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.
A transport equation for eddy viscosity
NASA Technical Reports Server (NTRS)
Durbin, P. A.; Yang, Z.
1992-01-01
A transport equation for eddy viscosity is proposed for wall bounded turbulent flows. The proposed model reduces to a quasi-homogeneous form far from surfaces. Near to a surface, the nonhomogeneous effect of the wall is modeled by an elliptic relaxation model. All the model terms are expressed in local variables and are coordinate independent; the model is intended to be used in complex flows. Turbulent channel flow and turbulent boundary layer flows with/without pressure gradient are calculated using the present model. Comparisons between model calculations and direct numerical simulation or experimental data show good agreement.
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.
A local eddy viscosity model for turbulent shear flow
NASA Technical Reports Server (NTRS)
Ortwerth, P. J.; Rabe, D. C.; Mcerlean, D. P.
1973-01-01
In the model described, the eddy viscosity is assumed to be a fluid property dependent on the state of the fluid locally, namely the local density, turbulent kinetic energy, turbulence scale, and Mach number. An empirical law was found which related eddy viscosity to these properties satisfactorily for free jets. This law is used without modification for a set of test cases in free shear layers, free-jet decay, coaxial mixing, and wakes. The scale of turbulence is taken as a constant at any axial location equal to the width of the shear layer. By utilizing the boundary-layer order-of-magnitude analysis, a coupled set of fluid dynamic equations is formulated, which of necessity includes the equation for the production of turbulent kinetic energy.
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.
RAS one-equation turbulence model with non-singular eddy-viscosity coefficient
NASA Astrophysics Data System (ADS)
Rahman, M. M.; Agarwal, R. K.; Siikonen, T.
2016-02-01
A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.
Dependence of red edge on eddy viscosity model parameters
NASA Technical Reports Server (NTRS)
Deupree, R. G.; Cole, P. W.
1980-01-01
The dependence of the red edge location on the two fundamental free parameters in the eddy viscosity treatment was extensively studied. It is found that the convective flux is rather insensitive to any reasonable or allowed value of the two free parameters of the treatment. This must be due in part to the fact that the convective flux is determined more by the properties of the hydrogen ionization region than by differences in convective structure. The changes in the effective temperature of the red edge of the RR Lyrae gap resulting from these parameter variations is quite small (approximately 150 K). This is true both because the parameter variation causes only small changes and because large changes in the convective flux are required to produce any significant change in red edge location. The possible changes found are substantially less than the approximately 600 K required to change the predicted helium abundance mass fraction from 0.3 to 0.2.
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 kinematic eddy viscosity model including the influence of density variations and preturbulence
NASA Technical Reports Server (NTRS)
Cohen, L. S.
1973-01-01
A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
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)
Tian, Zhigang; Perlin, Marc; Choi, Wooyoung
2012-03-01
An eddy viscosity model to describe energy dissipation in two-dimensional breaking waves in deep water is implemented in a numerical model for the evolution of nonlinear surface waves and evaluated with experimental results. In the experiments, to develop a reliable eddy viscosity model, breaking waves are generated by both energy focusing and modulated wave groups. Local wave parameters prior to and following breaking are defined and then determined. Significant correlations between the pre-breaking and post-breaking parameters are identified and adopted in the eddy viscosity model. The numerical model detects automatically wave breaking onset based on local surface slope, determines pre-breaking local wave parameters, predicts post-breaking time and length scales, and estimates eddy viscosity to dissipate energy in wave breaking events. Numerical simulations with the model are performed and compared to the experiments. It is found that the model predicts well the total energy dissipation due to breaking waves. In addition, the computed surface elevations after wave breaking agree reasonably well with the measurements for the energy focusing (plunging) wave groups. However, for breaking wave groups due to modulational instability (plunging and spilling), a relatively large discrepancy between the surface elevation predictions and the experimental measurements is observed, in particular, at the downstream wave probe locations. This is possibly due to wave reflection and three-dimensionality in the experiments. To further validate the eddy viscosity model, the evolution of highly nonlinear irregular waves is studied numerically and the numerical solutions are compared with additional independent laboratory experiments for long-crested irregular waves. It is shown that the numerical model is capable of predicting the wave evolution subsequent to wave breaking.
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.
A dynamic subgrid-scale eddy viscosity model with a global model coefficient
NASA Astrophysics Data System (ADS)
Park, Noma; Lee, Sungwon; Lee, Jungil; Choi, Haecheon
2006-12-01
In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the "global equilibrium" between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, turbulent channel flows at Reτ=180 and 590, flow over a circular cylinder at Red=3900, and flows over a sphere at Red=3700 and 104. The proposed dynamic model produces excellent performance for all flows considered. As shown in the present paper, the proposed model is robust and it can be readily applied to complex flows without homogeneous direction.
NASA Astrophysics Data System (ADS)
Oberai, Assad A.; Hughes, Thomas J. R.
2016-04-01
We explore a general family of eddy viscosity models for the large-eddy simulation of turbulence within the framework of the Variational Multiscale Method. Our investigation encompasses various fine-scale eddy viscosities and coarse-scale residual-based constructs. We delineate the domain of parameter space in which physically and mathematically suitable models exist, and identify several sub-families of potentially useful models that are either entirely new or extend previously proposed ones. We also combine classical modeling ideas, that lead to turbulent kinetic energy evolution equations, with the residual-based approach to derive a new residual-driven, one-equation dynamic model.
Turbulent eddy viscosity modeling in transonic shock/boundary-layer interactions
NASA Technical Reports Server (NTRS)
Inger, G. R.
1989-01-01
The treatment of turbulence effects on transonic shock/turbulent boundary layer interaction is addressed within the context of a triple deck approach valid for arbitrary practical Reynolds numbers between 1000 and 10 billion. The modeling of the eddy viscosity and basic turbulent boundary profile effects in each deck is examined in detail using Law-of-the-Wall/Law-of-the-Wake concepts as the foundation. Results of parametric studies showing how each of these turbulence model aspects influences typical interaction zone property distributions (wall pressure, displacement thickness and local skin friction) are presented and discussed.
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.
NASA Astrophysics Data System (ADS)
Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J.
1994-08-01
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)
Foreman, Richard J.; Emeis, Stefan; Canadillas, Beatriz
2015-02-01
A turbulence parametrization for wind speed in the stable boundary layer consisting of a single empirical parameter is proposed without the use of the eddy viscosity concept or turbulent kinetic energy equation. Instead, a drag-coefficient-type formulation as a function of the bulk Richardson number has been found to be able to reproduce observed stable boundary-layer wind speeds as effectively as a model based on the eddy viscosity approach. The advantage of this simpler approach is that the model can, in theory, be modified more easily for certain applications, such as the effects of large-scale wind parks on mesoscale meteorology.
NASA Astrophysics Data System (ADS)
Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.
2014-06-01
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
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
Building proper invariants for eddy-viscosity subgrid-scale models
NASA Astrophysics Data System (ADS)
Trias, F. X.; Folch, D.; Gorobets, A.; Oliva, A.
2015-06-01
Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, G = ∇ u ¯ . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants PGGT, QGGT, and RGGT of the tensor G GT, and imposing the proper cubic near-wall behavior, i.e., ν e = O ( y 3 ) , we deduce that the eddy-viscosity is given by ν e = ( C s 3 p q r Δ ) 2 PG G T p QG G T - ( p + 1 ) RG G T ( p + 5 / 2 ) / 3 . Moreover, only RGGT-dependent models, i.e., p > - 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman's model constant via C s 3 p q r = √{ 3 } C V r ≈ 0 . 458 ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman's model, i.e., 0 ≤ ν e ≤ νe V r . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, Cs3pqr, should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., Cs3pq = 0.572 (p = - 5/2), Cs3pr = 0.709 (p = - 1), and Cs3qr = 0.762 (p = 0).
Three-fluid, 3D MHD solar wind modeling with turbulence transport and eddy viscosity
NASA Astrophysics Data System (ADS)
Usmanov, A. V.; Goldstein, M. L.; Matthaeus, W. H.
2014-12-01
We present results from a three-fluid, fully three-dimensional MHD solar wind model that includes turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a co-moving system of three species: the solar wind protons, electrons, and interstellar pickup protons. Separate energy equations are employed for each species. We obtain numerical solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations in the region from 0.3 to 100 AU. The integrated system of equations includes 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. 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 turbulence parameters, throughout the heliosphere. The model results are compared with observations on WIND, Ulysses and Voyager 2 spacecraft. This work is partially supported by LWS and Heliophysics Grand Challenges programs.
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.
NASA Astrophysics Data System (ADS)
Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.
2012-05-01
Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.
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.
Solar tachocline dynamics: eddy viscosity, anti-friction, or something in between?
NASA Astrophysics Data System (ADS)
McIntyre, Michael E.
The tachocline has values of the stratification or buoyancy frequency N two or more orders of magnitude greater than the Coriolis frequency. In this and other respects it is very like the Earth's atmosphere, viewed globally, except that the Earth's solid surface is replaced by an abrupt, magnetically-constrained "tachopause" (Gough & McIntyre 1998). The tachocline is helium-poor through fast ventilation from above, down to the tachopause, on timescales of only a few million years. The corresponding sound-speed anomaly fits helioseismic data with a tachocline thickness (0.019±0.001) Rsolar, about 0.13×105km (Elliott & Gough 1999), implying large values of the gradient Richardson number such that stratification dominates vertical shear even more strongly than in the Earth's stratosphere, as earlier postulated by Spiegel & Zahn (1992). Therefore the tachocline ventilation circulation cannot be driven by vertically-transmitted frictional torques, any more than the ozone-transporting circulation and differential rotation of the Earth's stratosphere can thus be driven. Rather, the tachocline circulation must be driven mainly by the Reynolds and Maxwell stresses interior to the convection zone, through a gyroscopic pumping action and the downward-burrowing response to it. If layerwise-two-dimensional turbulence is important, then because of its potential-vorticity-transporting properties the effect will be anti-frictional rather than eddy-viscosity-like. In order to correctly predict the differential rotation of the Sun's convection zone, even qualitatively, a convection-zone model must be fully coupled to a tachocline model.
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 Astrophysics Data System (ADS)
Lee, Jong Chan; Jung, Kyung Tae
1999-03-01
A three-dimensional mode-splitting, σ-coordinate barotropic finite-difference model, with subgrid scale diffusion represented using a range of eddy viscosity closure models, is used to examine M2 tidal elevation and currents in the Yellow Sea and the East China Sea. Four eddy viscosity formulations are considered: q2- q2l turbulence energy model (Blumberg and Mellor, 1987), Prandtl mixing length model, Davies and Furnes' (1980) simple flow-related model with mixing length which includes the bottom boundary layer thickness, and a time and space invariant eddy viscosity with 650 cm 2/s. The bottom friction at the sea bed is given in a quadratic form using a constant bottom friction coefficient, cf and near-bottom velocities. A series of M2 tide model runs were carried out and optimal values of cf were determined through the comparison with tidal elevation amplitudes and phases at 203 stations. From these comparisons it is shown that the M2 tidal charts computed with a range of eddy viscosity formulations are in good agreement with each other when optimal values of cf are chosen; comparing with M2 tidal current amplitudes and phases at 15 stations, it is shown that tidal current distributions and its profiles are in reasonably good agreement with winter-time observations in the central part of the Yellow Sea; relatively poor results are obtained near the Chinese coast where non-tidal effects such as abrupt changes in tidal current phase in the vertical due to large freshwater discharge are pronounced. It is noted that the bottom friction coefficient has a major influence on tidal elevation and tidal currents and optimal values of bottom friction coefficient are closely related to the near-bottom eddy viscosity. The considered eddy viscosity closure models appear to work well for tidal problem when the bottom friction parameter is optimized. Results indicate that for a barotropic tide the Prandtl mixing length model which can account of the boundary layer thickness
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)
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
Turbulent Damping without Eddy Viscosity
NASA Astrophysics Data System (ADS)
Thalabard, Simon
2015-11-01
The intrinsic Non-Gaussianity of turbulence may explain why the standard Quasi-Normal cumulant discard closures can fail dramatically, an example being the development of negative energy spectra in Millionshtchikov's 1941 Quasi-Normal (QN) theory. While Orszag's 1977 EDQNM provides an ingenious patch to the issue, the reason why QN fails so badly is not so clear. Is it because of the Gaussian Ansatz itself? Or rather its inconsistent use? The purpose of the talk is to argue in favor of the latter option, using the lights of a new ``optimal closure'' recently exposed by [Turkington,2013], which allows Gaussians to be used consistently with an intrinsic damping. The key to this apparent paradox lies in a clear distinction between the ensemble averages and their proxies, most easily grasped provided one uses the Liouville equation rather than the cumulant hierarchy as a starting point. Schematically said, closure is achieved by minimizing a lack-of-fit residual, that retains the intrinsic features of the dynamics. For the sake of clarity, I will discuss the optimal closure on a problem where it can be entirely implemented and compared to DNS: the relaxation of an arbitrarily far from equilibrium energy shell towards the Gibbs equilibrium for truncated Euler dynamics.
NASA Technical Reports Server (NTRS)
Ahn, Kyung H.
1994-01-01
The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.
Computation of turbulent rotating channel flow with an algebraic Reynolds stress model
NASA Technical Reports Server (NTRS)
Warfield, M. J.; Lakshminarayana, B.
1986-01-01
An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.
Algebraic turbulence modeling for unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
Constrained Large Eddy Simulation of Separated Turbulent Flows
NASA Astrophysics Data System (ADS)
Xia, Zhenhua; Shi, Yipeng; Wang, Jianchun; Xiao, Zuoli; Yang, Yantao; Chen, Shiyi
2011-11-01
Constrained Large-eddy Simulation (CLES) has been recently proposed to simulate turbulent flows with massive separation. Different from traditional large eddy simulation (LES) and hybrid RANS/LES approaches, the CLES simulates the whole flow domain by large eddy simulation while enforcing a RANS Reynolds stress constraint on the subgrid-scale (SGS) stress models in the near-wall region. Algebraic eddy-viscosity models and one-equation Spalart-Allmaras (S-A) model have been used to constrain the Reynolds stress. The CLES approach is validated a posteriori through simulation of flow past a circular cylinder and periodic hill flow at high Reynolds numbers. The simulation results are compared with those from RANS, DES, DDES and other available hybrid RANS/LES methods. It is shown that the capability of the CLES method in predicting separated flows is comparable to that of DES. Detailed discussions are also presented about the effects of the RANS models as constraint in the near-wall layers. Our results demonstrate that the CLES method is a promising alternative towards engineering applications.
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.
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.
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.
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…
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.
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.
