Calculation of Irreducible Water Saturation (S wirr) from NMR Logs in Tight Gas Sands

It is difficult to calculate irreducible water saturation (S _wirr) from nuclear magnetic resonance (NMR) logs in tight gas sands due to the effect of diffusion relaxation on the NMR T ₂ spectrum at present. By combining with classical Timur and Schlumberger—Doll Research (SDR) models, a novel model of calculating S _wirr is derived. The advantage of this novel model is that S _wirr can be calculated without a T ₂ cutoff, and all input information can be acquired from NMR logs accurately. With the calibration of 36 core samples, which were drilled from Xujiahe Formation in Bao-jie region of Triassic, Sichuan basin, southwest China, the values of these statistic model parameters are defined. Field examples of tight gas sands show that the proposed model is reliable. The S _wirr calculated with the proposed model match well with core analyzed results both in tight gas formations and water-saturated layers, the absolute error is in the range of ±4%. The calculated results by using 20.75 ms as the T ₂ cutoff are accurate in water-saturated layers but are overestimated in gas-bearing intervals. Defining 33 ms as the T ₂ cutoff is unusable both in gas-bearing and water layers.     

Saturation of density-charge algebra

It is shown, with rather general assumptions, that the U(6)_W density-charge commutation relations at infinite momentum cannot be saturated with nonexotic states.     

Saturation of thermoacoustic mixture separation

The theory for thermoacoustic mixture separation is extended to include the effects of a nonzero concentration gradient. New data are presented, which are in excellent agreement with this theory. The maximum concentration gradient which may be achieved in a binary mixture of gases through this separation process is intrinsically limited by the fractional pressure amplitude, by the tidal displacement, and by the size of the thermal diffusion ratio. Ordinary diffusion further detracts from the attainable final concentration gradient and can become the dominant remixing process as the cross section of the duct is increased. Rayleigh streaming also works against thermoacoustic separation, and an estimate of the molar flux from streaming is given.     

Saturation Approach in Top Production

The reduced cross section for the top production, in deep inelastic scattering, determined when we use the Kharzeev–Levin–Nardi (KLN) model of the low x gluon distributions. With respect to this model, a compact formula for the ratio R^t(τ) provided that it is approximately independent of τ behavior at low- τ values. For the top production where Q_sr_⊥ ? 1, the model reduced to color transparency.     

Saturation in small-x and heavy-ion physics

The idea of parton saturation is reviewed. The use of saturation in describing HERA data is discussed in the context of the McLerran-Venugopalan and Golec-Biernat Wüsthoff models. Applications of saturation ideas to RHIC data are reviewed and a comparison between applications at HERA and at RHIC is given.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.10.-z Field theory     

Saturation of optical absorption in InSb

Saturation of optical absorption in InSb has been observed by using near absorption edge wavelenght radiation of subnanosecond duration at 5.3μm to affect a wavelenght dependence on the optical absorption edge. A nearly three orders of magnitude self-induced enhancement of transparency has been measured for optical energy transmission through the absorption medium. The residual absorption losses are anomalously low.     

相对论相干三次谐波的饱和

研究了短脉冲强激光在非稠密均匀等离子体中传播时产生的相对论相干三次谐波和饱和问题，在准静态近似（ｑｕｓｉｓｔａｔｉｃａｐｐｒｏｘｍａｔｉｏｎ）下得出波动方程，用此方程计算了三阶谐波的饱和值及失相长度，并分析了影响失相长度的因素。     

Saturation of interband magneto-absorption in InSb

The saturation of interband magneto-absorption in InSb has been observed using low power incident radiation from a c.w. CO laser. The measured absorption lineshape and saturation characteristic for a pair of nearly isolated Landau levels is compared to theory (ibid) to yield information on the coherent electron-hole dephasing time and the carrier relaxation time both of which are of fundamental importance to the electro-optic device potential of semiconductors.     

Saturation spectroscopy of thep-Ge far-infrared laser

We study the non-linear interaction of high-power far-infrared radiation on both the passive and activep-Ge laser material. Effects of dynamical spectral hole burning and cross-saturation are observed. Transiently increased gain is seen early in thep-Ge laser pulse. We present a detailed analysis, in a model of inhomogeneouslybroadened two-level systems, together with results obtained earlier at mid-infrared frequency.     

Saturation dips in optical transient signals

Optical nutation and free induction decay (FID) signals are reduced when the molecules producing them are in resonance with counterpropagating laser beams. Dips in the transient signals can be identified which correspond to transitions separated by less than their Doppler widths, and the dephasing and decay of the individual levels investigated.     

Saturation of the all-optical Kerr effect

Saturation of the intensity dependence of the refractive index is directly computed from ionization rates via a Kramers-Kronig transform. The linear intensity dependence and its dispersion are found to be in excellent agreement with complete quantum mechanical orbital computations. Higher-order terms concur with solutions of the time-dependent Schr?dinger equation. Expanding the formalism to all orders up to the ionization potential of the atom, we derive a model for saturation of the Kerr effect. This model widely confirms recently published and controversially discussed experimental data and corroborates the importance of higher-order Kerr terms for filamentation.     

Determinantal Processes with Number Variance Saturation

Consider Dysons Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N. This limting determinantal process has the interesting feature that it shows number variance saturation. The variance of the number of particles in an interval converges to a limiting value as the length of the interval goes to infinity. Number variance saturation is also seen for example in the zeros of the Riemann -function, [21, 2]. The process can also be constructed using non-intersecting paths and we consider several variants of this construction. One construction leads to a model which shows a transition from a non-universal behaviour with number variance saturation to a universal sine-kernel behaviour as we go up the line.Dedicated to Freeman J. Dyson on his 80^th birthdaySupported by the Swedish Science Research Council and the Göran Gustafsson Foundation (KVA).     

Saturation stabilization of the CO fundamental-band laser

We recently reported the extension of CO laser operation to a variety of single-line transitions in the fundamental band (v=1 0). Now saturation stabilization of these lines could be achieved using an intracavity absorption cell with CO at low pressure. A 3f-detection technique allowed reliable frequency locking on transitions from P(8) to P(14). A frequency stability of better than 10kHz was indicated. The frequency of the P(14) transition was measured in a heterodyne experiment to be 62, 546, 358.324 (50) MHz.     

Saturation of Photoassociation in Cs Magneto-optical Trap

An ultrahigh resolution photoassociation spectrum of caesium atoms in a magneto-optical trap is presented. Hyperfine structure of the excited state molecule is obtained by using the lock-in method based on modulated cold atoms in this spectrum. Amplitude of resonant lines related to the rotational levels increases with photoassociation laser intensity, and saturation effect of photoassociation of cold atoms is observed in our experiment. The saturation intensity of photoassociation is deduced by fitting the experimental data to asaturation model based on scattering theory. Differences among saturation intensities of different rotational progressions in the υ=55 vibrational state of the caesium molecular long-range 0_g^- state have been found.