油水饱和球管孔隙模型弛豫的理论计算与计算机模拟

根据Brownstein-Tarr理论，采用特征函数展开法，通过求解基于扩散效应的Bloch控制方程，给出了油水饱和球管孔隙模型弛豫的理论计算公式.理论计算结果表明，在水润湿条件下，油的弛豫过程只与含油饱和度有关，而与岩石的孔隙结构无关.根据理论计算结果对球管模型中水的弛豫进行了数值模拟，模拟结果显示，球和管的主弛豫过程是一个单指数函数，其余部分与之相比可以忽略，即球管模型中水的弛豫可近似为一个双指数衰减过程.     

基于ADI-FDTD模拟的岩石核磁共振横向弛豫特征分析

将复杂的骨架-孔隙系统抽象成等效双孔介质,根据Bloch方程构建数学模型,用交替隐式时域有限差分(ADI-FDTD)和联合反演迭代法(SIRT)进行横向宏观磁化矢量的数值模拟与核磁共振T₂谱的反演,定量研究扩散系数、弛豫速率、孔隙组分比和孔隙宽度对核磁响应的影响.结果表明:横向宏观磁化矢量衰减速率与扩散系数和微孔隙分量成正比,与孔隙宽度成反比,与表面弛豫速率基本无关.当扩散系数较大、孔隙宽度较小时,核磁共振T₂谱难以直观反映孔隙组分及孔隙结构.应用核磁共振评价孔隙结构时需特别注意扩散系数和孔隙尺寸的影响.     

射频场照射下多自旋体系弛豫的理论计算

根据Liouville-von Neumann方程，对射频场照射下多自旋体系的弛豫进行了理论描述，并用WBR理论推导出了体系的弛豫方程组，给出了各类弛豫速率的理论计算公式.在此基础上，编制了弛豫方程组数值解的计算程序，分别用此程序和Bloch方程计算了双自旋体系在不同情况下的稳态解，并对计算结果进行了简要的分析和讨论. 关键词： 核磁共振 弛豫 射频场 多自旋体系     

弛豫过程对能级AC Zeeman(Stark)移动的影响

以衰减的Bloch方程理论为基础计算了二能级原子能级ACZeeman(Stark)移动,结果表明纵向和横向弛豫过程均会对原子能级移动产生影响,随纵向和横向弛豫率的增加,能级移动呈现出不同的变化趋势。两种弛豫相对强弱的不同也会直接影响能级移动的色散性和饱和性。     

玻璃化转变的分子串模型中分子串弛豫模式的计算机模拟

基于玻璃化转变的分子串模型的哈密顿量(Hamiltonian),提出了模拟分子串第一和第二弛豫模式的蒙特卡罗(Monte Carlo)模拟方案.模拟得出的第一和第二弛豫模式的弛豫时间,与分子串模型中分子串弛豫方程所预言的结果完全一致,即理论预期和模拟结果相互印证.这不仅说明了分子串模型的分子串弛豫方程、至少是第一和第二弛豫模式的理论预言的正确性,同时也表明了本文所提出的模拟方法的有效性,并进一步明晰了分子串中分子的随机涨落和跃迁运动的图像,也为三态甚至是多态的分子串弛豫动力学研究,以及对进一步模拟分子串之 关键词： 弛豫动力学 蒙特卡罗模拟 分子串     

可激发气体分子声弛豫过程振动模式能量转移速率计算

研究可激发气体中振动模式能量转移速率和声弛豫过程形成的关系,将单一气体Tanczos弛豫方程理论[J.Chem.Phys.25,439(1956)]扩展应用于混合气体中振动模式的振动-振动(V-V)和振动-平动(V-T)能量转移速率的计算。在室温下CO₂,CH₄,CL₂,N₂和O₂组成的多种混合气体中,振动模式能量转移速率的计算结果表明:对于多个振动模式所形成的声复合弛豫过程,各振动模式的声激发能可由V-V能量转移相互耦合后传递给具有最快V-T转移速率的最低振动频率振动模式,再通过该振动模式的V-T转移退激发形成主弛豫过程。这种选择最快转移路径的声激发量弛豫方式,造成了大多数可激发气体中声弛豫吸收谱的实测数据只存在一个吸收峰的现象。从而提供了一个可通过计算微观振动能量转移速率分析混合气体声弛豫过程形成机理的理论模型。      