Eddies and vortices in ocean basin dynamics
NASA Astrophysics Data System (ADS)
Siegel, A.; Weiss, Jeffrey B.; Toomre, Juri; McWilliams, James C.; Berloff, Pavel S.; Yavneh, Irad
A wind-driven, closed-basin quasi-geostrophic ocean model is computed at very high horizontal resolution to study the effect of increasing Reynolds number (Re) on eddy variability. Five numerical simulations are performed with identical configurations, varying only in horizontal resolution and viscosity coefficient (and therefore Re). Qualitative changes in the structure of eddy variability are evident in the dramatic increase of isolated vortex structures at the highest Re. While the time-mean kinetic energy is relatively independent of Re, the vortex emergence contributes to a continual increase with Re of eddy kinetic energy and meridional vorticity flux. The rate of increase slows somewhat at the highest Re, indicating the possibility of a regime where eddy variability becomes insensitive to further increases in Re.
Large Eddy Simulations using Lattice Boltzmann algorithms. Final report
Serling, J.D.
1993-09-28
This report contains the results of a study performed to implement eddy-viscosity models for Large-Eddy-Simulations (LES) into Lattice Boltzmann (LB) algorithms for simulating fluid flows. This implementation requires modification of the LB method of simulating the incompressible Navier-Stokes equations to allow simulation of the filtered Navier-Stokes equations with some subgrid model for the Reynolds stress term. We demonstrate that the LB method can indeed be used for LES by simply locally adjusting the value of the BGK relaxation time to obtain the desired eddy-viscosity. Thus, many forms of eddy-viscosity models including the standard Smagorinsky model or the Dynamic model may be implemented using LB algorithms. Since underresolved LB simulations often lead to instability, the LES model actually serves to stabilize the method. An alternative method of ensuring stability is presented which requires that entropy increase during the collision step of the LB method. Thus, an alternative collision operator is locally applied if the entropy becomes too low. This stable LB method then acts as an LES scheme that effectively introduces its own eddy viscosity to damp short wavelength oscillations.
Large Eddy Simulation of Transitional Boundary Layer
NASA Astrophysics Data System (ADS)
Sayadi, Taraneh; Moin, Parviz
2009-11-01
A sixth order compact finite difference code is employed to investigate compressible Large Eddy Simulation (LES) of subharmonic transition of a spatially developing zero pressure gradient boundary layer, at Ma = 0.2. The computational domain extends from Rex= 10^5, where laminar blowing and suction excites the most unstable fundamental and sub-harmonic modes, to fully turbulent stage at Rex= 10.1x10^5. Numerical sponges are used in the neighborhood of external boundaries to provide non-reflective conditions. Our interest lies in the performance of the dynamic subgrid scale (SGS) model [1] in the transition process. It is observed that in early stages of transition the eddy viscosity is much smaller than the physical viscosity. As a result the amplitudes of selected harmonics are in very good agreement with the experimental data [2]. The model's contribution gradually increases during the last stages of transition process and the dynamic eddy viscosity becomes fully active and dominant in the turbulent region. Consistent with this trend the skin friction coefficient versus Rex diverges from its laminar profile and converges to the turbulent profile after an overshoot. 1. Moin P. et. al. Phys Fluids A, 3(11), 2746-2757, 1991. 2. Kachanov Yu. S. et. al. JFM, 138, 209-247, 1983.
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.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
Transport by negative eddy viscosity in soliton turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The forced Schrodinger equation is used to describe the microhydrodynamical state of strong soliton turbulence. The Schrodinger equation is transformed into a master equation and is decomposed into a macrogroup, a microgroup, and a submicrogroup, representative of the three transport processes of spectral evolution, transport property, and relaxation. The kinetic equation for the macrodistribution is derived and reverted to the continuum by the method of moments in order to find the equation of spectral evolution. The spectral flow is found to be governed by three types of transport, which are discussed.
Hall Viscosity II: Extracting Viscosity from Conductivity
NASA Astrophysics Data System (ADS)
Goldstein, Moshe; Bradlyn, Barry; Read, Nicholas
2012-02-01
When time reversal symmetry is broken, the viscosity tensor of a fluid can have non-dissipative components, similarly to the non-dissipative off-diagonal Hall conductivity. This ``Hall viscosity'' was recently shown to be half the particle density times the orbital angular momentum per particle. Its observation can thus help elucidate the nature of the more exotic quantum Hall states and related systems (e.g., p+ip superconductors). However, no concrete measurement scheme has hitherto been proposed. Motivated by this question we use linear response theory to derive a general relation between the viscosity tensor and the wave-vector dependent conductivity tensor for a Galilean-invariant quantum fluid. This relation enables one to extract the Hall viscosity, as well as other viscosity coefficients (shear and bulk) when relevant, from electromagnetic response measurements. We also discuss the connection between this result and a similar one recently derived by C. Hoyos and D. T. Son [arXiv:1109.2651].
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Nonequilibrium viscosity of glass
NASA Astrophysics Data System (ADS)
Mauro, John C.; Allan, Douglas C.; Potuzak, Marcel
2009-09-01
Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or “isostructural”), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10-12 to 1012K/s . Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 1016Pas . Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Pal, Abhro; Anupindi, Kameswararao; Delorme, Yann; Ghaisas, Niranjan; Shetty, Dinesh A; Frankel, Steven H
2014-07-01
In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo. PMID:24801556
Dynamics of gelling liquids: algebraic relaxation.
Srivastava, Sunita; Kumar, C N; Tankeshwar, K
2009-08-19
The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories. PMID:21828600
Viscosity of paraproteinemic sera.
Tichý, M
1996-01-01
Viscosity was determined in a series of 1402 paraproteinemic sera. Viscosity was measured on an ultrasonic viscosimeter of domestic design and was expressed in relative units(ru). Increased viscosity over 2.1 ru was found in 288 sera, i.e. 20.5%. Clinical symptoms of the hyperviscosity syndrome were found in 44 cases (3%) with viscosity over 4.0 ru. Malignant monoclonal gammopathy as proved in all 44 cases. In 17 determinations with the presence of paraprotein IgM, the mean viscosity was 6.35% +/- 2.6 ru, and the mean paraprotein concentration was 41.12 +/- 11.26g/l. In 17 cases we found paraprotein IgG with a mean viscosity of 6.38 +/- 2.4 ru and a mean concentration of paraprotein was 63.66 +/- 14.52g/l. In 9 determinations with the presence of paraprotein IgA, the mean viscosity as 5.22 +/- 1.02 ru and the mean paraprotein concentration was 49.77 +/- 13.89g/1. In one case we found a double paraproteinemia of IgG-lambda + IgA-kappa (31.9 + 24.2g/l), with a viscosity of 10.5 ru. PMID:9106390
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.
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)
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
Time Filtering in Large Eddy Simulations
NASA Technical Reports Server (NTRS)
Carati, Daniele; Wray, Alan A.
2000-01-01
An explicit time filter is applied to the Navier-Stokes equation prior to a space filter. The time filter is supposed to be smooth, and an exact expansion depending on the time derivatives of the velocity is derived for the associated stress tensor. On the contrary, the effect of the space filter is treated as usual and an eddy viscosity model is introduced in the LES equation. The total stress is thus represented using a new class of mixed models combining time and space derivatives of the LES field.
NASA Astrophysics Data System (ADS)
Workman, G. L.
1980-10-01
Since a large number of the procedures used for inspecting the external tank are concerned with determining flaws in welds, there is a need to develop an inspection technique, which can be automated, to determine flaws in welds and structures with complex geometries. Techniques whereby an eddy current is generated in a metallic material and the changes in the circuit parameters due to material differences are observed, were chosen as one possible approach. Pulsed eddy current and its relationship to multifrequency techniques is discussed as well as some preliminary results obtained from observing pulsed waveforms with apparatus and algorithms currently in use for ultrasonic testing of welds. It can be shown the pulsed eddy current techniques can provide similar results, can eliminate some of the noncritical parameters affecting the eddy current signals, and can facilitate in the detection of critical parameter such as flaws, subsurface voids, and corrosion.
NASA Technical Reports Server (NTRS)
Pasley, R. L.; Birdwell, J. A.
1973-01-01
Eddy-current inspection is discussed as a method for locating subsurface flaws in electrically conductive materials. The physical principles and electrical circuitry are described along with the test equipment.
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
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…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
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.
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…
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
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…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
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.
Turbulent viscosity in natural surf zones
NASA Astrophysics Data System (ADS)
Grasso, F.; Ruessink, B. G.
2012-12-01
Waves breaking in the shallow surf zone near the shoreline inject turbulence into the water column that may reach the bed to suspend sediment. Breaking-wave turbulence in the surf zone is, however, poorly understood, which is one of the reasons why many process-based coastal-evolution models predict coastal change during severe storms inadequately. Here, we use data collected in two natural surf zones to derive a new parameterization for the stability function Cμ that determines the magnitude of the eddy viscosity νt in two-equation turbulent-viscosity models, νt = Cμk2/ε, where k is turbulent kinetic energy and ε is the turbulence dissipation rate. In both data sets, the ratio of turbulence production to dissipation is small (≈0.15), while vertical turbulence diffusion is significant. This differs from assumptions underlying existing Cμ parameterizations, which we show to severely overpredict observed Cμ for most conditions. Additionally, we rewrite our new Cμ parameterization into a formulation that accurately reproduces our Reynolds-stress based estimates of turbulence production. This formulation is linear with strain, consistent with earlier theoritical work for large strain rates. Also, it does not depend on ε and can, therefore, also be applied in one-equation turbulent-viscosity models. We anticipate our work to improve turbulence modeling in natural surf zones and to eventually lead to more reliable predictions of coastal evolution in response to severe storms.
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.
Groove dimensioning using remote field eddy current inspection
NASA Astrophysics Data System (ADS)
Davoust, M.-E.; Fleury, G.
2000-09-01
The remote field eddy current technique is used for dimensioning the grooves that may occur in the ferromagnetic pipes. We propose a method to estimate the depth and the length of corrosion grooves from measurement of a pick-up coil signal phase at different positions close to the defect. Groove dimensioning requires the knowledge of the physical relation between measurements and defect dimensions; therefore finite-element calculations are performed to design parametric algebraic functions for modeling the physical phenomena. Different models are possible; the choice of this algebraic function is discussed from identification criteria. By means of new measurement formalism and two previously defined measurement relations, estimates of groove sizes may be given. In the first approach, algebraic function parameters and groove dimensions are linked through a polynomial function; this approach is proved to be better than a second one which tries to take advantage of more physical considerations.
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.
Micromagnetics with eddy currents
NASA Astrophysics Data System (ADS)
Iyer, R.; Millhollon, J.; Long, K.
2011-01-01
In this paper, we study the modified Landau-Lifshitz-Gilbert (LLG) equation for of a conducting, magnetic body. The modified LLG equations include the magnetic field due to eddy currents in the total effective magnetic field. We derive an expression for the magnetic field due to eddy current losses and show that it is well defined. We then show that the work done by the eddy currents in opposing the change of magnetization is a Rayleigh type dissipation function, and derive the modified LLG equations using the calculus of variations. Finally, we show that the modified LLG equations lead to a decrease in the Gibbs energy. This implies that the LLG equations describes a dynamic process proceeding spontaneously forward in time.
NASA Technical Reports Server (NTRS)
Lissauer, J. J.; Shu, F. H.; Cuzzi, J. N.
1982-01-01
The technique of estimating the viscosity in Saturn's rings from the damping rate of waves observed to be propagating within the rings is discussed. The wavetrains of attempts using spiral density waves as a diagnostic suffer significant complications that compromise the interpretations. A method that considers the damping of spiral bending waves was used to deduce a kinematic viscosity of 260 (+150, -100) sqcm/sec for the middle of the A ring where bending waves are excited by the 5:3 vertical resonance with Mimas. This value implies upper limits on the particle velocity dispersion and local ring thickness of 0.4 cm/sec and 30 m, respectively.
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.
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.
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…
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).
ERIC Educational Resources Information Center
Owen, Hazel
2013-01-01
Eddie Reisch is currently working as a policy advisor for Te Reo Maori Operational Policy within the Student Achievement group with the Ministry of Education in New Zealand, where he has implemented and led a range of e-learning initiatives and developments, particularly the Virtual Learning Network (VLN). He is regarded as one of the leading…
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
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)
Turbulence Modeling: A NASA Perspective
NASA Technical Reports Server (NTRS)
Gatski, T. B.
2001-01-01
This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.
VERTICAL STRUCTURE OF TIME-DEPENDENT FLOW FOR VISCOSITY THAT DEPENDS ON BOTH DEPTH AND TIME
A previously developed eigenfunction expansion, that describes horizontal current as a function of depth and time, is extended to include any eddy viscosity given as a product of a function of depth and a function of time. (Copyright (c) 1982 American Meteorological Society.)
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.
Ballato, Arthur
2010-03-01
Quartz shear resonators are employed widely as sensors to measure Newtonian viscosities of liquids. Perturbation of the electrical equivalent circuit parameters of the plate resonator by the fluid loading permits calculation of the mass density-shear viscosity product. Use of doubly rotated resonators does permit additional information to be obtained, but in no case can the viscosity and mass density values be separated. In these measurements, the resonator surface is exposed to a measurand bath whose extent greatly exceeds the penetration depth of the evanescent shear mode excited by the active element. Here we briefly review past techniques and current art, and sketch a proposal involving the interesting situation in which the separation between the resonator and a confining wall is less than the penetration depth of the fluid occupying the intervening region. To highlight the salient features of this novel case, the discussion is limited to the very idealized circumstance of a strictly 1-D problem, unencumbered by the vicissitudes inevitably encountered in practice. An appendix mentions some of these functional impedimenta and indicates how deviations from ideality might be approached in engineering embodiments. When the fluid confinement is of the order of the penetration depth, the resonator perturbation becomes a sensitive function of the separation, and it is found that viscosity and density may be separately and uniquely determined. Moreover, extreme miniaturization is a natural consequence because the penetration depth generally is on the order of micrometers for frequencies around 1 MHz at temperatures and pressures ordinarily encountered with gases and liquids. Micro-electro-mechanical (MEMS) versions of viscometers and associated types of fluid sensors are thereby enabled. PMID:20211786
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…
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…
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
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
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.
Large eddy simulation of longitudinal stationary vortices
NASA Astrophysics Data System (ADS)
Sreedhar, Madhu; Ragab, Saad
1994-07-01
The response of longitudinal stationary vortices when subjected to random perturbations is investigated using temporal large-eddy simulation. Simulations are obtained for high Reynolds numbers and at a low subsonic Mach number. The subgrid-scale stress tensor is modeled using the dynamic eddy-viscosity model. The generation of large-scale structures due to centrifugal instability and their subsequent breakdown to turbulence is studied. The following events are observed. Initially, ring-shaped structures appear around the vortex core. These structures are counter-rotating vortices similar to the donut-shaped structures observed in a Taylor-Couette flow between rotating cylinders. These structures subsequently interact with the vortex core resulting in a rapid decay of the vortex. The turbulent kinetic energy increases rapidly until saturation, and then a period of slow decay prevails. During the period of maximum turbulent kinetic energy, the normalized mean circulation profile exhibits a logarithmic region, in agreement with the universal inner profile of Hoffman and Joubert [J. Fluid Mech. 16, 395 (1963)].
