Thermoelectric efficiency has three Degrees of Freedom

Thermal energy can be directly converted to electrical energy as a result of thermoelectric effects. Because this conversion realises clean energy technology, such as waste heat recovery and energy harvesting, substantial efforts have been made to search for thermoelectric materials. Under the belief that the material figure of merit $zT$ represents the energy conversion efficiencies of thermoelectric devices, various high peak-$zT$ materials have been explored for half a century. However, thermoelectric properties vary greatly with temperature $T$, so the single value $zT$ does not represent device efficiency accurately. Here we show that the efficiency of thermoelectric conversion is completely determined by \emph{three} parameters $Z_{\mathrm{gen}}$, $\tau$, and $\beta$, which we call the \emph{thermoelectric degrees of freedom}. The $Z_{\mathrm{gen}}$, which is an average of material properties, is a generalisation of the traditional figure of merit. The $\tau$ and $\beta$, which reflect the gradients of the material properties, are proportional to escaped heat caused by the Thomson effect and asymmetric Joule heat, respectively. Our finding proposes new directions for achieving high thermoelectric efficiency; increasing one of the thermoelectric degrees of freedom results in higher efficiency. For example, thermoelectric efficiency can be enhanced up to 176\% by tuning the thermoelectric degrees of freedom in segmented legs, compared to the best efficiency of single-material legs.Comment: main articles with 9 pages, 4 figures, supplementary information with 35 pages, 9 figures, 6 table

A Mathematical Programming Approach for Integrated Multiple Linear Regression Subset Selection and Validation

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. We also propose an efficient constraint to approximate the constraint for the coefficient t-test. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to the state-of-the-art benchmark models while maintaining similar explanatory power

Nonstationary Nonlinear Heteroskedasticity in Regression

This paper considers the regression with errors having nonstationary nonlinear heteroskedasticity. For both the usual stationary regression and the nonstationary cointegrating regression, we develop the asymptotic theories for the least squares methods in the presence of conditional heterogeneity given as a nonlinear function of an integrated process. In particular, it is shown that the nonstationarity of volatility in the regression errors may induce spuriousness of the underlying regression. This is true for both the usual stationary regression and the nonstationary cointegrating regression, if excessive nonstationary volatility is present in the errors. Mild nonstationary volatilities do not render the underlying regression spurious. However, their presence makes the least squares estimator asymptotically biased and inefficient and the usual chi-square test invalid. In the paper, we develop an unbiased and efficient method of estimation and a chi-square test applicable for the regression with mild nonstationary volatilities in the errors. We provide some illustrations to demonstrate the empirical relevancy of the model and theory developed in the paper. For this purpose, examined are US consumption function, EURO/USD forward-spot spreads and capital-asset pricing models for some major NYSE stocksvolatility, nonstationary nonlinear heteroskedasticity, regression with heteroskedastic errors, spurious regression, cointegration

Shuttle rocket booster computational fluid dynamics

Additional results and a revised and improved computer program listing from the shuttle rocket booster computational fluid dynamics formulations are presented. Numerical calculations for the flame zone of solid propellants are carried out using the Galerkin finite elements, with perturbations expanded to the zeroth, first, and second orders. The results indicate that amplification of oscillatory motions does indeed prevail in high frequency regions. For the second order system, the trend is similar to the first order system for low frequencies, but instabilities may appear at frequencies lower than those of the first order system. The most significant effect of the second order system is that the admittance is extremely oscillatory between moderately high frequency ranges

Development of a computerized analysis for solid propellant combustion instability with turbulence

A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed