Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions

We investigate exact results of isotropic turbulence in three-dimensions when the pressure gradient is negligible. We derive exact two-point correlation functions of density in three-dimensions and show that the density-density correlator behaves as $|{x_1 - x_2}|^{-\alpha_3}$, where $\alpha_3 = 2 + \frac{\sqrt{33}}{6}$. It is shown that, in three-dimensions, the energy spectrum $E(k)$ in the inertial range scales with exponent $2 - \frac {\sqrt{33}}{12} \simeq 1.5212$. We also discuss the time scale for which our exact results are valid for strong 3D--turbulence in the presence of the pressure. We confirm our predictions by using the recent results of numerical calculations and experiment.Comment: 9 pages, latex, no figures, we have corrected the our basic equations. We predict the inertial-range exponent for the energy spectrum for 3D-turbulence without pressure. We will present the detail of calculation and the results for 2D-turbulence elsewhere. Also some references are adde

The association of mammographic density with ductal carcinoma in situ of the breast: the Multiethnic Cohort

INTRODUCTION: It is well established that women with high mammographic density are at greater risk for breast cancer than are women with low breast density. However, little research has been done on mammographic density and ductal carcinoma in situ (DCIS) of the breast, which is thought to be a precursor lesion to some invasive breast cancers. METHOD: We conducted a nested case-control study within the Multiethnic Cohort, and compared the mammographic densities of 482 patients with invasive breast cancer and 119 with breast DCIS cases versus those of 667 cancer-free control subjects. A reader blinded to disease status performed computer-assisted density assessment. For women with more than one mammogram, mean density values were computed. Polytomous logistic regression models were used to compute adjusted odds ratios (ORs) and 95% confidence intervals (CIs) for two measurements of mammographic density: percentage density and dense area. RESULTS: Mammographic density was associated with invasive breast cancer and breast DCIS. For the highest category of percentage breast density (≥50%) as compared with the lowest (<10%), the OR was 3.58 (95% CI 2.26–5.66) for invasive breast cancer and 2.86 (1.38–5.94) for breast DCIS. Similarly, for the highest category of dense area (≥45 cm(2)) as compared with the lowest (<15 cm(2)), the OR was 2.92 (95% CI 2.01–4.25) for invasive breast cancer and 2.59 (1.39–4.82) for breast DCIS. Trend tests were significant for invasive breast cancer (P for trend < 0.0001) and breast DCIS (P for trend < 0.001) for both percentage density and dense area. CONCLUSION: The similar strength of association for mammographic density with breast DCIS and invasive breast cancer supports the hypothesis that both diseases may have a common etiology

A theoretical investigation of the two-fluid model of liquid HE-11 using linear irreversible thermodynamics

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