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
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.
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 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.
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.
Critical exponent for viscosity
NASA Technical Reports Server (NTRS)
Berg, Robert F.; Moldover, Michael R.
1990-01-01
The critical exponent y characterizing the divergence of the viscosity for carbon dioxide and xenon has been measured. The values of y for both fluids fall within the range y = 0.041 + or - 0.001 and are consistent with the range y = 0.042 + or - 0.002 spanned by earlier data for four binary liquid mixtures. This agreement is the strongest evidence that pure fluids and binary liquids are in the same dynamic universality class; however, the results for y are inconsistent with the recent theoretical value of 0.032.
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.
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
Viscosity of Hydrous Rhyolitic Melts
NASA Astrophysics Data System (ADS)
Zhang, Y.; Xu, Z.; Liu, Y.
2002-12-01
It is critical to understand and to be able to predict viscosity of hydrous silicate melts for understanding magma transport, bubble growth, volcanic eruptions, and magma fragmentation. We report new viscosity data for hydrous rhyolitic melt in the viscosity range of 109 to 1015 Pa s based on the kinetics of hydrous species reaction in the melt upon cooling (i.e., based on the equivalence between the glass transition temperature and the apparent equilibrium temperature). We also report viscosity data obtained from bubble growth experiments. Our data show that the viscosity model of Hess and Dingwell (1996) systematically overestimates the viscosity of hydrous rhyolitic melt at the high viscosity range by a factor of 2 to 4 (still within their stated 2σ uncertainty). Another problem with the model of Hess and Dingwell is that the functional dependence of viscosity on total H2O content cannot be extended to dry melt: as total H2O content decreases to zero, the viscosity would first increase, and then decrease to zero. A zero viscosity for a dry melt makes no sense. Hence we need a mixing law for hydrous melt viscosity that is extendible to dry melts. By examining the viscosity of rhyolitic melts containing 6 ppm to about 8.0 wt% total H2O (both our own data and literature data), we propose the following relation for the dependence of viscosity on total H2O content: 1/η = 1/η 1+(1/η 2-1/η 1)xn ≈ 1/η 1+xn/η 2 where η is viscosity and 1/η is fluidity, η 1 is the viscosity of the dry melt, x is the mole fraction of total dissolved H2O, n and η 2 are two fitting parameters, and η 2 can be identified to be the viscosity of the hypothetical melt consisting of pure H2O (η 2 cannot be directly measured since such a melt does not exist). The above equation appears to work well for the viscosity of hydrous rhyolitic melts. By fitting hydrous rhyolitic melt viscosity with the above equation, we find that rhyolitic melt viscosity vary by 1.2 orders of magnitude
A subfilter-scale stress model for large eddy simulations
NASA Astrophysics Data System (ADS)
Rouhi, Amirreza; Piomelli, Ugo
2013-11-01
In most large eddy simulations, the filter width is related to the grid. This method of specification, however, causes problems in complex flows where local refinement results in grid discontinuities. Following the work of Piomelli and Geurts (Proce. 8th Workshop on DLES, 2010) we propose an eddy-viscosity approach in which the filter width is based on the flow parameters only, with no explicit relationship to the grid size. This model can achieve grid-independent LES solutions, vanishing dynamically in the regions of low turbulence activity and a computational cost less than the dynamic models. The Successive Inverse Polynomial Interpolation (Geurts & Meyers Phys. Fluids 18, 2006) was used to calculate the model parameter. Calculating implicitly the eddy-viscosity at each time-step removes the numerical instabilities found in previous studies, while maintaining the local character of the model. Results of simulations of channel flow at Reτ up to 2,000, and forced homogeneous isotropic turbulence will be presented.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
Gyrokinetic large eddy simulations
Morel, P.; Navarro, A. Banon; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-07-15
The large eddy simulation approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the GENE code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
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)
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.
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.
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.
High-Frequency Shear Viscosity of Low-Viscosity Liquids
NASA Astrophysics Data System (ADS)
Kaatze, U.; Behrends, R.
2014-11-01
A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times of about 0.3 ns for -pentadecane and -hexadecane at 25 C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which values between 0.3 ns (-hexanol) and 1.5 ns (-dodecanol) have been found at 25 C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in appear also in the shear-viscosity spectra with, for example, 2 ns for the critical triethylamine-water binary mixture at temperatures between 10 C and 18 C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.
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.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
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.
Viscosity measuring instrument
NASA Technical Reports Server (NTRS)
Feinstein, S. P. (Inventor)
1980-01-01
A method and apparatus are provided for enabling the measurement of the viscosity of substances, especially those containing volatiles at elevated temperatures, with greater accuracy and at less cost than before. The apparatus includes a cylinder with a narrow exit opening at one end and a piston which closely slides within the cylinder to apply force against a sample in the cylinder to force the sample through the exit opening. In order to more rapidly heat a sample the ends of the cylinder and piston are tapered and the sample is correspondingly tapered, to provide a large surface to volume ratio. A corresponding coal sample is formed by compressing particles of coal under high pressure in a mold of appropriate shape.
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 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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Roitman, Michael
2008-08-01
In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
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.
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…
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.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
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.
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.
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.
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.
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.
Latitude dependence of eddy variances
NASA Technical Reports Server (NTRS)
Bowman, Kenneth P.; Bell, Thomas L.
1987-01-01
The eddy variance of a meteorological field must tend to zero at high latitudes due solely to the nature of spherical polar coordinates. The zonal averaging operator defines a length scale: the circumference of the latitude circle. When the circumference of the latitude circle is greater than the correlation length of the field, the eddy variance from transient eddies is the result of differences between statistically independent regions. When the circumference is less than the correlation length, the eddy variance is computed from points that are well correlated with each other, and so is reduced. The expansion of a field into zonal Fourier components is also influenced by the use of spherical coordinates. As is well known, a phenomenon of fixed wavelength will have different zonal wavenumbers at different latitudes. Simple analytical examples of these effects are presented along with an observational example from satellite ozone data. It is found that geometrical effects can be important even in middle latitudes.
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
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…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
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
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
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
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
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,…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
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…
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
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
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.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
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.
Applied large eddy simulation.
Tucker, Paul G; Lardeau, Sylvain
2009-07-28
Large eddy simulation (LES) is now seen more and more as a viable alternative to current industrial practice, usually based on problem-specific Reynolds-averaged Navier-Stokes (RANS) methods. Access to detailed flow physics is attractive to industry, especially in an environment in which computer modelling is bound to play an ever increasing role. However, the improvement in accuracy and flow detail has substantial cost. This has so far prevented wider industrial use of LES. The purpose of the applied LES discussion meeting was to address questions regarding what is achievable and what is not, given the current technology and knowledge, for an industrial practitioner who is interested in using LES. The use of LES was explored in an application-centred context between diverse fields. The general flow-governing equation form was explored along with various LES models. The errors occurring in LES were analysed. Also, the hybridization of RANS and LES was considered. The importance of modelling relative to boundary conditions, problem definition and other more mundane aspects were examined. It was to an extent concluded that for LES to make most rapid industrial impact, pragmatic hybrid use of LES, implicit LES and RANS elements will probably be needed. Added to this further, highly industrial sector model parametrizations will be required with clear thought on the key target design parameter(s). The combination of good numerical modelling expertise, a sound understanding of turbulence, along with artistry, pragmatism and the use of recent developments in computer science should dramatically add impetus to the industrial uptake of LES. In the light of the numerous technical challenges that remain it appears that for some time to come LES will have echoes of the high levels of technical knowledge required for safe use of RANS but with much greater fidelity. PMID:19531503
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
Might eddies dominate carbon export ?
NASA Astrophysics Data System (ADS)
Allen, J.; Rixen, M.; Fielding, S.; Mustard, A.; Brown, L.; Sanders, R.
2003-04-01
Yes - from a review of recent data sets we present a scale analysis of the potential for globally integrated carbon export, from the surface ocean, due to the vertical transports of mesoscale eddies. Mesoscale eddies are the oceanic equivalent of atmospheric storms, most are a fundamental result of horizontally unstable density gradients on the surface of a rotating sphere (baroclinic instability) and ~ 90% of the oceans energy exchanges take place at this scale. Recent studies from satellite remote sensing and high resolution models show that mesoscale eddies are a ubiquitous feature of the open ocean in both time and space; they are even present in sub-tropical oligotrophic gyres. Individual atmospheric weather systems generally have little ecological impact on terrestrial or marine biological systems. Grass grows and herbivores munch through many cyclone and anticyclone periods. In the open ocean we have a very different picture. The primary producers and herbivores have shorter time scales; time scales that coincide with those of mesoscale eddies. Plankton can have either good or bad weather lifetimes associated with just a single cyclone or anticyclone period. Furthermore, although the spring bloom may be the single largest source of material for the export of carbon from the upper ocean, it is short lived and may not be dominant everywhere in the annual export budget. The magnitude of vertical motion associated with mesoscale eddies is significant on biological timescales both for phytoplankton growth and the development of zooplankton grazing pressure. Critically this motion does not form a closed vertical circulation; baroclinic instability releases potential energy and thus water masses are exchanged both vertically and horizontally across water mass boundaries. Thus mesoscale eddies have been shown to provide a mechanism for export both in the direct transport of biomass downwards out of the surface mixed layer and the fertilisation of an exhausted
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®,…
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.
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
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.
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
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.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
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.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Minimum-dissipation models for large-eddy simulation
NASA Astrophysics Data System (ADS)
Rozema, Wybe; Bae, Hyun J.; Moin, Parviz; Verstappen, Roel
2015-08-01
Minimum-dissipation eddy-viscosity models are a class of sub-filter models for large-eddy simulation that give the minimum eddy dissipation required to dissipate the energy of sub-filter scales. A previously derived minimum-dissipation model is the QR model. This model is based on the invariants of the resolved rate-of-strain tensor and has many desirable properties. It appropriately switches off for laminar and transitional flows, has low computational complexity, and is consistent with the exact sub-filter tensor on isotropic grids. However, the QR model proposed in the literature gives insufficient eddy dissipation. It is demonstrated that this can be corrected by increasing the model constant. The corrected QR model gives good results in simulations of decaying grid turbulence on an isotropic grid. On anisotropic grids the QR model is not consistent with the exact sub-filter tensor and requires an approximation of the filter width. It is demonstrated that the results of the QR model on anisotropic grids are primarily determined by the used filter width approximation, and that no approximation gives satisfactory results in simulations of both a temporal mixing layer and turbulent channel flow. A new minimum-dissipation model for anisotropic grids is proposed. This anisotropic minimum-dissipation (AMD) model generalizes the desirable practical and theoretical properties of the QR model to anisotropic grids and does not require an approximation of the filter width. The AMD model is successfully applied in simulations of decaying grid turbulence on an isotropic grid and in simulations of a temporal mixing layer and turbulent channel flow on anisotropic grids.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
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
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…
Eddy diffusion at Saturn's homopause
NASA Technical Reports Server (NTRS)
Sandel, B. R.; Mcconnell, J. C.; Strobel, D. F.
1982-01-01
Measurements of Saturn's He 584 A dayglow and the CH4 density profile deduced from stellar occultation data near the homopause have been combined to infer an eddy diffusion coefficient of 8 + or - 4 x 10 to the 7th sq cm/s and a temperature of 125 + 40 or - 25 K near the homopause at Voyager 2 encounter. It appears that the eddy diffusion coefficient may have increased between the Voyager encounters. Saturn's H Ly-alpha dayglow is qualitatively compatible with this increase and the interpretation of the He 584 A dayglow and CH4 absorption measurement.
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
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…
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
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.
Expert system for analyzing eddy current measurements
Levy, A.J.; Oppenlander, J.E.; Brudnoy, D.M.; Englund, J.M.; Loomis, K.C.
1994-08-16
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. 21 figs.
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.
Viscosity in spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Ray, Arnab K.
2003-10-01
The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.
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.
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.
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…
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…
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…
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
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
Eddy fluxes in baroclinic turbulence
NASA Astrophysics Data System (ADS)
Thompson, Andrew F.
The eddy heat flux generated by the statistically equilibrated baroclinic instability of a uniform, horizontal temperature gradient is studied using a two-mode quasigeostrophic model. An overview of the dependence of the eddy diffusivity of heat Dtau on the planetary potential vorticity gradient beta, the bottom friction kappa, the deformation radius lambda, the vertical shear of the large-scale flow 2U and the domain size L is provided at 70 numerical simulations with beta = 0 (f-plane) and 110 simulations with beta ≠ 0 (beta-plane). Strong, axisymmetric, well-separated baroclinic vortices dominate the equilibrated barotropic vorticity and temperature fields of f-plane turbulence. The heat flux arises from a systematic northward (southward) migration of anti-cyclonic (cyclonic) eddies with warm (cold) fluid trapped in the cores. Zonal jets form spontaneously on the beta-plane, and stationary, isotropic, jet-scale eddies align within the strong eastward-flowing regions of the jets. In both studies, the vortices and jets give rise to a strong anti-correlation between the barotropic vorticity zeta and the temperature field tau. The baroclinic mode is also an important contributor to dissipation by bottom friction and energizes the barotropic mode at scales larger than lambda. This in part explains why previous parameterizations for the eddy heat flux based on Kolmogorovian cascade theories are found to be unreliable. In a separate study, temperature and salinity profiles obtained with expendable conductivity, temperature and depth (XCTD) probes within Drake Passage, Southern Ocean are used to analyze the turbulent diapycnal eddy diffusivity kappa rho to a depth of 1000 meters. The Polar Front separates two dynamically different regions with strong, surface-intensified mixing north of the Front. South of the Polar Front mixing is weaker and peaks at a depth of approximately 500 m, near the local temperature maximum. Peak values of kapparho are found to exceed 10-3 m
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
A new climatological oceanic eddy census
NASA Astrophysics Data System (ADS)
Mason, Evan; Pascual, Ananda; Pujol, Isabel; Faugère, Yannice; Delepoulle, Antoine; Briol, Frederic
2015-04-01
We present a new climatological oceanic eddy census dataset based on gridded sea level anomalies from satellite altimeter observations that is due for release by Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO). The identification and automated tracking of oceanic eddies is carried out using the py-eddy-tracker of Mason et al. (2014). Daily outputs of eddy properties (including position, radius, amplitude and nonlinearity) covering the period 1993-2013 over the global domain are presented and discussed. Validation and comparison is made with the published global eddy track database of Chelton et al. (2011).
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
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…
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.)
