity in collisional magnetized plasmas
Liu, C.; Fox, W.; Bhattacharjee, A.
2015-05-15
Momentum transport in collisional magnetized plasmas due to gradients in the heat flux, a “heat flux viscosity,” is demonstrated. Even though no net particle flux is associated with a heat flux, in a plasma there can still be momentum transport owing to the velocity dependence of the Coulomb collision frequency, analogous to the thermal force. This heat-flux viscosity may play an important role in numerous plasma environments, in particular, in strongly driven high-energy-density plasma, where strong heat flux can dominate over ordinary plasma flows. The heat flux viscosity can influence the dynamics of the magnetic field in plasmas through the generalized Ohm's law and may therefore play an important role as a dissipation mechanism allowing magnetic field line reconnection. The heat flux viscosity is calculated directly using the finite-difference method of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], which is shown to be more accurate than Braginskii's method [S. I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)], and confirmed with one-dimensional collisional particle-in-cell simulations. The resulting transport coefficients are tabulated for ease of application.
Pressure viscosity coefficient of vegetable oils
Technology Transfer Automated Retrieval System (TEKTRAN)
The elastohydrodynamic (EHD) pressure viscosity coefficient (PVC) of ten vegetable oils from commodity and new crops, and two petroleum-based oils, polyalphaolefin (PAO) and hexadecane, were investigated. PVC was measured using three different methods: the So and Klaus (S-K) procedure from oil visco...
Spiders Tune Glue Viscosity to Maximize Adhesion.
Amarpuri, Gaurav; Zhang, Ci; Diaz, Candido; Opell, Brent D; Blackledge, Todd A; Dhinojwala, Ali
2015-11-24
Adhesion in humid conditions is a fundamental challenge to both natural and synthetic adhesives. Yet, glue from most spider species becomes stickier as humidity increases. We find the adhesion of spider glue, from five diverse spider species, maximizes at very different humidities that matches their foraging habitats. By using high-speed imaging and spreading power law, we find that the glue viscosity varies over 5 orders of magnitude with humidity for each species, yet the viscosity at maximal adhesion for each species is nearly identical, 10(5)-10(6) cP. Many natural systems take advantage of viscosity to improve functional response, but spider glue's humidity responsiveness is a novel adaptation that makes the glue stickiest in each species' preferred habitat. This tuning is achieved by a combination of proteins and hygroscopic organic salts that determines water uptake in the glue. We therefore anticipate that manipulation of polymer-salts interaction to control viscosity can provide a simple mechanism to design humidity responsive smart adhesives.
Electron perpendicular viscosity in Braginskii's equations
Wong, S. K.; Chan, V. S.
2013-07-15
The viscosity coefficient of the electron perpendicular stress tensor in Braginskii's theory is corrected by the addition of a term of the same order of magnitude, through the inclusion of a term beyond pitch angle scattering in the mass-ratio expansion of the electron-ion collision operator.
Viscosity in a lepton-photon universe
NASA Astrophysics Data System (ADS)
Husdal, Lars
2016-08-01
We look at viscosity production in a universe consisting purely of leptons and photons. This is quite close to what the universe actually look like when the temperature was between 10^{10} K and 10^{12} K (1-100 MeV). By taking the strong force and the hadronic particles out of the equation, we can examine how the viscous forces behave with all the 12 leptons present. By this we study how shear- and (more interestingly) bulk viscosity is affected during periods with particle annihilation. We use the theory given by Hoogeveen et al. from 1986, replicate their 9-particle results and expanded it to include the muon and tau particles as well. This will impact the bulk viscosity immensely for high temperatures. We will show that during the beginning of the lepton era, when the temperature is around 100 MeV, the bulk viscosity will be roughly 100 million times larger with muons included in the model compared to a model without.
Heat flux viscosity in collisional magnetized plasmas
NASA Astrophysics Data System (ADS)
Liu, C.; Fox, W.; Bhattacharjee, A.
2015-05-01
Momentum transport in collisional magnetized plasmas due to gradients in the heat flux, a "heat flux viscosity," is demonstrated. Even though no net particle flux is associated with a heat flux, in a plasma there can still be momentum transport owing to the velocity dependence of the Coulomb collision frequency, analogous to the thermal force. This heat-flux viscosity may play an important role in numerous plasma environments, in particular, in strongly driven high-energy-density plasma, where strong heat flux can dominate over ordinary plasma flows. The heat flux viscosity can influence the dynamics of the magnetic field in plasmas through the generalized Ohm's law and may therefore play an important role as a dissipation mechanism allowing magnetic field line reconnection. The heat flux viscosity is calculated directly using the finite-difference method of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], which is shown to be more accurate than Braginskii's method [S. I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)], and confirmed with one-dimensional collisional particle-in-cell simulations. The resulting transport coefficients are tabulated for ease of application.