球坐标动量空间下相对论Vlasov方程的数值算法

针对相对论Vlasov方程动量区间跨度大、难以计算的困难,将相对论Vlasov方程在球坐标动量空间中进行数值求解.对相对论Vlasov方程球坐标动量空间构造4阶非分裂守恒型数值格式.数值模拟相对论Landau阻尼问题并与解析理论进行比较,验证数值模型和算法的有效性.对激光等离子体相互作用进行初步模拟分析,表明通过采用球坐标下的动量空间,可在相对较少动量网格情形下,获得与粒子模拟可相互验证的结果.     

四能级增益介质光子晶体激光器的时域有限差分模型与模拟

基于Maxwell-Bloch方程和速率方程相结合的模型,模拟包括四能级增益介质光子晶体激光器的光学特性.根据FDTD法的基本原理,给出方程的Yee氏离散方程.通过计算电场的时域特性,模拟光子晶体激光器的频谱特性、阈值特性、动力学演化等过程,模拟结果和理论结论一致,检验了该模型的有效性.     

增殖剂球床载气体流动特性

增殖剂球床是聚变堆或混合堆产氚包层可选结构之一,准确把握增殖剂球床中载带气体的流动特性有助于提高对球床载氚过程的认识并优化包层设计。采用离散元程序PFC3D模拟增殖剂小球的填充行为,在球床内不同位置随机截取不同尺寸的控制体,利用布尔运算中的"差集"得到孔隙范围,建立孔隙分布的三维几何模型,进一步划分网格并用计算流体力学(CFD)方法求解,得出控制体上单位长度的压降以及单元体内的速度分布特征,计算结果发现载带气体速度分布与γ分布很类似,且只要选取恰当的控制体,通过计算流体力学方法可以较好地分析整个球床孔隙内流体的流动,有利于进一步研究载氚及相关过程。     

特形脉冲的设计与计算机模拟

根据LiouvillevonNeumann方程从理论上对特形脉冲做了全面的描述,提出了一种具体的调幅特形脉冲设计方案:首先将待设计的脉冲展成一个有限Fourier级数,然后根据Bloch方程的解析解准确计算出各阶正弦、余弦波的频谱,再将这些频谱组合后与该脉冲的理想频谱进行比较构成误差函数,最后运用鲍威尔-模拟退火组合优化算法计算出全局最优Fourier系数,即可得到所需脉冲的表达式.应用此设计方案,得到了体系处于热平衡态时的特形激励脉冲和反转脉冲的具体表达式.计算机模拟表明,所得脉冲的频谱具有较好的选择性 关键词： 核磁共振 特形脉冲 Bloch方程 鲍威尔模拟退火组合优化算法     

Absorption of intense regular and noise waves in relaxing media

An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. It is shown that for weak waves, the general integral leads to well-known results of a linear approximation. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.     

Hierarchical description for a non-Markoff relaxation process

A phenomenal model is proposed in this paper to describe a non-Markoff relaxation process. The main feature of the model is the fractal time concept introduced to take account of the coupling of a relaxation mode with a heat bath. The theoretical investigation indicates that a weakly non-Markoff relaxation process can be related to a set of hierarchically distributed Markoff relaxation processes and the fractal exponential law exp [?(t/τ)^1?σ] is the character of a non-Markoff relaxation process. Calculations about the temperature and time scale dependence of the exponent σ have been made, and comparison with recent experiments is also given.     

CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: numerical simulation and application

Carr-Purcell-Meiboom-Gill (CPMG) measurements are the primary nuclear magnetic resonance (NMR) technique used for evaluating formation properties and reservoir fluid properties in the well logging industry and laboratory sample analysis. The estimation of bulk volume irreducible (BVI), permeability, and fluid type relies on the accurate interpretation of the spin-spin relaxation time (T(2)) distribution. The interpretation is complicated when spin's self-diffusion in an inhomogeneous field and restricted geometry becomes dominant. The combined effects of field gradient, diffusion, and a restricted geometry are not easily evaluated analytically. We used a numerical method to evaluate the dependence of the free and restricted diffusion on the system parameters in the absence of surface relaxation, which usually can be neglected for the non-wetting fluids (e.g., oil or gas). The parameter space that defines the relaxation process is reduced to two dimensionless groups: D* and tau*. Three relaxation regimes: free diffusion, localization, and motionally averaging regimes are identified in the (log(10)D*, log(10)tau*) domain. The hypothesis that the normalized magnetization, M*, relaxes as a single exponential with a constant dimensionless relaxation time T*(2) is justified for most regions of the parameter space. The numerical simulation results are compared with the analytical solutions from the contour plots of T*(2). The locations of the boundaries between different relaxation regimes, derived from equalizing length scales, are challenged by observed discrepancies between numerical and analytical solutions. After adjustment of boundaries by equalizing T*(2), numerical simulation result and analytical solution match each other for every relaxation regime. The parameters, fluid diffusivity and pore length, can be estimated from analytical solutions in the free diffusion and motionally averaging regimes, respectively. Estimation of the parameters near the boundaries of the regimes may require numerical simulation.     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

An Ising model for the stress relaxation of solids

A kinetic theory of stress relaxation of solids as a cooperative process is proposed. The theory is based on a two-state model for the relaxation. It is shown that the conventional mean field approximation leads to an exponential dependence of the rate of stress relaxation on the stress while the multiplicative approximation of Vol'kenstein et al. leads to a power law. It is argued that the exponential law should be valid initially in the relaxation process while the power law is appropriate when the system is nearer equilibrium, which is in qualitative agreement with recent experimental findings.     

Relaxation processes of water confined to AlMCM-41 molecular sieves. Influence of the hydroxyl groups of the pore surface

A series of AlMCM-41 molecular sieves was prepared with constant composition (Si/Al = 14.7) and presumably same pore structure but different pore diameters (from 2.3 to 4.6 nm). The pore size distribution is narrow for each sample. The rotational fluctuations of water molecules confined inside the pores were investigated applying broadband dielectric spectroscopy (10⁻²–10⁷ Hz) over a large temperature interval (213–333K). A relaxation process, slower than that expected for bulk water, was observed which is assigned to water molecules forming a surface layer on the pore walls. The estimated relaxation time has an unusual non-monotonic temperature dependence, which is rationalized and modeled assuming two competing processes: rotational fluctuations of constrained water molecules and defect formation (Ryabov model). This paper focuses on the defects and notably the influence of the hydroxyl groups of the pore walls. The Ryabov model is fitted to the data and characteristic parameters are obtained. Their dependence on pore diameter is considered for the first time. The found results are compared with those obtained for other types of molecular sieves and related materials.     

Product operator analysis of the influence of chemical exchange on relaxation rates

Measurements of chemical-exchange processes by NMR are widely used to obtain valuable information about molecular dynamics and structure. Here, a computational method is introduced to assess the influence of chemical exchange on spin relaxation rates. The method is based on the inclusion of a random exchange process in product operator calculations on a microscopic level. This product operator approach can be applied to estimate exchange contributions when using sophisticated pulse sequences that cannot be easily described analytically. The method applies to the full range of exchange times measurable by NMR and can incorporate interference effects between exchange and other processes such as scalar coupling. To demonstrate its utility, simulated relaxation data were compared with theoretical predictions of spin-locking and Carr-Purcell spin-echo sequences with hard and adiabatic pulses, using different time scales for a two-site chemical-exchange process. Finally, simulations were used to examine a system in which a second random process is superimposed on a simple two-site exchange process. The method was found to provide a simple and robust tool to analyze pulse sequences and equations commonly used to study exchange-induced relaxation.