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…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
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.)
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…
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…
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.
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'
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
NASA Technical Reports Server (NTRS)
Hide, R.
1972-01-01
Estimates of the coefficient of kinematical viscosity nu of the earth's liquid metallic core that are given in the geophysical literature range from approximately 0.001 sq cm/s, the viscosity of molten iron at ordinary pressures, to approximately less than 10 to the 8th power sq cm/s, based on the observation that compressional waves traverse the core without suffering serious attenuation. Bumps on the core-mantle boundary with typical horizontal dimensions up to a few thousand km and vertical dimensions h of a few km would produce the topographic coupling between the core and mantle that is evidently implied by the observed decade variations in the length of the day (unless the coupling is due to the presence of rapidly fluctuating magnetic fields in the core).
Viscosity-stabilized aqueous solutions
Wier, D. R.
1981-01-27
Thiourea functions as a solution viscosity stabilizer in aqueous compositions comprising thiourea, nonionic polymers such as polyalkylene oxides and anionic surfactants such as petroleum sulfonates. The aqueous compositions are useful in connection with fluid-drive oil recovery processes, processes for drilling, completing, or working over wells, or the like processes in which a thickened fluid is injected into or brought into contact with a subterranean earth formation.
NASA Astrophysics Data System (ADS)
Wang, W. Q.; Hao, D. W.; Zhang, L. X.; Guo, Y. K.
2012-11-01
In the present study, the subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the inhomogeneous turbulent flow in a full passage of Francis turbine. Distributions of pressure, velocity and vortices as well as some flow structure are gained, which is helpful to examine the performance of SGS model for complex turbulent flow and understand the flow characters in full passage of Francis turbine.
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.
Liquid Viscosities of Fluorinated Dialkylethers
NASA Astrophysics Data System (ADS)
Nakazawa, Noriaki; Kawamura, Mitsutaka; Sekiya, Akira; Ootake, Katsuto; Tamai, Ryoichi; Kurokawa, Yuji; Murata, Junji
The liquid viscosities of thirteen fluorinated dialkylethers which are expected as promising candidates of CFC alternatives were measured at temperatures from 276 K to 328 K and atmospheric pressure. The fluorinated dialkylethers used in this study are 1-methoxy-1, 1, 2, 2- tetrafluoroethane; 1-difluoromethoxy- 1, 1 , 2 -trifluoroethane; 1-methoxy-1, 1 , 2 , 2 , 3 , 3 -hexafluoropropane; 1-methoxy-1-trifluoro-methyl-2, 2 , 2-trifluoroethane; 1-difluoro-methoxy-2, 2, 3, 3-tetrafluoropropane; 1-(2, 2, 2-trifruoroethoxy)-1, 1, 2, 2-tetrafluoroethane 1-difluoromethoxy-2, 2, 3, 3, 3-pentafluoropropane 1-methoxy-2, 2, 3, 3 -tetrafluoropropane; 1-methoxy-1, 1, 2, 2, 3, 3, 3-heptafluoropropane; 1-pentafluoroethoxy-1, 1, 2, 2-tetrafluoroethane; 2-trifluoromethoxy-1, 1, 1, 2-tetrafluorobutane; 1-proxy-nonafluorobutane; and 1-ethoxyundeca-fluoropentane. The liquid viscosities have been measured by the torsionally vibrating viscometer (YAMAICHI DENKI, F VM-80A) within an uncertainty of ±3%.The liquid viscosities of those compounds decrease exponentially with increase of temperature.
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...
Eddy transport of reacting substances
NASA Astrophysics Data System (ADS)
Flierl, Glenn
2015-11-01
We examine an exact formulation of eddy fluxes but extended to tracers which react with each other. The resulting formula is evaluated using the lattice model approach, allowing not only control (including elimination) of sub-grid-scale diffusion and efficient enough computation to generate an adequate ensemble. The theory predicts that the flux is a non-local average of the mean gradients, even for passive scalars, and we can calculate the averaging kernel. The reaction terms alter the effective transport for a single scalar depending on decay time scale compared to that of the Lagrangian covariance. But, in addition, the eddies produce ``cross-fluxes'' whereby the transport of each tracer depends on the gradients of all of them.
Remote field eddy current inspection
Atherton, D.L.
1995-11-01
The Remote Field Eddy Current (RFEC) technique uses an internal probe to inspect conducting tubes nondestructively. A coaxial solenoidal exciter, energized with low frequency AC, and detector coils near the inside of the pipe wall are separated by about two pipe diameters to obtain through wall transmission and equal sensitivity to defects on the outside or inside of the pipe wall. Calculation methods are outlined and the voltage plane polar plot signal representation for defect measurement is described. Slit defect interactions in ferromagnetic and non-ferromagnetic tubes are discussed. Defect-induced anomalous fields are interpreted in terms of anomalous source eddy current and missing magnetization defect models. The use of computer animations to represent the time variations of high resolution field measurements and calculations is described.
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').
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)
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.
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.
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.
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.
Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation
NASA Astrophysics Data System (ADS)
De Stefano, Giuliano; Vasilyev, Oleg V.; Goldstein, Daniel E.
2008-04-01
Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most "energetic" coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier-Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Reλ=72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.
NASA Astrophysics Data System (ADS)
Hunt, Julian C. R.; Moustaoui, Mohamed; Mahalov, Alex
2015-09-01
High resolution three-dimensional simulations are presented of the interactions between turbulent shear flows moving with mean relative velocity ΔU below a stably stratified region with buoyancy frequency (N+). An artificial forcing in the simulation, with a similar effect as a small negative eddy viscosity, leads to a steady state flow which models thin interfaces. Characteristic eddies of the turbulence have length scale L. If the bulk Richardson number Rib=(LN+/ΔU)2 lies between lower and upper critical values denoted as Ri∗(<1/5) and R~i(˜ 1), a "detached" layer is formed in the stable region with thickness L+ greater than L, in which rotational fluctuations and inhomogeneous turbulence are induced above an interface with large gradients of density/temperature. Comparisons are made with shear turbulent interfaces with no stratification. When Rib>R~i, vertical propagating waves are generated, with shear stresses carrying significant momentum flux and progressively less as Rib increases. Simulations for a jet and a turbulent mixing layer show similar results. A perturbation analysis, using inhomogeneous Rapid Distortion Theory, models the transition zone between shear eddies below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave-momentum-flux has a maximum when Rib˜2 and then decreases as Rib increases. This coupling mechanism between eddies and waves, which is neglected in eddy viscosity models for shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short- and long-term flow phenomena. The "detached layer" is a mechanism that contributes to the formation of stratus clouds and polluted layers above the atmospheric boundary layer.
The morphology of shelfbreak eddies
NASA Astrophysics Data System (ADS)
Garvine, R. W.; Wong, K.-C.; Gawarkiewicz, G. G.; McCarthy, R. K.; Houghton, R. W.; Aikman, F.
1988-12-01
We used a combination of buoy tracking, intensive hydrography, satellite thermal imagery, and moored current meters to resolve the structure of eddies at the shelfbreak front in the Middle Atlantic Bight south of New England. Eddylike features were always present at the front in our study area throughout the 15-day period of observations in June 1984. We found that hydrographic features in our across-shelf hydrographic transects that appeared to represent the detached parcels of shelf water often reported in the literature were, in fact, part of the three-dimensional structure of shelfbreak eddies. Adequate alongshelf resolution, in particular, enabled us to determine that no detached parcels were present. The two prominent features of the eddy groups we found were plumes of lighter shelf water that protruded into slope water, curling "backward" opposite the direction of mean shelf flow, and neighboring cyclones with warmer, saltier slope water in their cores, partly or wholly encircled by the plumes. The plumes have the potential especially for producing vigorous across-front exchange of heat, salt, and nutrients and may play roles analogous to the "squirts" found on the California shelf.
The effective tidal viscosity in close solar-type binaries
NASA Astrophysics Data System (ADS)
Goldman, I.
2008-09-01
A major problem confronting the understanding of tidal evolution of close solar-type binaries is the inefficiency of the turbulent convection. The value of the effective viscosity estimated, in the framework of the mixing length theory (MLT), implies circularization timescales which are almost two orders of magnitude longer than observed. Moreover, the reduction of the effective viscosity due to the fast time-variation of the tidal shear in short period binaries, increases the discrepancy to about three orders of magnitude. This state of affairs has motivated suggestions that tidal orbital evolution, notably circularization occurs mainly during the pre-main-sequence phase. However, observational data accumulated over the recent decades imply that circularization does occur during the the main-sequence phase (Mazeh 2008). In this work, we examine the possibility that the apparent inefficiency of turbulent convection is merely a shortcoming of MLT approach. Indeed, a recent 3D numerical simulation (Penev et al. 2007), suggests that the true convective viscosity is probably larger than the MLT value and that the reduction due to the time-variation of the shear is not drastic. We employ a model for stellar turbulent convection (Canuto, Goldman & Mazzitelli 1996) to evaluate the effective viscosity both for a steady for and time dependent tidal shear. The model is physically based, self-consistent, and accounts for the full spectrum of the turbulent eddies. It has been found advantageous, compared to the MLT, in many applications. We use an analytic approximation to the turbulent spectrum to obtain the reduction of the efficiency due to the time-variation of the tide. The results are: (i) an enhanced effective viscosity (by a factor of ˜ 4.5), and more importantly (ii) only a mild reduction due to the time-variation of the tidal shear. Overall, for binaries with orbital period of 15 days the discrepancy is ``only" a factor of ˜ 30 down from a factor of ˜ 1000. These
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
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.
Large eddy simulation of incompressible turbulent channel flow
NASA Technical Reports Server (NTRS)
Moin, P.; Reynolds, W. C.; Ferziger, J. H.
1978-01-01
The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.
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.
A family of dynamic models for large-eddy simulation
NASA Technical Reports Server (NTRS)
Carati, D.; Jansen, K.; Lund, T.
1995-01-01
Since its first application, the dynamic procedure has been recognized as an effective means to compute rather than prescribe the unknown coefficients that appear in a subgrid-scale model for Large-Eddy Simulation (LES). The dynamic procedure is usually used to determine the nondimensional coefficient in the Smagorinsky (1963) model. In reality the procedure is quite general and it is not limited to the Smagorinsky model by any theoretical or practical constraints. The purpose of this note is to consider a generalized family of dynamic eddy viscosity models that do not necessarily rely on the local equilibrium assumption built into the Smagorinsky model. By invoking an inertial range assumption, it will be shown that the coefficients in the new models need not be nondimensional. This additional degree of freedom allows the use of models that are scaled on traditionally unknown quantities such as the dissipation rate. In certain cases, the dynamic models with dimensional coefficients are simpler to implement, and allow for a 30% reduction in the number of required filtering operations.
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.
Prediction and evaluation of eddy-viscosity models for free mixing
NASA Technical Reports Server (NTRS)
Zakkay, V.; Sinha, R.; Normura, S.
1973-01-01
Analysis for the turbulent mixing of free jets is presented in this paper and compared to recent experimental results. A turbulent mass diffusion model is presented and is based on the concentration potential core. The model yielded good results when compared with the experimental results except for low-speed flows where few experimental data are available. A review of recent experimental results verifies again that the three diffusion processes in turbulent mixing are interrelated; however, no single diffusion model may be used for all three processes. This is especially true when pressure gradients are present in the flow field. It is shown that even though momentum diffusion is significantly affected by pressure gradients, mass diffusion is not. It is further indicated that the mass diffusion model has been derived and is based on the accurate correlations of experimental results obtained for the concentration potential core. Similar techniques may be used in deriving an expression for the momentum and thermal diffusion coefficients. These expressions would be more complicated since they would have to take care of the boundary layer at the start of the mixing region. Finally, a comparison of the analyses, using this particular model and Ferri's model, with available experimental results is made.
Applicability of eddy viscosity turbulence models in low specific speed centrifugal pump
NASA Astrophysics Data System (ADS)
Wang, Y.; Wang, W. J.
2012-11-01
The accuracy of numerical simulation determines the performance prediction whether to be successful or not in the research of centrifugal pump. In order to study the applicability of different turbulence models in the low specific speed centrifugal pump, the object was based on XST45-200 stamping and welding centrifugal pump. Five different kinds of standards which are k-epsilon model, RNG k-epsilon model, Realizable k-epsilon model, Standard k-ω model and SST k-ω model are adopted in steady numerical simulations of the centrifugal pump flow fields. Then, inner and outside characteristics of the centrifugal pump were gotten .And it also provides the calculation of pressure distribution using different turbulence models in the five conditions. Lastly, the performance curves of head, power and efficiency are compared with the test. The results show a good agreement between five kinds of turbulence models and tests obtained in small flow and design condition. In large flow, the standard k-ε model is worse than the other four, which is larger than the tested head with a relative deviation of 47.9% and efficiency with 50%.The calculation accuracy which used RNG k-epsilon model is highest. SST k-ω model takes the second place. Standard k-ω model can be used for the numerical simulation in the low specific speed centrifugal pump.
Sequential products on effect algebras
NASA Astrophysics Data System (ADS)
Gudder, Stan; Greechie, Richard
2002-02-01
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.
Curvature calculations with spacetime algebra
Hestenes, D.
1986-06-01
A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
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)
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.
Semiclassical states on Lie algebras
Tsobanjan, Artur
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
NASA Astrophysics Data System (ADS)
Lannes, A.; Teunissen, P. J. G.
2011-05-01
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is
Effective Viscosity of Microswimmer Suspensions
NASA Astrophysics Data System (ADS)
Rafaï, Salima; Jibuti, Levan; Peyla, Philippe
2010-03-01
The measurement of a quantitative and macroscopic parameter to estimate the global motility of a large population of swimming biological cells is a challenge. Experiments on the rheology of active suspensions have been performed. Effective viscosity of sheared suspensions of live unicellular motile microalgae (Chlamydomonas Reinhardtii) is far greater than for suspensions containing the same volume fraction of dead cells. In addition, suspensions show shear thinning behavior. We relate these macroscopic measurements to the orientation of individual swimming cells under flow and discuss our results in the light of several existing models.
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.
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.
Numerical simulation of a closed rotor-stator system using Large Eddy Simulation
NASA Astrophysics Data System (ADS)
Amouyal, Solal Abraham Teva
A large eddy simulation of an enclosed annular rotor stator cavity is presented. The geometry is characterized by a large aspect ratio G = (b-a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate o under consideration is equivalent to the rotational Reynolds number Re = o b2 /nu= 9.5x104 , where nu is the kinematic viscosity. The main objective of this study is to correctly simulate the rotor stator cavity using a low order numerical scheme on unstructured grids. The numerical simulations were run on the software AVBP developed by the Centre Europeen de Recherche et de Formation Avancee en Calcul Scientific. The results were compared to the experimental results obtained by Sebastien Poncet of Universit e Aix-Marseille. Two large eddy simulations techniques were used: the Smagorinsky and Wall-adapting local eddy-viscosity models. The simulations were run on three set of grids, each with a different cell resolution-14, 35 and 50- along the thickness of the system. Results from each mesh show a good qualitative agreement of the mean velocity field with Poncet's experimental results. It was found that the Samgorinsky model to be more appropriate for this configuration.