Sensor for Viscosity and Shear Strength Measurement
Dillon, J.; Moore, J.E. Jr.; Ebadian, M.A.; Jones, W.K.
1998-10-20
Measurement of the physical properties (viscosity and density) of waste slurries is critical in evaluating transport parameters to ensure turbulent flow through transport pipes. The environment for measurement and sensor exposure is extremely harsh; therefore, reliability and ruggedness are critical in the sensor design. The work for this project will be performed in three phases. The first phase, carried out in FY96, involved (1) an evaluation of acoustic and other methods for viscosity measurement; (2) measurement of the parameters of slurries over the range of percent solids found in tanks and transport systems; (3) a comparison of physical properties (e.g., viscosity and density) to percent solids found composition; and (4) the design of a prototype sensor. The second phase (FY97) will involve the fabrication of a prototype hybrid sensor to measure the viscosity and mechanical properties of slurries in remote, high-radiation environments. Two different viscometer designs are being investigated in this study: a magnetostrictive pulse wave guide viscometer; an oscillating cylinder viscometer. In FY97, the Hemispheric Center for Environmental Technology (HCET) at Florida International University (FIU), which has printed circuit, thick film, thin film, and co-fired ceramic fabrication capability, will fabricate five probes for demonstration after technology selection and evaluation.
Spiders Tune Glue Viscosity to Maximize Adhesion.
Amarpuri, Gaurav; Zhang, Ci; Diaz, Candido; Opell, Brent D; Blackledge, Todd A; Dhinojwala, Ali
2015-11-24
Adhesion in humid conditions is a fundamental challenge to both natural and synthetic adhesives. Yet, glue from most spider species becomes stickier as humidity increases. We find the adhesion of spider glue, from five diverse spider species, maximizes at very different humidities that matches their foraging habitats. By using high-speed imaging and spreading power law, we find that the glue viscosity varies over 5 orders of magnitude with humidity for each species, yet the viscosity at maximal adhesion for each species is nearly identical, 10(5)-10(6) cP. Many natural systems take advantage of viscosity to improve functional response, but spider glue's humidity responsiveness is a novel adaptation that makes the glue stickiest in each species' preferred habitat. This tuning is achieved by a combination of proteins and hygroscopic organic salts that determines water uptake in the glue. We therefore anticipate that manipulation of polymer-salts interaction to control viscosity can provide a simple mechanism to design humidity responsive smart adhesives. PMID:26513350
Pressure-viscosity coefficient of biobased lubricants
Technology Transfer Automated Retrieval System (TEKTRAN)
Film thickness is an important tribological property that is dependent on the combined effect of lubricant properties, material property of friction surfaces, and the operating conditions of the tribological process. Pressure-viscosity coefficient (PVC) is one of the lubricant properties that influe...
From Stopping to Viscosity in Nuclear Reactions
Danielewicz, Pawel; Barker, Brent; Shi Lijun
2009-05-07
Data on stopping in intermediate-energy central heavy-ion collisions are analyzed following transport theory based on the Boltzmann equation. In consequence, values of nuclear shear viscosity are inferred. The inferred values are significantly larger than obtained for free nucleon dispersion relations and free nucleon-nucleon cross sections.
Working memory, worry, and algebraic ability.
Trezise, Kelly; Reeve, Robert A
2014-05-01
Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra). Moreover, researchers have tended to examine MA/worry separate from math problem solving activities and have used general WM tasks rather than domain-relevant WM measures. Furthermore, it seems to have been assumed that MA affects all areas of math. It is possible, however, that MA is restricted to particular math domains. To examine these issues, the current research assessed claims about the impact on algebraic problem solving of differences in WM and algebraic worry. A sample of 80 14-year-old female students completed algebraic worry, algebraic WM, algebraic problem solving, nonverbal IQ, and general math ability tasks. Latent profile analysis of worry and WM measures identified four performance profiles (subgroups) that differed in worry level and WM capacity. Consistent with expectations, subgroup membership was associated with algebraic problem solving performance: high WM/low worry>moderate WM/low worry=moderate WM/high worry>low WM/high worry. Findings are discussed in terms of the conceptual relationship between emotion and cognition in mathematics and implications for the MA-WM-performance relationship.
Weak homological dimensions and biflat Koethe algebras
Pirkovskii, A Yu
2008-06-30
The homological properties of metrizable Koethe algebras {lambda}(P) are studied. A criterion for an algebra A={lambda}(P) to be biflat in terms of the Koethe set P is obtained, which implies, in particular, that for such algebras the properties of being biprojective, biflat, and flat on the left are equivalent to the surjectivity of the multiplication operator A otimes-hat A{yields}A. The weak homological dimensions (the weak global dimension w.dg and the weak bidimension w.db) of biflat Koethe algebras are calculated. Namely, it is shown that the conditions w.db {lambda}(P)<=1 and w.dg {lambda}(P)<=1 are equivalent to the nuclearity of {lambda}(P); and if {lambda}(P) is non-nuclear, then w.dg {lambda}(P)=w.db {lambda}(P)=2. It is established that the nuclearity of a biflat Koethe algebra {lambda}(P), under certain additional conditions on the Koethe set P, implies the stronger estimate db {lambda}(P), where db is the (projective) bidimension. On the other hand, an example is constructed of a nuclear biflat Koethe algebra {lambda}(P) such that db {lambda}(P)=2 (while w.db {lambda}(P)=1). Finally, it is shown that many biflat Koethe algebras, while not being amenable, have trivial Hochschild homology groups in positive degrees (with arbitrary coefficients). Bibliography: 37 titles.
Algebraic curves of maximal cyclicity
NASA Astrophysics Data System (ADS)
Caubergh, Magdalena; Dumortier, Freddy
2006-01-01
The paper deals with analytic families of planar vector fields, studying methods to detect the cyclicity of a non-isolated closed orbit, i.e. the maximum number of limit cycles that can locally bifurcate from it. It is known that this multi-parameter problem can be reduced to a single-parameter one, in the sense that there exist analytic curves in parameter space along which the maximal cyclicity can be attained. In that case one speaks about a maximal cyclicity curve (mcc) in case only the number is considered and of a maximal multiplicity curve (mmc) in case the multiplicity is also taken into account. In view of obtaining efficient algorithms for detecting the cyclicity, we investigate whether such mcc or mmc can be algebraic or even linear depending on certain general properties of the families or of their associated Bautin ideal. In any case by well chosen examples we show that prudence is appropriate.
Inequalities, assessment and computer algebra
NASA Astrophysics Data System (ADS)
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.
Local Algebras of Differential Operators
NASA Astrophysics Data System (ADS)
Church, P. T.; Timourian, J. G.
2002-05-01
There is an increasing literature devoted to the study of boundary value problems using singularity theory. The resulting differential operators are typically Fredholm with index 0, defined on infinite-dimensional spaces, and they have often led to folds, cusps, and even higher-order Morin singularities. In this paper we develop some of the local algebras of germs of such differential Fredholm operators, extending the theory of the finite-dimensional case. We apply this work to nonlinear elliptic boundary value problems: in particular, we make further progress on a question proposed and initially studied by Ruf [1999, J. Differential Equations 151, 111-133]. We also make comments on several problems raised by others.
PC Basic Linear Algebra Subroutines
1992-03-09
PC-BLAS is a highly optimized version of the Basic Linear Algebra Subprograms (BLAS), a standardized set of thirty-eight routines that perform low-level operations on vectors of numbers in single and double-precision real and complex arithmetic. Routines are included to find the index of the largest component of a vector, apply a Givens or modified Givens rotation, multiply a vector by a constant, determine the Euclidean length, perform a dot product, swap and copy vectors, andmore » find the norm of a vector. The BLAS have been carefully written to minimize numerical problems such as loss of precision and underflow and are designed so that the computation is independent of the interface with the calling program. This independence is achieved through judicious use of Assembly language macros. Interfaces are provided for Lahey Fortran 77, Microsoft Fortran 77, and Ryan-McFarland IBM Professional Fortran.« less
NASA Astrophysics Data System (ADS)
Kadantsev, Evgeny; Fortelius, Carl; Druzhinin, Oleg; Mortikov, Evgeny; Glazunov, Andrey; Zilitinkevich, Sergej
2016-04-01
We examine and validate the EFB turbulence closure model (Zilitinkevich et al., 2013), which is based on the budget equations for basic second moments, namely, two energies: turbulent kinetic energy EK and turbulent potential energy EP, and vertical turbulent fluxes of momentum and potential temperature, τi (i = 1, 2) and Fz. Instead of traditional postulation of down-gradient turbulent transport, the EFB closure determines the eddy viscosity and eddy conductivity from the steady-state version of the budget equations for τi and Fz. Furthermore, the EFB closure involves new prognostic equation for turbulent dissipation time scale tT, and extends the theory to non-steady turbulence regimes accounting for non-gradient and non-local turbulent transports (when the traditional concepts of eddy viscosity and eddy conductivity become generally inconsistent). Our special interest is in asymptotic behavior of the EFB closure in strongly stable stratification. For this purpose, we consider plane Couette flow, namely, the flow between two infinite parallel plates, one of which is moving relative to another. We use a set of Direct Numerical Simulation (DNS) experiments at the highest possible Reynolds numbers for different bulk Richardson numbers (Druzhinin et al., 2015). To demonstrate potential improvements in Numerical Weather Prediction models, we test the new closure model in various idealized cases, varying stratification from the neutral and conventionally neutral to stable (GABLS1) running a test RANS model and HARMONIE/AROME model in single-column mode. Results are compared with DNS and LES (Large Eddy Simulation) runs and different numerical weather prediction models.
