Experiments and modeling

The usual approach in establishing the correctness and accuracy of turbulence models is to numerically solve the modeled differential equations and then compare the results with the experiment. However, in the case of a discrepancy, this procedure does not pinpoint where in the model the drawback lies. It is also possible that the model overcompensates one physical phenomenon and undercompensates the other so that the net result is a good agreement between the two. Therefore, a more desirable approach is to directly compare the individual terms in the equations with their models. To achieve this objective, primary physical experiments were used to carry out the second moment budgets. These can then be used to analyze and assess various models and closure assumptions and seek improvements/modifications where models prove deficient

Turbulence modeling and experiments

The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat flux equations for the buoyant plume

Intangible Capital, Barriers to Technology Adoption and Cross-Country Income Differences

I add intangible capital to a variant of the neoclassical growth model and study the implications of this extension for cross-country income differences. I calibrate the parameters associated with intangible capital by using new estimates of investment in intangibles by Corrado et al. [2006]. I find that the addition of intangible capital significantly improves the model's ability to account for cross-country income differences. Specifically, when intangible capital is added to the model, the required TFP ratio to explain observed income differences falls from 4.05 to 2.97. I also study variants of the model with endogenous and exogenous barriers to accumulation of technology capital, which consists of intangible capital and a fraction of physical capital that embodies technology. The addition of endogenous barriers, for reasonable parameter values, has a very small positive effect on the ability of the model to account for income differences. The addition of exogenous barriers suggests that huge cross-country differences in such barriers are needed to generate the observed income differences.Cross-country Income Differences; Intangible Capital; Technology Adoption

A note on the transitional behavior of the saving rate in the neo-classical growth model (the Cobb-Douglas case)

In this short note I clarify two features of Figure 2.3 in Barro and Sala-i-Martin (2004). The figure, as it appeared in the first and second editions of the book, is confusing if not wrong. I hope this note will serve as a corrigendum to the figure.Transition dynamics; Saving rate; Neo-classical growth model

Intangible Capital and International Income Differences

I add intangible capital to a variant of the neoclassical growth model and study the implications for cross-country income differences. I calibrate the parameters associated with intangible capital by using new estimates of investment in intangibles by Corrado et al. (2006). When intangible capital is added to the model, the TFP elasticity of output increases from 2.14 to 2.64. This finding implies that the addition of intangible capital increases the ability of the neoclassical growth model to explain international income differences by more than a factor of two.International Income Differences; Intangible Capital

Maximum-likelihood coherent-state quantum process tomography

Coherent-state quantum process tomography (csQPT) is a method of completely characterizing a quantum-optical "black box" by probing it with coherent states and performing homodyne measurements on the output [M. Lobino et al, Science 322, 563 (2008)]. We present a technique for csQPT that is fully based on statistical inference, specifically, quantum expectation-maximization. The method relies on the Jamiolkowski isomorphism and iteratively reconstructs the process tensor in the Fock basis directly from the experimental data. This approach permits incorporation of a priori constraints into the reconstruction procedure, thereby guaranteeing that the resulting process tensor is physically consistent. Furthermore, our method is easier to implement and requires a narrower range of coherent states than its predecessors. We test its feasibility using simulations on several experimentally relevant processes.Comment: 17 pages, 4 figure