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.
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).
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.
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
Scientific Objectives of the Critical Viscosity Experiment
NASA Technical Reports Server (NTRS)
Berg, R. F.; Moldover, M. R.
1993-01-01
In microgravity, the Critical Viscosity Experiment will measure the viscosity of xenon 15 times closer to the critical point than is possible on earth. The results are expected to include the first direct observation of the predicted power-law divergence of viscosity in a pure fluid and they will test calculations of the value of the exponent associated with the divergence. The results, when combined with Zeno's decay-rate data, will strengthen the test of mode coupling theory. Without microgravity viscosity data, the Zeno test will require an extrapolation of existing 1-g viscosity data by as much as factor of 100 in reduced temperature. By necessity, the extrapolation would use an incompletely verified theory of viscosity crossover. With the microgravity viscosity data, the reliance on crossover models will be negligible allowing a more reliable extrapolation. During the past year, new theoretical calculations for the viscosity exponent finally achieved consistency with the best experimental data for pure fluids. This report gives the justification for the proposed microgravity Critical Viscosity Experiment in this new context. This report also combines for the first time the best available light scattering data with our recent viscosity data to demonstrate the current status of tests of mode coupling theory.
Viscosity of ring polymer melts
Pasquino, Rossana; Vasilakopoulos, Thodoris C.; Jeong, Youn Cheol; Lee, Hyojoon; Rogers, Simon; Sakellariou, George; Allgaier, Jürgen; Takano, Atsushi; Brás, Ana R.; Chang, Taihyun; Gooßen, Sebastian; Pyckhout-Hintzen, Wim; Wischnewski, Andreas; Hadjichristidis, Nikos; Richter, Dieter; Rubinstein, Michael; Vlassopoulos, Dimitris
2015-01-01
We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η0,linear to their ring counterparts η0,ring at isofrictional conditions is discussed as function of the number of entanglements Z. In the unentangled regime η0,linear/η0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η0,linear/η0,ring=2. In the entanglement regime, the Z-dependence of rings viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1
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.
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.
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
Gomez, T; Sagaut, P; Schilling, O; Zhou, Y
2006-07-05
A spectral subggrid-scale eddy viscosity and magnetic resisitivity model based on the eddy-damped quasi-normal Markovian (EDQNM) spectral kinetic and magnetic energy transfer presented in [12] is used in large-eddy simulation (LES) of large kinetic and magnetic Reynold number magneto-hydrodynamic (MHD) turbulence. The proposed model is assessed via a posteri tests on three-dimensional, incompressible, isotropic, non-helical, freely-decaying MHD turbulence at asymptotically large Reynolds numbers. Using LES with an initial condition characterized by an Alfv{acute e}n ratio of kinetic to magnetic energy {tau}{sub A} equal to unity, it is shown that at the kinetic energy spectrum E{sub K}(k) and magnetic energy spectrum E{sub M}(k) exhibit Kolmogorov -5/3 inertial subrange scalings in the LES, consistent with the EDQNM model.
Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces
Koibuchi, H. )
1991-10-10
In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.
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.
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
NASA Astrophysics Data System (ADS)
Olyanina, N. V.; Bel'tyukov, A. L.; Lad'yanov, V. I.
2016-02-01
The temperature and concentration dependences of the kinematic viscosity of Co-B melts with a boron content up to 50 at % are studied by torsional vibrations. The viscosity polytherms are satisfactorily described by the Arrhenius equation. An increase in the viscosity with an increase in the boron content from 15 to 36 at % is observed in the concentration dependence of the viscosity. The viscosity of the melt is almost independent of the boron content in concentration ranges of 0-15 and 36-50 at %. The concentration dependence of the melt viscosity of the system is calculated using various equations. The best coincidence with the experimental data is obtained for the calculation using the Kaptay equation.
Saybolt universal viscosity converted to kinematic
Anaya, C.; Bermudez, O.
1987-09-21
This article describes a program for personal and handheld computers, written in Basic, which has been developed for the conversion of Saybolt universal viscosity in Saybolt Universal Seconds (SSU or SUS) to kinematic viscosity in centistokes (cSt), at any selected temperature. It was developed using the mathematical relationship presented in the American Society for Testing and Materials (ASTM) standard D2161-82. In the standard, an equation is presented to convert kinematic viscosity to Saybolt universal viscosity, but nothing is presented to convert from Saybolt to kinematic because it is necessary to find the roots of a nonexplicit function. There are several numerical methods that can be used to determine the roots of the nonexplicit function, and therefore, convert Saybolt universal viscosity to kinematic viscosity. In the program, the first iteration of the second-order Newton-Raphson method is followed by the Wegstein method as a convergence accelerator.
Compositional dependence of lower crustal viscosity
NASA Astrophysics Data System (ADS)
Shinevar, William J.; Behn, Mark D.; Hirth, Greg
2015-10-01
We calculate the viscosity structure of the lower continental crust as a function of its bulk composition using multiphase mixing theory. We use the Gibbs free-energy minimization routine Perple_X to calculate mineral assemblages for different crustal compositions under pressure and temperature conditions appropriate for the lower continental crust. The effective aggregate viscosities are then calculated using a rheologic mixing model and flow laws for the major crust-forming minerals. We investigate the viscosity of two lower crustal compositions: (i) basaltic (53 wt % SiO2) and (ii) andesitic (64 wt % SiO2). The andesitic model predicts aggregate viscosities similar to feldspar and approximately 1 order of magnitude greater than that of wet quartz. The viscosity range calculated for the andesitic crustal composition (particularly when hydrous phases are stable) is most similar to independent estimates of lower crust viscosity in actively deforming regions based on postglacial isostatic rebound, postseismic relaxation, and paleolake shoreline deflection.
Mesoscale Ocean Large Eddy Simulations
NASA Astrophysics Data System (ADS)
Pearson, Brodie; Fox-Kemper, Baylor; Bachman, Scott; Bryan, Frank
2015-11-01
The highest resolution global climate models (GCMs) can now resolve the largest scales of mesoscale dynamics in the ocean. This has the potential to increase the fidelity of GCMs. However, the effects of the smallest, unresolved, scales of mesoscale dynamics must still be parametrized. One such family of parametrizations are mesoscale ocean large eddy simulations (MOLES), but the effects of including MOLES in a GCM are not well understood. In this presentation, several MOLES schemes are implemented in a mesoscale-resolving GCM (CESM), and the resulting flow is compared with that produced by more traditional sub-grid parametrizations. Large eddy simulation (LES) is used to simulate flows where the largest scales of turbulent motion are resolved, but the smallest scales are not resolved. LES has traditionally been used to study 3D turbulence, but recently it has also been applied to idealized 2D and quasi-geostrophic (QG) turbulence. The MOLES presented here are based on 2D and QG LES schemes.
Exploring Eddy-Covariance Measurements Using a Spatial Approach: The Eddy Matrix
NASA Astrophysics Data System (ADS)
Engelmann, Christian; Bernhofer, Christian
2016-04-01
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.
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.
Tracking Loop Current eddies with satellite altimetry
NASA Astrophysics Data System (ADS)
Leben, Robert R.; Born, George H.
1993-11-01
Geosat altimeter derived sea surface height (SSH) anomaly fields have been optimally interpolated onto a regular space time grid using both crossover data from the nonrepeating Geodetic Mission (Geosat-GM) and collinear data from the Exact Repeat Mission (Geosat-ERM). Over four years of data were collected from the combined missions, spanning the time period from April 1985 through August 1989, during which six major and at least two minor Loop Current eddies were directly observed. Eddy paths determined by automated tracking of the local maximum values in the SSH anomaly fields were compared with eddy centers estimated from drifting buoy trajectories, validating the data processing and tracking techniques. Accurate tracking of eddy centers allowed transits of 90°W to be used as a benchmark for determination of eddy shedding periods. For this data set the average period between major eddy transits was 9.8 months, with individual separation periods ranging from 6 to 14 months. The two minor eddies observed were associated with the deepest penetrations of the Loop Current into the gulf, and were nearly coincident with the shedding of the strongest major Loop Current eddies.
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
Southern Ocean Eddies as Weather Makers
NASA Astrophysics Data System (ADS)
Frenger, Ivy; Byrne, David; Gruber, Nicolas; Knutti, Reto; Münnich, Matthias; Papritz, Lukas
2013-04-01
Several hundred mesoscale eddies populate the Southern Ocean south of 30°S at any time, however, little is known about their effect on the overlying atmosphere. As these eddies feature sea surface temperature (SST) anomalies one can expect them to play a role in the coupling of the atmosphere and the ocean. Here we show based on satellite observations of about 600,000 eddies occurring between 1997 and 2010, that these ocean eddies significantly alter near surface wind, cloud properties and rainfall by several percent. Relative to the atmospheric variability, the magnitude of the anomalies related to ocean eddies represents ±13-15 % (wind, cloud fraction), ±6-10 % (cloud water content) and ±2-6 % (rain). This impact on the atmosphere is striking given the fact that oceanic eddies constitute non-stationary SST fronts of moderate size relative to the much larger atmospheric low pressure systems which are constantly passing by at these latitudes. The spatial pattern of these changes is consistent with a mechanism labeled downward momentum mechanism in which the SST anomalies related to eddies modify the stability and thus turbulence of the atmospheric boundary layer. We will investigate the mechanisms and impact of the atmospheric modifications associated with ocean eddies in a regional high-resolution coupled atmosphere-ocean model (COSMO-ROMS) over the Southern Ocean.
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
Mesoscale Eddies in the Solomon Sea
NASA Astrophysics Data System (ADS)
Hristova, H. G.; Kessler, W. S.; McWilliams, J. C.; Molemaker, M. J.
2011-12-01
Water mass transformation in the strong equatorward flows through the Solomon Sea influences the properties of the Equatorial Undercurrent and subsequent cold tongue upwelling. High eddy activity in the interior Solomon Sea seen in altimetric sea surface height (SSH) and in several models may provide a mechanism for these transformations. We investigate these effects using a mesoscale (4-km resolution) sigma-coordinate (ROMS) model of the Solomon Sea nested in a basin solution, forced by a repeating seasonal cycle, and evaluated against observational data. The model generates a vigorous upper layer eddy field; some of these are apparently shed as the New Guinea Coastal Undercurrent threads through the complex topography of the region, others are independent of the strong western boundary current. We diagnose the scales and vertical structure of the eddies in different parts of the Solomon Sea to illuminate their generation processes and propagation characteristics, and compare these to observed eddy statistics. Hypotheses tested are that the Solomon Sea mesoscale eddies are generated locally by baroclinic instability, that the eddies are shed as the South Equatorial Current passes around and through the Solomon Island chain, that eddies are generated by the New Guinea Coastal Undercurrent, or that eddies occurring outside of the Solomon Sea propagate into the Solomon Sea. These different mechanisms have different implications for the resulting mixing and property fluxes. They also provide different interpretations for SSH signals observed from satellites (e.g., that will be observed by the upcoming SWOT satellite).
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
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
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.
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.
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.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
Observed characteristics of Mozambique Channel eddies
NASA Astrophysics Data System (ADS)
Swart, N. C.; Lutjeharms, J. R. E.; Ridderinkhof, H.; de Ruijter, W. P. M.
2010-09-01
The flow in the Mozambique Channel is dominated by large, southward propagating, anti-cyclonic eddies, as opposed to a steady western boundary current. These Mozambique Channel eddies feed their waters into the Agulhas Current system, where they are thought to have a significant influence on the formation of the Natal Pulse and Agulhas Ring shedding. Here we use in situ hydrographic and nutrient data, together with satellite altimetry and surface velocity profilers to provide a detailed characterization of the Mozambique Channel eddies. Two warm eddies in the Channel at 20°S and 24°S had diameters of over 200 km. They rotated anti-cyclonically with a tangential velocity of over 0.5 m.s-1. Vertical sections show that the eddies reached to the bottom of the water column. Relative to the surrounding waters, the features were warm and saline. The total heat and salt anomalies for the southernmost eddy were computed relative to a reference station close by. At 24°S the total anomalies were 1.3 × 1020 J and 6.9 × 1012 kg, respectively, being on par with Agulhas rings. Mozambique Channel eddies thus have the potential to form a major contribution to the southward eddy heat flux in the Agulhas Current system. The feature also had positive nutrient and negative oxygen anomalies. The large magnitude of the water mass anomalies within the eddy suggests that interannual variability in Mozambique Channel eddy numbers would have a significant impact on downstream water mass characteristics.
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.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
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.
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.
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.
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.
Computer Algebra Systems in Undergraduate Instruction.
ERIC Educational Resources Information Center
Small, Don; And Others
1986-01-01
Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)
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.
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.
Computational triadic algebras of signs
Zadrozny, W.
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
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.
Plasma viscosity in inflammatory bowel disease.
Lobo, A J; Jones, S C; Juby, L D; Axon, A T
1992-01-01
AIMS: To assess the relation of plasma viscosity to disease activity in patients with inflammatory bowel disease. METHODS: Crohn's disease (n = 60) and ulcerative colitis (n = 71) were diagnosed on the basis of typical histological or radiological features. Active Crohn's disease was defined as a Crohn's disease activity index of 150 or over. Active ulcerative colitis was defined as a liquid stool passed three times a day or more with blood. Blood samples were assessed for haemoglobin concentration, total white cell count, platelets, plasma viscosity, erythrocyte sedimentation rate, serum albumin, and C-reactive protein. RESULTS: Plasma viscosity was higher in those with active Crohn's disease compared with those with inactive Crohn's disease or active ulcerative colitis. Plasma viscosity correlated significantly with erythrocyte sedimentation rate, C-reactive protein, and platelet count in patients with Crohn's disease. In ulcerative colitis plasma viscosity correlated only with serum C-reactive protein. Plasma viscosity showed a low sensitivity for detecting active Crohn's disease, with 48% of those with active disease having a plasma viscosity within the laboratory reference range. CONCLUSIONS: Plasma viscosity is related to disease activity in Crohn's disease, but is insufficiently sensitive for it to replace erythrocyte sedimentation rate as a measure of the acute phase response in Crohn's disease. PMID:1740516
The addition of algebraic turbulence modeling to program LAURA
NASA Technical Reports Server (NTRS)
Cheatwood, F. Mcneil; Thompson, R. A.
1993-01-01
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.
ERIC Educational Resources Information Center
Star, Jon R.; Rittle-Johnson, Bethany
2009-01-01
Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…
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.
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.