Novel residual-based large eddy simulation turbulence models for incompressible magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Sondak, David
The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting
Jucys-Murphy elements for Birman-Murakami-Wenzl algebras
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2011-05-01
The Burman-Wenzl-Murakami algebra, considered as the quotient of the braid group algebra, possesses the commutative set of Jucys-Murphy elements. We show that the set of Jucys-Murphy elements is maximal commutative for the generic Birman-Wenzl-Murakami algebra and reconstruct the representation theory of the tower of Birman-Wenzl-Murakami algebras.
Kinematical superalgebras and Lie algebras of order 3
Campoamor-Stursberg, R.; Rausch de Traubenberg, M.
2008-06-15
We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order 3. All these algebras are related through generalized Inonue-Wigner contractions from either the orthosymplectic superalgebra or the de Sitter Lie algebra of order 3.
Becchi-Rouet-Stora-Tyutin operators for W algebras
Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.
2008-07-15
The study of quantum Lie algebras motivates a use of noncanonical ghosts and antighosts for nonlinear algebras, such as W-algebras. This leads, for the W{sub 3} and W{sub 3}{sup (2)} algebras, to the Becchi-Rouet-Stora-Tyutin operator having the conventional cubic form.
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
Sondak, David; Oberai, Assad A.
2012-10-15
Novel large eddy simulation (LES) models are developed for incompressible magnetohydrodynamics (MHD). These models include the application of the variational multiscale formulation of LES to the equations of incompressible MHD. Additionally, a new residual-based eddy viscosity model is introduced for MHD. A mixed LES model that combines the strengths of both of these models is also derived. The new models result in a consistent numerical method that is relatively simple to implement. The need for a dynamic procedure in determining model coefficients is no longer required. The new LES models are tested on a decaying Taylor-Green vortex generalized to MHD and benchmarked against classical LES turbulence models. The LES simulations are run in a periodic box of size [-{pi}, {pi}]{sup 3} with 32 modes in each direction and are compared to a direct numerical simulation (DNS) with 512 modes in each direction. The new models are able to account for the essential MHD physics which is demonstrated via comparisons of energy spectra. We also compare the performance of our models to a DNS simulation by Pouquet et al.['The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD,' Geophys. Astrophys. Fluid Dyn. 104, 115-134 (2010)], for which the ratio of DNS modes to LES modes is 262:144.
Large Eddy Simulation of Dilute Sediment Suspension in an Open Channel Flow
NASA Astrophysics Data System (ADS)
Agegnehu, Getnet; Smith, Heather D.
2012-11-01
Flow and suspended sediment transport in fully developed turbulent open channel flow has been investigated using Large Eddy Simulation. We used a three-dimensional, non-hydrostatic model, OpenFOAM for this study. Pre-evaluation of three existing turbulence closure schemes is performed by comparing the mean flow and turbulent quantities with the direct numerical simulation results of Moser et al. (1999). It is found that the Dynamic Mixed Smagorinsky model underestimates the wall shear stress compared to the Dynamic Smagorinsky and one equation Eddy Viscosity schemes. Moreover, the Dynamic Smagorinsky scheme gives relatively better results in both the mean and turbulent quantities. The advection-diffusion equation is solved for suspended sediment transport and the effect of sediment roughness is included in the momentum equation based on the rough wall formulation proposed by Cebeci and Bradshaw (1977). A pick up function based on van Rijn (1984) is used to determine the sediment erosion. The settling process is taken into account with a settling velocity appearing in the concentration equation. Sediment and flow quantities are validated by comparing with the experimental data of Lyn (1988). The coupled hydrodynamics results are in good agreement with the experimental data.
Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities
NASA Astrophysics Data System (ADS)
Giometto, M. G.; Grandi, R.; Fang, J.; Monkewitz, P. A.; Parlange, M. B.
2016-08-01
The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O'Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters z_0 ≡ hat{z}_0 hat{N}^2 Pr sin {(α )} |hat{b}_s |^{-1} and λ ≡ hat{u}_{ref}hat{N} √{Pr} |hat{b}_s |^{-1} , where hat{z}_0 is the hydrodynamic roughness length, hat{N} is the Brunt-Väisälä frequency, α is the surface sloping angle, hat{b}_s is the imposed surface buoyancy, and hat{u}_{ref} is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant K model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to z_0 and to λ . In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both z_0 and λ.