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We consider the effects of external electric field and anisotropic long-range reactivity on the recombination dynamics of a geminate charge pair. A closed-form analytic expression for the ultimate separation probability of the pair is presented. In previous theories, analytic expressions for the separation probability were obtained only for the case where the recombination reaction can be assumed to occur at a contact separation. For this case, Noolandi and Hong obtained an exact solution, but their expression for the separation probability was too complicated to evaluate. Hence an approximate analytic expression proposed by Braun has been widely used. However, Braun's expression overestimates the separation probability when the electric field is large. In this work, we present an approximate analytic expression that is accurate enough for all parameter values. In addition, the expression is also applicable when the interaction between the geminate charge pair is described by screened Coulombic potential, and the recombination reaction has an anisotropic and long-range reactivity. We also provide the expression for the separation probability when the initial separation between the geminate charge pair is larger than the contact distance. [ABSTRACT FROM AUTHOR]

We present an elementary, but still quite rigorous derivation of the Clausius inequality, which sheds a new perspective on the second law. Unlike the classical approach, our derivation does not employ the Carnot cycle. The Clausius inequality follows in a straightforward way from the first law and thermodynamic stability conditions without invoking the Clausius or the Kelvin-Planck statement of the second law. The background knowledge required for this article is the same as that for the usual textbook presentation of the second law. The new presentation of the second law is, therefore, appropriate for an introductory thermodynamics course. [ABSTRACT FROM AUTHOR]

This letter is to respond to "Comment on 'An Alternative Presentation of the Second Law of Thermodynamics"', which discusses some shortcomings of our approach of teaching the second law of thermodynamics. [ABSTRACT FROM AUTHOR]

Objectives: Body mass index (BMI) is commonly used in epidemiological study or clinical center. However, it is not exactly correlated with body fat composition and does not reflect sex, age, or race. The aim of this article is to evaluate the validity of BMI standards relative to total body fat (TBF) and to estimate new BMI criteria that correspond to TBF for obesity, especially for Asian postmenopausal women. Methods: A total 3,936 patients were included in this cross-sectional study, including 1,565 premenopausal and 2,371 postmenopausal women. At the time of visit, demographic data were collected. We demonstrated the validity of BMI cut-point of 25 kg/m2 by using area under the curve (AUC), and presented the empirical optimal BMI cut-point by using Youden's index and overall accuracy in both premenopausal and postmenopausal women. Results: BMI-defined obesity (≥ 25 kg/m2) represents high AUC values (> 0.9) for each TBF. In premenopausal women, TBF ≥ 38% and corresponding BMI value was 29.45 kg/m2 indicated the highest both Youden's index and overall accuracy. In comparison, postmenopausal women who were TBF ≥ 38% showed the highest Youden's index and overall accuracy, and corresponding BMI value was 26.45 kg/m2. Conclusions: We proposed new BMI criteria for obesity by using TBF reference. With application of bioelectrical impedance analysis, the diagnosis of obesity using BMI criteria may differ between premenopausal and postmenopausal women. [ABSTRACT FROM AUTHOR]