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.
Optical fiber-based fluorescent viscosity sensor
NASA Astrophysics Data System (ADS)
Haidekker, Mark A.; Akers, Walter J.; Fischer, Derek; Theodorakis, Emmanuel A.
2006-09-01
Molecular rotors are a unique group of viscosity-sensitive fluorescent probes. Several recent studies have shown their applicability as nonmechanical fluid viscosity sensors, particularly in biofluids containing proteins. To date, molecular rotors have had to be dissolved in the fluid for the measurement to be taken. We now show that molecular rotors may be covalently bound to a fiber-optic tip without loss of viscosity sensitivity. The optical fiber itself may be used as a light guide for emission light (external illumination of the tip) as well as for both emission and excitation light. Covalently bound molecular rotors exhibit a viscosity-dependent intensity increase similar to molecular rotors in solution. An optical fiber-based fluorescent viscosity sensor may be used in real-time measurement applications ranging from biomedical applications to the food industry.
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.
The weak Hopf algebras related to generalized Kac-Moody algebra
Wu Zhixiang
2006-06-15
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.
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…
UCSMP Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…
Graphing Calculator Use in Algebra Teaching
ERIC Educational Resources Information Center
Dewey, Brenda L.; Singletary, Ted J.; Kinzel, Margaret T.
2009-01-01
This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…
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.
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…
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…
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…
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"…
Lessons for Algebraic Thinking. Grades K-2.
ERIC Educational Resources Information Center
von Rotz, Leyani; Burns, Marilyn
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
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…
NASA Astrophysics Data System (ADS)
Lee, Jungil; Choi, Haecheon; Park, Noma
2008-11-01
In the present study, a dynamic subgrid-scale eddy diffusivity model is proposed for large eddy simulation of passive scalar transport in complex geometry. The eddy viscosity model proposed by Vreman [Phys. Fluids, 16, 3670 (2004)], which guarantees theoretically zero SGS dissipation for various laminar shear flows, is utilized as the base eddy diffusivity model. The model coefficient is determined by the dynamic procedure based on the method proposed by Park et al. [Phys. Fluids, 18, 125109 (2006)] such that the model coefficient is globally constant in space but varies only in time. The large eddy simulations of passive scalar transport in turbulent channel flow and turbulent boundary layer are conducted and the proposed model shows nearly the same performance as the dynamic Smagorinsky model does. Since the proposed model does not require any ad hoc clipping and averaging over the homogeneous direction, it can be readily applied to transport of passive scalar in complex flows. Some other examples such as heat transfer in a ribbed channel will be shown in the final presentation.
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.
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.
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.
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,…
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…
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…
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…
Implementing Change in College Algebra
ERIC Educational Resources Information Center
Haver, William E.
2007-01-01
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…
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…
Fuzzy-algebra uncertainty assessment
Cooper, J.A.; Cooper, D.K.
1994-12-01
A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.
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.
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…
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…
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…
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
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…
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…
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…
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…
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.
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.
Principals + Algebra (- Fear) = Instructional Leadership
ERIC Educational Resources Information Center
Carver, Cynthia L.
2010-01-01
Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…
Experts Question California's Algebra Edict
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…
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. PMID:23057823
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.
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.
The Exocenter of a Generalized Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2011-12-01
Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.
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.
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.
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.
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.
Detection of subsurface eddies from satellite observations
NASA Astrophysics Data System (ADS)
Assassi, Charefeddine; Morel, Yves; Chaigneau, Alexis; Pegliasco, Cori; Vandermeirsch, Frederic; Rosemary, Morrow; Colas, François; Fleury, Sara; Cambra, Rémi
2014-05-01
This study aims to develop an index that allows distinguishing between surface and subsurface intensified eddies from surface data only, in particular using the sea surface height and the sea surface temperature available from satellite observations. To do this, we propose the use of a simple index based on the ratio of the sea surface temperature anomaly (SSTa) and the sea level anomaly (SLA). This index is first derived using an academic approach, based on idealized assumptions of geostrophic balance and Gaussian-shaped vortices. This index depends on the vertical extent (or decreasing rate) of the eddy and because of its sensitivity to the exact shape of the vortex, we were not able to evaluate these depths from the surface fields and our results remain qualitative. Then, in order to examine the pertinence and validity of the proposed index, SSTa and SLA were computed using outputs of a realistic regional circulation model in the Peru-Chile upwelling system where both surface and subsurface eddies coexist. Over a seven year simulation, the statistics shows that 71% of eddies are correctly identified as surface or subsurface intensified. Multi-core eddies are also largely present and represent an average of 37% of all vortices. These multi-core eddies contribute to a large number of the wrong identification (15%). Finally, the index was successfully applied on in-situ data to detect a previously observed subsurface-intensified Swoddy (slope water eddy) in the Bay of Biscay. This study suggests that the index can be successfully used to determine the exact nature of mesoscale eddies (surface or subsurface- intensified) from satellite observations only.
Eddy-current sensor measures bolt loading
NASA Technical Reports Server (NTRS)
Burr, M. E.
1980-01-01
Thin wire welded to bottom of hole down center of bolt permits measurement of tension in bolt. Bolt lengthens under strain, but wire is not loaded, so gap between wire and eddy-current gap transducer mounted on bolt head indicates bolt loading. Eddy-current transducer could measure gap within 0.05 mm. Method does not require separate "standard" for each bolt type, and is not sensitive to dirt or oil in bolt hole, unlike ultrasonic probes.
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.
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.
Viscosity of multicomponent partially ionized gas mixtures
NASA Astrophysics Data System (ADS)
Armaly, B. F.; Sutton, K.
1980-07-01
An approximate method is proposed for predicting the viscosity of partially ionized gas mixtures. This technique expresses the viscosity of a mixture in terms of the viscosities of the individual pure components, is simple in form, and does not require large computer run times or storage. Thus, the technique is suitable for use with complex flowfields and heat-transfer calculations. Results for gas mixtures which are representative of the atmospheres of Jupiter, Earth, and Venus, are presented and it is shown that the results compare favorably with detailed kinetic-theory analyses.
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.
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.
Free Volume in Membranes: Viscosity or Tension?
Markin, V. S.; Sachs, F.
2016-01-01
Many papers have used fluorescent probe diffusion to infer membrane viscosity but the measurement is actually an assay of the free volume of the membrane. The free volume is also related to the membrane tension. Thus, changes in probe mobility refer equally well to changes in membrane tension. In complicated structures like cell membranes, it appears more intuitive to consider variations in free volume as referring to the effect of domains structures and interactions with the cytoskeleton than changes in viscosity since tension is a state variable and viscosity is not.
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.
NASA Astrophysics Data System (ADS)
Lu, Egang; Moore, Guy D.
2011-04-01
We compute the bulk viscosity of a gas of pions at temperatures below the QCD crossover temperature, for the physical value of mπ, 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 ζ~(F08/mπ5)exp(2mπ/T), where F0≃93MeV is the pion decay constant.
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.
Bulk viscosity of multiparticle collision dynamics fluids.
Theers, Mario; Winkler, Roland G
2015-03-01
We determine the viscosity parameters of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation method for fluids. We perform analytical calculations and verify our results by simulations. The stochastic rotation dynamics and the Andersen thermostat variant of MPC are considered, both with and without angular momentum conservation. As an important result, we find a nonzero bulk viscosity for every MPC version. The explicit calculation shows that the bulk viscosity is determined solely by the collisional interactions of MPC. PMID:25871248
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.
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.
Atomic effect algebras with compression bases
NASA Astrophysics Data System (ADS)
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-01
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.
Eddies in eastern boundary subtropical upwelling systems
NASA Astrophysics Data System (ADS)
Capet, X.; Colas, F.; McWilliams, J. C.; Penven, P.; Marchesiello, P.
Over the last decade, mesoscale-resolving ocean models of eastern boundary upwelling systems (EBS) have helped improve our understanding of the functioning of EBS and, in particular, assess the role of eddy activity in these systems. We review the main achievements in this regard and highlight remaining issues and challenges. In EBS, eddy activity arises from baroclinic/barotropic instability of the inshore and also offshore currents. Mesoscale eddies play a significant (although not leading) role in shaping the EBS dynamical structure, both directly and through associated submesoscale activity (i.e., primarily frontal). They do so by modifying both momentum and tracer balances in ways that cannot simply be understood in terms of diffusion. The relative degree to which these assertions about eddy activity and eddy role apply to each of the four major EBS (Canary, Benguela, Peru-Chile, and California Current Systems) remains to be established. Besides resolving the eddies, benefits from EBS high-resolution modeling include the possibility of accounting for the fine-scale structures of the nearshore wind, a better representation of the Ekman-driven coastal divergence, and (at resolution σ (1 km) or lower) inclusion of submesoscale (i.e., mainly frontal) processes. Recent numerical experiments suggest that accounting for these various processes in climate models, through resolution increase (possibly locally) or parameterization, would lead to significant basin-scale bias reduction. The mechanisms involved in upscaling from EBS toward the larger scale remain to be fully elucidated.
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 and variability in the Mozambique Channel
NASA Astrophysics Data System (ADS)
Schouten, Mathijs W.; de Ruijter, Wilhelmus P. M.; van Leeuwen, Peter Jan; Ridderinkhof, Herman
2003-07-01
Between 1995 and 2000, on average 4 eddies per year are observed from satellite altimetry to propagate southward through the Mozambique Channel, into the upstream Agulhas region. Further south, these eddies have been found to control the timing and frequency of Agulhas ring shedding. Within the Mozambique Channel, anomalous SSH amplitudes rise to 30 cm, in agreement with in situ measured velocities. Comparison of an observed velocity section with GCM model results shows that the Mozambique Channel eddies in these models are too surface intensified. Also, the number of eddies formed in the models is in disagreement with our observational analysis. Moored current meter measurements observing the passage of three eddies in 2000 are extended to a 5-year time series by referencing the anomalous surface currents estimated from altimeter data to a synoptic LADCP velocity measurement. The results show intermittent eddy passage at the mooring location. A statistical analysis of SSH observations in different parts of the Mozambique Channel shows a southward decrease of the dominant frequency of the variability, going from 7 per year in the extension of the South Equatorial Current north of Madagascar to 4 per year south of Madagascar. The observations suggest that frequency reduction is related to the Rossby waves coming in from the east.
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
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.
Shear viscosity in magnetized neutron star crust
NASA Astrophysics Data System (ADS)
Ofengeim, D. D.; Yakovlev, D. G.
2015-12-01
The electron shear viscosity due to Coulomb scattering of degenerate electrons by atomic nuclei throughout a magnetized neutron star crust is calculated. The theory is based on the shear viscosity coefficient calculated neglecting magnetic fields but taking into account gaseous, liquid and solid states of atomic nuclei, multiphonon scattering processes, and finite sizes of the nuclei albeit neglecting the effects of electron band structure. The effects of strong magnetic fields are included in the relaxation time approximation with the effective electron relaxation time taken from the field-free theory. The viscosity in a magnetized matter is described by five shear viscosity coefficients. They are calculated and their dependence on the magnetic field and other parameters of dense matter is analyzed. Possible applications and open problems are outlined.
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.
Sludge based Bacillus thuringiensis biopesticides: viscosity impacts.
Brar, S K; Verma, M; Tyagi, R D; Valéro, J R; Surampalli, R Y
2005-08-01
Viscosity studies were performed on raw, pre-treated (sterilised and thermal alkaline hydrolysed or both types of treatment) and Bacillus thuringiensis (Bt) fermented sludges at different solids concentration (10-40 g/L) for production of biopesticides. Correlations were established among rheological parameter (viscosity), solids (total and dissolved) concentration and entomotoxicity (Tx) of Bt fermented sludges. Exponential and power laws were preferentially followed by hydrolysed fermented compared to raw fermented sludge. Soluble chemical oxygen demand variation corroborated with increase in dissolved solids concentration on pre-treatments, contributing to changes in viscosity. Moreover, Tx was higher for hydrolysed fermented sludge in comparison to raw fermented sludge owing to increased availability of nutrients and lower viscosity that improved oxygen transfer. The shake flask results were reproducible in fermenter. This study will have major impact on selecting fermentation, harvesting and formulation techniques of Bt fermented sludges for biopesticide production. PMID:15979118
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.
Hydrophilicity and the viscosity of interfacial water.
Goertz, Matthew P; Houston, J E; Zhu, X-Y
2007-05-01
We measure the viscosity of nanometer-thick water films at the interface with an amorphous silica surface. We obtain viscosity values from three different measurements: friction force in a water meniscus formed between an oxide-terminated W tip and the silica surface under ambient conditions; similar measurements for these interfaces under water; and the repulsive "drainage" force as the two surfaces approach at various speeds in water. In all three cases, we obtain effective viscosities that are approximately 10(6) times greater than that of bulk water for nanometer-scale interfacial separations. This enhanced viscosity is not observed when we degrade the hydrophilicity of the surface by terminating it with -H or -CH3. In view of recent results from other interfaces, we conclude that the criterion for the formation of a viscous interphase is the degree of hydrophilicity of the interfacial pair. PMID:17408290
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.
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).
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.
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.
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
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
NASA Astrophysics Data System (ADS)
Khongsap, Ta; Wang, Weiqiang
2009-01-01
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.
Oral sensory discrimination of fluid viscosity.
Smith, C H; Logemann, J A; Burghardt, W R; Carrell, T D; Zecker, S G
1997-01-01
This study was designed to investigate the ability of normal young adult volunteers to sensorially identify Newtonian fluids of specified viscosities. Twenty subjects, 10 men and 10 women between the ages of 18 and 29 years participated. Seven stimuli, consisting of combinations of corn syrup and water, with viscosities ranging from 2 to 2,240 centipoise (cP) were prepared and characterized using a coaxial rotational viscometer. Subjects were presented with two anchor stimuli representing the extremes of the range of viscosities as a basis from which the experimental stimuli were judged. The seven experimental stimuli were randomly presented to each subject 10 times. The accuracy with which the subjects identified the viscosity of the fluid was significant at p < 0.01. The pattern of response was not significantly different across subjects nor gender. There were no differences in performance throughout the duration of the study. The repeat presentation of the anchor points did not significantly affect performance. Further research on oral perception of viscosity, and the processes that mediate changes in swallow physiology resulting from changes in viscosity is required. PMID:9071805
The viscosity of short polyelectrolyte solutions.
