Algebraic Rainich conditions for the tensor V

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$, a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor $B_{\alpha\beta\mu\nu}$ fulfill these conditions, but so also does our recently proposed tensor $V_{\alpha\beta\mu\nu}$, which has many of the desirable properties of $B_{\alpha\beta\mu\nu}$. For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors $B_{\alpha\beta\mu\nu}$ and $V_{\alpha\beta\mu\nu}$ which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions. Furthermore, relaxing the quasilocal restriction and considering the general fourth rank tensor, we found two remarkable results: (i) without any symmetry requirement, the algebraic Rainich conditions only require totally trace free; (ii) with a symmetry requirement, we recovered the same result as in the quasilocal small sphere limit.Comment: 17 page

On the modeling of low-Reynolds-number turbulence

A full Reynolds-stress closure that is capable of describing the flow all the way to the wall was formulated for turbulent flow through circular pipe. Since viscosity does not appear explicitly in the pressure redistribution terms, conventional high-number models for these terms are found to be applicable. However, the models for turbulent diffusion and viscous dissipation have to be modified to account for viscous diffusion near a wall. Two redistribution and two diffusion models are investigated for their effects on the model calculations. Wall correction to pressure redistribution modeling is also examined. Diffusion effects on calculated turbulent properties are further investigated by simplifying the transport equations to algebraic equations for Reynolds stress. Two approximations are explored. These are the equilibrium and nonequilibrium turbulence assumptions. Finally, the two-equation closure is also used to calculate the flow in question and the results compared with all the other model calculations. Fully developed pipe flows at two moderate Reynolds numbers are used to validate these model calculations

Gravitational energy in a small region for the modified Einstein and Landau-Lifshitz pseudotensors

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$. However, we propose a new tensor $V_{\alpha\beta\mu\nu}$ which is the sum of certain tensors $S_{\alpha\beta\mu\nu}$ and $K_{\alpha\beta\mu\nu}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{\alpha\beta\mu\nu}$ does. Moreover, we show that a modified Einstein pseudotensor turns out to be one of the Chen-Nester quasilocal expressions, while the modified Landau-Lifshitz pseudotensor becomes the Papapetrou pseudotensor; these two modified pseudotensors have positive gravitational energy in a small region.Comment:

Development of growth rate, body lipid, moisture, and energy models for white sturgeon (Acipenser transmontanus) fed at various feeding rates.

The objectives were to develop and evaluate: 1) growth rate models, 2) body lipid, moisture, and energy models for white sturgeon fed at various feeding rates (FR; % body weight [BW] per day) and then evaluate responses at proportions of optimum feeding rate (OFR) across increasing BW (g). For objective 1, 19 datasets from the literature containing initial BW, FR and specific growth rate (SGR; % BW increase per day) were used. For objective 2, 12 datasets from the literature (11 from objective 1) containing SGR, FR, final BW, body lipid (%), protein (%), ash (%), moisture (%), and energy (kJ/g) were used. The average rearing temperatures was 19.2 ± 1.5 °C (mean ± SD). The average nutrient compositions and gross energy of the diets were 45.7 ± 4.3% protein, 14.8 ± 3.2% lipid, and 20.4 ± 1.3 kJ/g, respectively. The logistic model was used for objectives 1 and 2 to develop a statistical relationship between SGR and FR, then an iterative technique was used to estimate OFR for each dataset. For objective 2, the statistical relationship between body lipid, energy, and moisture and FR was established. Using the OFR estimate, SGR, body lipid, energy and moisture were computed at various FR as a proportion of OFR. Finally, a nonparametric fitting procedure was used to establish relationships between SGR, body lipid, energy and moisture (responses) compared with BW (predictor) at various proportions of OFR. This allows visualization of the effect of under- or over-feeding on the various responses. When examining the differences between OFR at 100% and various proportions of OFR, SGR differences decrease and moisture differences increase as BW increases. Lipid and energy differences decrease as BW increases. To our knowledge, these are the first description of changes in nutrient compositions when white sturgeon are fed at various FR. Because physiological and behavioral properties that are unique to sturgeon, results from this study are specific to sturgeon under the conditions of this study and cannot be compared directly with salmonids even if some of the results are similar. This research provides insight to designing future nutritional studies in sturgeon

A modification of the Chen-Nester quasilocal expressions

Chen and Nester proposed four boundary expressions for the quasilocal quantities using the covariant Hamiltonian formalism. Based on these four expressions, there is a simple generalization that one can consider, so that a two parameter set of boundary expressions can be constructed. Using these modified expressions, a nice result for gravitational energy-momentum can be obtained in holonomic frames.Comment: 11 page

Inside the Black Box of Doctoral Education: What Program Characteristics Influence Doctoral Students’ Attrition and Graduation Probabilities?

[Excerpt] In this paper, we go inside the “black box” of graduate education to investigate what characteristics of graduate programs in the humanities and related social sciences actually influence PhD students’ attrition and graduation probabilities. We make use of data from the Graduate Education Survey; a retrospective survey of all graduate students who entered PhD programs in the treatment and control departments during the 1982-1997 period that was conducted by Mathematica Policy Research Inc. for the Mellon Foundation. After briefly describing the survey in the next section, section III outlines our methodological approach. Section IV presents our empirical findings and brief concluding remarks appear in section V. While our focus is on evaluating the effects of the GEI, we believe the methodological approach that we use can be profitably employed in a wide range of program evaluation studies

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper

A compressible near-wall turbulence model for boundary layer calculations

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects