In this paper, we study the moduli spaces of m‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient shrinking solitons. © 2012 Wiley Periodicals, Inc.
SUMMARYAccurate measurements of cigarette coal temperature are essential to understand the thermophysical and thermochemical processes in a burning cigarette. The last systematic studies of cigarette burning temperature measurements were conducted in the mid-1970s. Contemporary cigarettes have evolved in design features and multiple standard machine-smoking regimes have also become available, hence there is a need to re-examine cigarette combustion. In this work, we performed systematic measurements on gas-phase temperature of burning cigarettes using an improved fine thermocouple technique. The effects of machine-smoking parameters (puff volume and puff duration) and filter ventilation levels were studied with high spatial and time resolutions during single puffs. The experimental results were presented in a number of different ways to highlight the dynamic and complex thermal processes inside a burning coal. A mathematical distribution equation was used to fit the experimental temperature data. Extracting and plotting the distribution parameters against puffing time revealed complex temperature profiles under different coal volume as a function of puffing intensities or filter ventilation levels. By dividing the coal volume prior to puffing into three temperature ranges (lowtemperature from 200 to 400 °C, medium-temperature from 400 to 600 °C, and high-temperature volume above 600 °C) by following their development at different smoking regimes, useful mechanistic details were obtained. Finally, direct visualisation of the gas-phase temperature through detailed temperature and temperature gradient contour maps provided further insights into the complex thermophysics of the burning coal. [Beitr. Tabakforsch. Int. 26 (2014) 191-203]
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The borehole acoustic reflection imaging logging is a newly developed acoustic logging method that has attracted many interests. These converted and reflected waves for imaging are usually mixed up with borehole guided waves and therefore difficult to be clearly identified. To improve the downhole tool design and develop more sophisticate data processing and interpretation algorithms, studies on precisely numerical modeling of the wave fields in the acoustic reflection imaging logging are necessary and critical. This paper developed a parallelized scheme of 3D finite difference (3DFD) with nonuniform staggered grid and PML absorbing boundary to simulate the acoustic wave fields in isotropic and anisotropic formations. Applications of this scheme to the typical cases of isotropic and anisotropic formations and comparison with the results from published analytical solutions have demonstrated the validation and efficiency of the scheme. Higher accuracy and lower computation cost (3.5 times faster than the conventional schemes) have been achieved with this scheme for modeling such a complex wave fields of 60 dB dynamic range with higher frequency (10 kHz). This simulating program provides a quantitative analytical means for studying acoustic reflection imaging tool and development of the data processing and interpretation methods.acoustic reflection imaging, 3D wave field modeling, non-uniform staggered grid, PML absorb ring boundary, parallel schemeThe borehole acoustic reflection imaging logging is a newly developed acoustic logging method and has attracted many interests in recent years. After its pioneer tool, BARS (borehole acoustic reflection survey) [1] , developed in the last decade, Schlumberger recently introduced a new generation acoustic logging tool, sonic scanner, which was reported to have achieved much better reflected wave field imaging [2] . Tang et al. [3] have recently developed an algorithm for reflected wave imaging from the signal received by conventional tools like XMAC of Baker Hughes. In China, the Logging Service Company of Dagang Oilfield developed a new logging tool of ultra-long spacing with the similar functions as BARS in 2005 1) . These tools radiate wave energy into the surrounding formations as P and S waves. When encountered impedance discontinuity, these waves will be reflected and refracted, as shown in Figure 1, accompanying also the mode conversions between P and S. According to Snell's law, it is easy to see from the geometrical ray paths that the P-P reflections can be received when the transmitter and receiver transducers are all above (or below) the reflective interface, as shown in Figure 2. While the converted waves P-S and S-P can be received if the transmitter and receiver transducers are located above and below the interface separately, as shown in Figure 3. These converted and reflected waves can be utilized to image the position and geometry of the geological structures away from borehole to obtain the information like dips and azimuths of these structures [4,5] . Th...
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