Izzo, Dora; Cloitre, Michel; Leibler, Ludwik
2014-03-21
We consider the viscosity of solutions of highly charged short polyelectrolytes. Our system is a poly(styrene-maleic acid) copolymer solution (SMA) with various added salt concentrations in dilute and semidilute regimes. The SMA solutions show some particular features: (i) variations of the specific viscosity measured for different values of concentration and ionic strength can be rescaled on two universal curves when plotted as a function of the effective volume fraction; (ii) the reduced viscosity is proportional to the Debye length. In order to describe the viscosity of such a system we model the motion of the charged rods considering a simpler system: we replace each charged rod and its corresponding charge cloud by an effective neutral rod. This modified system is yet below the concentrated regime and, at most, steric interactions are left. In the semidilute regime, we model the rescaled rods moving under a mean field potential and obtain a dynamical equation for the orientational tensor, considered small, and the viscosity is derived from it. Within our mean field approach, the effects due to the rod Brownian motion and due to the potential cancel each other and the behavior of the viscosity is explained in terms of the effective volume fraction only. Our predictions are in good qualitative agreement with the experimental results over a wide range of parameters, and suggest a method for obtaining the rotational diffusion constant in the semidilute regime. PMID:24652236
High-Temperature Viscosity of Commercial Glasses
Hrma, Pavel R.
2006-08-31
Arrhenius models were developed for glass viscosity within the processing temperature of six types of commercial glasses: low-expansion-borosilicate glasses, E glasses, fiberglass wool glasses, TV panel glasses, container glasses, and float glasses. Both local models (for each of the six glass types) and a global model (for the composition region of commercial glasses, i.e., the six glass types taken together) are presented. The models are based on viscosity data previously obtained with rotating spindle viscometers within the temperature range between 900 C and 1550 C; the viscosity varied from 1 Pa?s to 750 Pa?s. First-order models were applied to relate Arrhenius coefficients to the mass fractions of 15 components: SiO2, TiO2, ZrO2, Al2O3, Fe2O3, B2O3, MgO, CaO, SrO, BaO, PbO, ZnO, Li2O, Na2O, K2O. The R2 is 0.98 for the global model and ranges from .097 to 0.99 for the six local models. The models are recommended for glasses containing 42 to 84 mass% SiO2 to estimate viscosities or temperatures at a constant viscosity for melts within both the temperature range from 1100 C to 1550 C and viscosity range from 5 to 400 Pa?s.
High-Temperature Viscosity Of Commercial Glasses
Hrma, Pavel R; See, Clem A; Lam, Oanh P; Minister, Kevin B
2005-01-01
Viscosity was measured for six types of commercial glasses: low-expansion-borosilicate glasses, E glasses, fiberglass wool glasses, TV panel glasses, container glasses, and float glasses. Viscosity data were obtained with rotating spindle viscometers within the temperature range between 900°C and 1550°C; the viscosity varied from 1 Pa∙s to 750 Pa∙s. Arrhenius coefficients were calculated for individual glasses and linear models were applied to relate them to the mass fractions of 11 major components (SiO2, CaO, Na2O, Al2O3, B2O3, BaO, SrO, K2O, MgO, PbO, and ZrO2) and 12 minor components (Fe2O3, ZnO, Li2O, TiO2, CeO2, F, Sb2O3, Cr2O3, As2O3, MnO2, SO3, and Co3O4). The models are recommended for glasses containing 42 to 84 mass% SiO2 to estimate viscosities or temperatures at a constant viscosity for melts within both the temperature range from 1100°C to 1550°C and viscosity range from 10 to 400 Pas.
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
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
NASA Astrophysics Data System (ADS)
Liebske, Christian; Schmickler, Bettina; Terasaki, Hidenori; Poe, Brent T.; Suzuki, Akio; Funakoshi, Ken-ichi; Ando, Ryota; Rubie, David C.
2005-12-01
The viscosity of synthetic peridotite liquid has been investigated at high pressures using in-situ falling sphere viscometry by combining a multi-anvil technique with synchrotron radiation. We used a newly designed capsule containing a small recessed reservoir outside of the hot spot of the heater, in which a viscosity marker sphere is embedded in a forsterite + enstatite mixture having a higher solidus temperature than the peridotite. This experimental setup prevents spheres from falling before a stable temperature above the liquidus is established and thus avoids difficulties in evaluating viscosities from velocities of spheres falling through a partially molten sample. Experiments have been performed between 2.8 and 13 GPa at temperatures ranging from 2043 to 2523 K. Measured viscosities range from 0.019 (± 0.004) to 0.13 (± 0.02) Pa s. At constant temperature, viscosity increases with increasing pressure up to ˜ 8.5 GPa but then decreases between ˜ 8.5 and 13 GPa. The change in the pressure dependence of viscosity is likely associated with structural changes of the liquid that occur upon compression. By combining our results with recently published 0.1 MPa peridotite liquid viscosities [D.B. Dingwell, C. Courtial, D. Giordano, A. Nichols, Viscosity of peridotite liquid, Earth Planet. Sci. Lett. 226 (2004) 127-138.], the experimental data can be described by a non-Arrhenian, empirical Vogel-Fulcher-Tamman equation, which has been modified by adding a term to account for the observed pressure dependence of viscosity. This equation reproduces measured viscosities to within 0.08 log 10-units on average. We use this model to calculate viscosities of a peridotitic magma ocean along a liquid adiabat to a depth of ˜ 400 km and discuss possible effects on viscosity at greater pressures and temperatures than experimentally investigated.
Single axioms for Boolean algebra.
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
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.
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Yang, D.; Chen, B.; Chamecki, M.; Meneveau, C. V.
2014-12-01
As the oil plumes from deep water blowouts reach the ocean mixed layer (OML), their near-surface dispersions are highly influenced by the wind and wave-generated submesoscale Langmuir turbulence in the OML. In this study, we use large eddy simulations (LES) to model the oil dispersion at scales < 1 km. We find that despite the complex patterns of the instantaneous surface oil slick, the time-averaged surface oil plume can be parameterized as a Gaussian-type plume. The mean surface plume grows linearly downstream, with the centerline inclined clockwise (in the Northern Hemisphere) with respect to the wind and wave direction due to the Ekman transport. The inclination angle increase as the droplet size decreases, while the plume growth rate varies non-monotonically with oil droplet size. Using LES data, we evaluate the eddy viscosity and diffusivity following the K-profile parameterization (KPP) framework. We also evaluate the stress-strain misalignments caused by Stokes drift and the enhancement of eddy viscosity and diffusivity caused by Langmuir circulations. Improvements to the KPP model will be discussed. This study is supported by a Gulf of Mexico Research Initiative research grant.
Large eddy simulation of controlled transition to turbulence
NASA Astrophysics Data System (ADS)
Sayadi, Taraneh; Moin, Parviz
2012-11-01
Large eddy simulation of H- and K-type transitions in a spatially developing zero-pressure-gradient boundary layer at Ma∞ = 0.2 is investigated using several subgrid scale (SGS) models including constant coefficient Smagorinsky and Vreman models and their dynamic extensions, dynamic mixed scale-similarity, dynamic one-equation kinetic energy model, and global coefficient Vreman models. A key objective of this study is to assess the capability of SGS models to predict the location of transition and the skin friction throughout the transition process. The constant coefficient models fail to detect transition, but the dynamic procedure allows for a negligible turbulent viscosity in the early transition region. As a result, the "point" of transition is estimated correctly. However, after secondary instabilities set in and result in the overshoot in the skin friction profile, all models fail to produce sufficient subgrid scale shear stress required for the correct prediction of skin friction and the mean velocity profile. The same underprediction of skin friction persists into the turbulent region. Spatially filtered direct numerical simulation data in the same boundary layers are used to provide guidelines for SGS model development and validation.
A spin-orbit constraint on the viscosity of a Mercurian liquid core
NASA Technical Reports Server (NTRS)
Peale, S. J.; Boss, A. P.
1977-01-01
The escape of Mercury from the stable spin-orbit resonance in which the spin angular velocity is twice the orbital mean motion (2n) requires that the kinematic viscosity of a molten core with a laminar boundary layer be comparable to that of water (0.01 sq cm/s) and the tidal Q be less than about 100. If the boundary layer is turbulent, escape from the resonance is only consistent with a liquid core of low viscosity if the critical Reynolds number for the onset of turbulence is above about 500, the moment difference (B - A)/C is below about 0.00001, and the tidal dissipation factor Q is less than about 40. These conclusions depend on the assumptions that Mercury's obliquity was near 0 deg at the time of resonance passage, that the liquid core was not stably stratified at the time at which Mercury passed through the resonance, that a turbulent boundary layer can be characterized by a turbulent or eddy viscosity coefficient, and that the most important coupling between core and mantle is a viscous coupling at a smooth spherical boundary.
Eddy stirring in the Southern Ocean
NASA Astrophysics Data System (ADS)
Naveira Garabato, A. C.; Ferrari, R.; Polzin, K. L.
2011-09-01
There is an ongoing debate concerning the distribution of eddy stirring across the Antarctic Circumpolar Current (ACC) and the nature of its controlling processes. The problem is addressed here by estimating the isentropic eddy diffusivity κ from a collection of hydrographic and altimetric observations, analyzed in a mixing length theoretical framework. It is shown that, typically, κ is suppressed by an order of magnitude in the upper kilometer of the ACC frontal jets relative to their surroundings, primarily as a result of a local reduction of the mixing length. This observation is reproduced by a quasi-geostrophic theory of eddy stirring across a broad barotropic jet based on the scaling law derived by Ferrari and Nikurashin (2010). The theory interprets the observed widespread suppression of the mixing length and κ in the upper layers of frontal jets as the kinematic consequence of eddy propagation relative to the mean flow within jet cores. Deviations from the prevalent regime of mixing suppression in the core of upper-ocean jets are encountered in a few special sites. Such `leaky jet' segments appear to be associated with sharp stationary meanders of the mean flow that are generated by the interaction of the ACC with major topographic features. It is contended that the characteristic thermohaline structure of the Southern Ocean, consisting of multiple upper-ocean thermohaline fronts separated and underlaid by regions of homogenized properties, is largely a result of the widespread suppression of eddy stirring by parallel jets.
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.
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.
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.
Estimating Heavy Oil Viscosity from Seismic Data
NASA Astrophysics Data System (ADS)
Vasheghani Farahani, Fereidoon
Heavy oils are viscoelastic material; therefore, their shear properties influence the seismic response and should not be ignored. Heavy oil viscosity, among other parameters, controls the attenuation of seismic waves which is measured in terms of quality factor Q. BISQ, a poroviscoelastic model that couples the effects of simultaneous Biot and squirt flow mechanisms, is used to relate Q to the fluid viscosity. The variation of quality factor with respect to fluid viscosity, as predicted by BISQ, matches the laboratory measurements. Quality factor is a measurable seismic attribute. Higher frequency data are more favourable for Q estimation. Crosswell seismic data from a heavy oil reservoir is used for estimating Q. Travel time tomography followed by attenuation tomography yields the quality factor. The resultingQ tomogram can be converted into the viscosity tomogram if the remaining reservoir parameters are known. Such parameters are populated for the zone of interest using the geostatistical methods from the available log and core data at borehole locations. Existing BISQ equations can only take one fluid phase into account. However, the porous reservoir rock is saturated with bitumen and water. A slightly modified version of the BISQ relations is used in order to accommodate the presence of a second fluid phase. The estimated viscosity tomogram shows ambiguity because for every given quality factor, more than one viscosity value can be calculated. Despite the ambiguity, the methodology introduced in this study demonstrates that seismic data have the potential to be used for estimation of fluid viscosity in heavy oil reservoirs, although further research is needed to improve the workflow.
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
Lax operator algebras and integrable systems
NASA Astrophysics Data System (ADS)
Sheinman, O. K.
2016-02-01
A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite-dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero-Moser and Hitchin systems. In particular, the approach includes (non-twisted) Kac-Moody algebras and integrable systems with a rational spectral parameter. The presentation is based on quite simple ideas about the use of gradings of semisimple Lie algebras and their interaction with the Riemann-Roch theorem. The basic properties of Lax operator algebras and the basic facts about the theory of the integrable systems in question are treated (and proved) from this general point of view. In particular, the existence of commutative hierarchies and their Hamiltonian properties are considered. The paper concludes with an application of Lax operator algebras to prequantization of finite-dimensional integrable systems. Bibliography: 51 titles.
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.…
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.
Stability of algebraically unstable dispersive flows
NASA Astrophysics Data System (ADS)
King, Kristina; Zaretzky, Paula; Weinstein, Steven; Cromer, Michael; Barlow, Nathaniel
2015-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to a class of partial differential equations describing wave propagation in dispersive media. There are several morphological differences between algebraically growing disturbances and the exponentially growing wave packets inherent to classical linear stability analysis, and these are elucidated in this study.
Explicit travelling waves and invariant algebraic curves
NASA Astrophysics Data System (ADS)
Gasull, Armengol; Giacomini, Hector
2015-06-01
We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.
Finite-dimensional simple graded algebras
Bahturin, Yu A; Zaicev, M V; Sehgal, S K
2008-08-31
Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. In the paper it is proved that if the characteristic of F is zero or does not divide the order of any finite subgroup of G, then R is graded simple if and only if it is isomorphic to a matrix algebra over a finite-dimensional graded skew field. Bibliography: 24 titles.
NASA Astrophysics Data System (ADS)
Manerowska, Anna; Nieznański, Edward; Mulawka, Jan
2013-10-01
Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.
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.
Viscosity of Campi Flregrei (Italy) magmas
NASA Astrophysics Data System (ADS)
Misiti, Valeria; Vetere, Francesco; Scarlato, Piergiorgio; Behrens, Harald; Mangiacapra, Annarita; Freda, Carmela
2010-05-01
Viscosity is an important factor governing both intrusive and volcanic processes. The most important parameters governing silicate melts viscosity are bulk composition of melt and temperature. Pressure has only minor effect at crustal depths, whereas crystals and bubbles have significant influence. Among compositional parameters, the water content is critical above all in terms of rheological behaviour of melts and explosive style of an eruption. Consequently, without an appropriate knowledge of magma viscosity depending on the amount of dissolved volatiles, it is not possible to model the processes (i.e., magma ascent, fragmentation, and dispersion) required to predict realistic volcanic scenarios and thus forecast volcanic hazards. The Campi Flegrei are a large volcanic complex (~150 km2) located west of the city of Naples, Italy, that has been the site of volcanic activity for more than 60 ka and represents a potential volcanic hazard owing to the large local population. In the frame of a INGV-DPC (Department of Civil Protection) project devoted to design a multidisciplinary system for short-term volcano hazard evaluation, we performed viscosity measurements, under dry and hydrous conditions, of primitive melt compositions representative of two Campi Flegrei eruptions (Minopoli-shoshonite and Fondo Riccio-latite). Viscosity of the two melts have been investigated in the high temperature/low viscosity range at atmospheric pressure in dry samples and at 0.5 GPa in runs having water content from nominally anhydrous to about 3 wt%. Data in the low temperature/high viscosity range were obtained near the glass transition temperature at atmospheric pressure on samples whose water contents vary from 0.3 up to 2.43 wt%. The combination of high- and low-viscosity data permits a general description of the viscosity as a function of temperature and water content using a modified Tamman-Vogel-Fulcher equation. logν = a+ --b--+ --d--×exp(g × w-) (T - c) (T - e) T (1) where
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills 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.
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.
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.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Type-Decomposition of an Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2010-10-01
Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras. We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice.
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.
Deep Eddies in the Gulf of Mexico
NASA Astrophysics Data System (ADS)
Furey, H. H.; Bower, A. S.; Perez-Brunius, P.; Hamilton, P.
2014-12-01
A major Lagrangian program is currently underway to map the deep (1500-2500 m) circulation of the entire Gulf of Mexico. Beginning in 2011, more than 120 acoustically tracked RAFOS floats have been released in the eastern, central and western Gulf, many in pairs and triplets. Most floats are programmed to drift for two years, obtaining position fixes and temperature/pressure measurements three times daily. More than 80 floats have completed their missions, and results from the trajectories will be described with a focus on mesoscale eddying behavior. In particular, the first-ever observations of deep energetic anticyclonic eddies (possibly lenses) forming at and separating from a northeastward-flowing boundary current west of Campeche Bank will be discussed. The existence of these eddies has major implications for exchange between the continental slope and interior Gulf. The project is being supported by the U.S. Bureau of Ocean Energy Management (BOEM).
Analysis of a California Catalina eddy event
NASA Technical Reports Server (NTRS)
Bosart, L. F.
1983-01-01
During the period 26-29 May 1968 a shallow cyclonic circulation, known locally as a Catalina eddy, developed in the offshore waters of southern California. A synoptic and mesoscale analysis of the event establishes the following: (1) the incipient circulation forms on the coast near Santa Barbara downwind of the coastal mountains, (2) cyclonic shear vorticity appears offshore in response to lee troughing downstream of the coastal mountains between Vandenberg and Pt. Mugu, California, (3) mountain wave activity may be aiding incipient eddy formation in association with synoptic-scale subsidence and the generation of a stable layer near the crest of the coastal mountains, (4) a southeastward displacement and offshore expansion of the circulation occurs following the passage of the synoptic-scale ridge line, and (5) dissipation of the eddy occurs with the onset of a broad onshore flow.
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.
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
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.
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)
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.
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.
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. PMID:15549963
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. PMID:19394350
Probing Rotational Viscosity in Synaptic Vesicles
Zeigler, Maxwell B.; Allen, Peter B.; Chiu, Daniel T.
2011-01-01
The synaptic vesicle (SV) is a central organelle in neurotransmission, and previous studies have suggested that SV protein 2 (SV2) may be responsible for forming a gel-like matrix within the vesicle. Here we measured the steady-state rotational anisotropy of the fluorescent dye, Oregon Green, within individual SVs. By also measuring the fluorescence lifetime of Oregon Green in SVs, we determined the mean rotational viscosity to be 16.49 ± 0.12 cP for wild-type (WT) empty mice vesicles (i.e., with no neurotransmitters), 11.21 ± 0.12 cP for empty vesicles from SV2 knock-out mice, and 11.40 ± 0.65 cP for WT mice vesicles loaded with the neurotransmitter glutamate (Glu). This measurement shows that SV2 is an important determinant of viscosity within the vesicle lumen, and that the viscosity decreases when the vesicles are filled with Glu. The viscosities of both empty SV2 knock-out vesicles and Glu-loaded WT vesicles were significantly different from that of empty WT SVs (p < 0.05). This measurement represents the smallest enclosed volume in which rotational viscosity has been measured thus far. PMID:21641331
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…
Results of Using Algebra Tiles as Meaningful Representations of Algebra Concepts.
ERIC Educational Resources Information Center
Sharp, Janet M.
Mathematical meanings can be developed when individuals construct translations between algebra symbol systems and physical systems that represent one another. Previous research studies indicated (1) few high school students connect whole number manipulations to algebraic manipulations and (2) students who encounter algebraic ideas through…
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.
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.
Tracking the PRIME eddy using satellite altimetry
NASA Astrophysics Data System (ADS)
Wade, Ian P.; Heywood, Karen J.
The PRIME cruise to the North Atlantic during June/July 1996 surveyed and sampled an extremely vigorous and deep-reaching eddy with a significant barotropic component. Although it exhibited anticyclonic flow and featured a warm core at depth, it had been capped at some point during its lifetime, so appeared as a cold feature in the upper 500 m. Satellite-derived sea-surface temperatures (SST) showed it to have moved little during the few weeks prior to the cruise. In this paper we discuss the origin of the PRIME eddy including where and when it is likely to have formed. Consistently large amounts of cloud cover restrict the use of SST imagery to track such features. Altimetry provides a better method to trace this eddy back in time and space since microwave radiation is not significantly affected by cloud cover. Sea-level anomaly (SLA) data from the TOPEX/POSEIDON and European Remote Sensing (ERS) satellites were used. Results show that the eddy remained almost stationary in the Iceland Basin since first being detected in late 1995 and that it almost certainly formed locally, probably as a result of an instability in the current flow around the northwest of the Hatton Bank. Comparisons between satellite SLAs and hydrographic estimates of sea-surface elevation confirm that the eddy had a substantial barotropic flow. Both the altimeter data and the sea-surface height derived from the acoustic Doppler current profiler agree that the PRIME eddy had a sea-surface elevation of about 20 cm and that its diameter was about 120 km.
Effect of bulk viscosity in low density, hypersonic blunt body flows
Rutledge, W.H. ); Hoffmann, K.A. )
1991-01-01
A computational fluids dynamics scheme is presented to solve the unsteady Thin-Layer Navier-Stokes (TLNS) equations over a blunt body at high altitude, high Mach number atmospheric reentry flow conditions. This continuum approach is directed to low density hypersonic flows by accounting for non-zero bulk viscosity effects in near frozen flow conditions. The TLNS equations are solved over an axisymmetric body at zero incidence relative to the free stream. The time dependent axisymmetric governing equations are transformed into a computational plane, then cast into weak conservative form and solved using a first-order fully implicit scheme in time with second-order flux vector splitting for spatial derivatives. The physical domain is defined over representative sphere and sphere/cone geometries using a body-fitted clustered algebraic grid within a fixed domain (i.e., shock capturing). At the present time, nonequilibrium thermo-chemistry effects are not modeled. Catalytic wall, ionization and radiation effects are also excluded from the current analysis. However, the significant difference from previous studies is the inclusion of the capability to model non-zero bulk viscosity effects. The importance of bulk viscosity is reviewed and blunt body flow field solutions are presented to illustrate the potential contribution of this phenomena at high altitude hypersonic conditions. The current technique is compared with experimental data and other approximate continuum solutions. A variety of test cases are also presented for a wide range of free stream Mach conditions. 18 refs., 42 figs.
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.
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 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. PMID:26659053
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.
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.
Cosmological two-fluid bulk viscosity
NASA Astrophysics Data System (ADS)
van den Horn, L. J.; Salvati, G. A. Q.
2016-04-01
A simple two-fluid model of cosmological bulk viscosity, in which small deviations from thermal equilibrium account for the viscous bulk pressure, is substantiated by kinetic theory. Some peculiar issues regarding its relation to the radiative fluid model are discussed. The microphysical picture underlying the viscous dissipation is made precise. We also consider a reactive `cross' viscosity associated with deviations from detailed balance, which includes the so-called creation pressure of the cosmological fluid. For collisional interactions between the fluid components, the reactive viscous pressure is not an independent mechanism for entropy production. Entropy from cross effects may be generated through an effective isentropic particle source. In both instances new results are obtained for the reactive viscosity, and applied to a representative case of non-equilibrium decay.
Increased blood viscosity in diabetic proliferative retinopathy.
Lowe, G D; Ghafour, I M; Belch, J J; Forbes, C D; Foulds, W S; MacCuish, A C
1986-02-01
Blood rheology and haemostasis were assessed in 18 diabetics with proliferative retinopathy and in 18 diabetics without proliferative retinopathy, matched for age, sex, smoking habit and type, duration and treatment of diabetes. Proliferative retinopathy was associated with significantly higher levels of blood viscosity at high and low shear rates, which were related to higher levels of plasma viscosity and fibrinogen. Blood urea, glucose, glycosylated haemoglobin and white cell count were also significantly higher, whereas haematocrit, red cell deformability and several other haematological and biochemical variables did not differ significantly in the 2 groups. In view of these findings, and of our recent demonstration that increased blood viscosity also exists in those patients with retinal vein occlusion who develop a similar proliferative retinopathy, we suggest that hyperviscosity may contribute to retinal ischaemia and hence proliferative retinopathy. PMID:3698481
The Algebra of Lexical Semantics
NASA Astrophysics Data System (ADS)
Kornai, András
The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.
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.
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.
Viscosity properties of sodium borophosphate glasses
Gaylord, S.; Tincher, B.; Petit, L. Richardson, K.
2009-05-06
The viscosity behavior of (1 - x)NaPO{sub 3}-xNa{sub 2}B{sub 4}O{sub 7} glasses (x = 0.05-0.20) have been measured as a function of temperature using beam-bending and parallel-plate viscometry. The viscosity was found to shift to higher temperatures with increasing sodium borate content. The kinetic fragility parameter, m, estimated from the viscosity curve, decreases from 52 to 33 when x increases from 0.05 to 0.20 indicating that the glass network transforms from fragile to strong with the addition of Na{sub 2}B{sub 4}O{sub 7}. The decrease in fragility with increasing x is due to the progressive depolymerization of the phosphate network by the preferred four-coordinated boron atoms present in the low alkali borate glasses. As confirmed by Raman spectroscopy increasing alkali borate leads to enhanced B-O-P linkages realized with the accompanying transition from solely four-coordinated boron (in BO{sub 4} units) to mixed BO{sub 4}/BO{sub 3} structures. The glass viscosity characteristics of the investigated glasses were compared to those of P-SF67 and N-FK5 commercial glasses from SCHOTT. We showed that the dependence of the viscosity of P-SF67 was similar to the investigated glasses due to similar phosphate network organization confirmed by Raman spectroscopy, whereas N-FK5 exhibited a very different viscosity curve and fragility parameter due to its highly coordinated silicate network.
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.
Thermal relics in cosmology with bulk viscosity
NASA Astrophysics Data System (ADS)
Iorio, A.; Lambiase, G.
2015-03-01
In this paper we discuss some consequences of cosmological models in which the primordial cosmic matter is described by a relativistic imperfect fluid. The latter takes into account the dissipative effects (bulk viscosity) arising from different cooling rates of the fluid components in the expanding Universe. We discuss, in particular, the effects of the bulk viscosity on Big Bang Nucleosynthesis and on the thermal relic abundance of particles, looking at recent results of PAMELA experiment. The latter has determined an anomalous excess of positron events, which cannot be explained by conventional cosmology and particle physics.
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.
Rare Gas Viscosities: A Learning Tool
NASA Astrophysics Data System (ADS)
Halpern, Arthur M.
2002-02-01
The viscosities, h, of the rare gases and SF6 are determined in a physical chemistry laboratory experiment using the evacuation method, which is based on Poiseuille's equation. Students become aware that h does not vary monotonically with row number (or atomic mass) and confirm this behavior on the basis of the kinetic theory expression for h. They find that the collision diameters of the gases, s, which are obtained from h values, increase monotonically with molar mass, as expected. Students can show that values of s obtained from gas viscosities agree reasonably well with ab initio calculations of atomic (molecular) diameters using Gaussian 98W.
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.
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.
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.
Gravimetric capillary method for kinematic viscosity measurements
NASA Technical Reports Server (NTRS)
Rosenberger, Franz; Iwan, J.; Alexander, D.; Jin, Wei-Qing
1992-01-01
A novel version of the capillary method for viscosity measurements of liquids is presented. Viscosity data can be deduced in a straightforward way from mass transfer data obtained by differential weighing during the gravity-induced flow of the liquid between two cylindrical chambers. Tests of this technique with water, carbon tetrachloride, and ethanol suggest that this arrangement provides an accuracy of about +/- 1 percent. The technique facilitates operation under sealed, isothermal conditions and, thus can readily be applied to reactive and/or high vapor pressure liquids.
Wave Speeds, Riemann Solvers and Artificial Viscosity
Rider, W.J.
1999-07-18
A common perspective on the numerical solution of the equation Euler equations for shock physics is examined. The common viewpoint is based upon the selection of nonlinear wavespeeds upon which the dissipation (implicit or explicit) is founded. This perspective shows commonality between Riemann solver based method (i.e. Godunov-type) and artificial viscosity (i.e. von Neumann-Richtmyer). As an example we derive an improved nonlinear viscous stabilization of a Richtmyer-Lax-Wendroff method. Additionally, we will define a form of classical artificial viscosity based upon the HLL Riemann solver.
Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras
NASA Astrophysics Data System (ADS)
Konig, Martinvaldo
2014-10-01
Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.
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.
Two contra-rotating eddies of the Mozambique Ridge Current
NASA Astrophysics Data System (ADS)
Gründlingh, Marten L.
1989-01-01
The combined existence of a cyclonic and anticyclonic eddy pair on the Mozambique Ridge tends to confirm the hypothesis that they are created by a westward-flowing Mozambique Ridge Current. The eddies are mutually comparable in size but smaller than cyclonic eddies previously observed in the region.
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.
Realizations of conformal current-type Lie algebras
Pei Yufeng; Bai Chengming
2010-05-15
In this paper we obtain the realizations of some infinite-dimensional Lie algebras, named 'conformal current-type Lie algebras', in terms of a two-dimensional Novikov algebra and its deformations. Furthermore, Ovsienko and Roger's loop cotangent Virasoro algebra, which can be regarded as a nice generalization of the Virasoro algebra with two space variables, is naturally realized as an affinization of the tensor product of a deformation of the two-dimensional Novikov algebra and the Laurent polynomial algebra. These realizations shed new light on various aspects of the structure and representation theory of the corresponding infinite-dimensional Lie algebras.
Is Algebra Really Difficult for All Students?
ERIC Educational Resources Information Center
Egodawatte, Gunawardena
2009-01-01
Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…
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)
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…
Algebra in the Early Years? Yes!
ERIC Educational Resources Information Center
Taylor-Cox, Jennifer
2003-01-01
Suggests ways early years educators can begin teaching young children to think algebraically and prepare them for success in algebra. Focuses on ways to promote mathematical patterns, mathematical situations and structures, models of quantitative relationship, and change. Describes how first-graders used real object representations to better…
Algebraic Thinking: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
2010-01-01
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
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.
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.
Cartan calculus on quantum Lie algebras
Schupp, P.; Watts, P.; Zumino, B.
1993-12-09
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``
Low Performers Found Unready to Take Algebra
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…
An algebraic approach to the scattering equations
NASA Astrophysics Data System (ADS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-12-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
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…