Energy average formula of photon gas rederived by using the generalised Hermann—Feynman theorem

By virtue of the generalised Hermann--Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.     

Temporal electronic structure of non-resonant Raman excited virtual state of P-nitroaniline by 514 nm excitation via bond polarisabilities

We have studied the temporal bond polarisabilities of para-nitroaniline from the Raman intensities by the algorithm proposed by Wu et al. in 1987 (Tian B, Wu G, Liu G 1987 J. Chem. Phys. 87 7300). The bond polarisabilities provide much information concerning the electronic structure of the non-resonant Raman excited virtual state. At the initial moment by the 514.5 nm excitation, the tendency of the excited electrons (mapped out by the bond polarisabilities) is to spread to the molecular periphery, and the electronic structure of the Raman virtual state is close to the pseudo-quinonoidic state. When the final stage of relaxation is approached, the bond polarisabilities of those peripheral bonds relax faster than those closer to the molecular core, the phenyl ring. The molecule is in the benzenoidic form as demonstrated by the bond polarisabilities after relaxation.     

Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds

Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Salt-Finger convection in the surface discharge of heated saline jets

Abstract

Experimental investigations of the surface discharge of two-dimensional heated saline jets into surroundings with stable, constant salt gradients were carried out. The discharge conditions were parameterized with the densimetric Froude number, and the Reynolds number. The evolution of the discharge was monitored by flow visualization methods, and by the measurements of temperature and salinity distributions. For comparison, experiments of the surface discharge of heated water into homogeneous surroundings at the corresponding discharge conditions were also conducted. The results clearly showed that while in the former case, the region away from the vicinity of the discharge manifold was marked by the presence of salt-finger convection, in the latter case this region exhibited stable thermal stratification. Furthermore the occurrence of salt-finger convection considerably retarded the motion of the jet, and increased the penetration depth of temperature and salinity fields.     

位场DFT算法研究

本文推广了经典的抽样定理,并据此导出了函数有限离散傅里叶变换误差方程（简称DFT误差方程,下同）。该方程把有限离散傅里叶变换中固有的离散效应和有限效应表示为确切的数学形式。离散效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数;有限效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数的DFT。 基于DFT误差方程和位函数特点,作者提出了两种位场数值傅里叶变换新算法--移样法和等效源续尾叠样法。移样法可近百倍地提高位场数值傅里叶反变换的精度,等效源续尾叠样法可数十倍地提高正变换精度。两种算法都不需要增加资料长度和取样密度,因而基本不需要增加计算机时间和内存。文中给出了算例。     

Theoretical background for the inversion of seismic waveforms including elasticity and attenuation

To account for elastic and attenuating effects in the elastic wave equation, the stress-strain relationship can be defined through a general, anisotropic, causal relaxation function ^ijkl (x, ). Then, the wave equation operator is not necessarily symmetric (self-adjoint), but the reciprocity property is still satisfied. The representation theorem contains a term proportional to the history of strain. The dual problem consists of solving the wave equation withfinal time conditions and an anti-causal relaxation function. The problem of interpretation of seismic waveforms can be set as the nonlinear inverse problem of estimating the matter density (x) and all the functions ^ijkl (x, ). This inverse problem can be solved using iterative gradient methods, each iteration consisting of the propagation of the actual source in the current medium, with causal attenuation, the propagation of the residuals—acting as if they were sources—backwards in time, with anti-causal attenuation, and the correlation of the two wavefields thus obtained.     

Reciprocity theorem to compute the static deformation due to a point dislocation buried in a spherically symmetric earth

Intriguing reciprocity relations exist between the static deformation excited by a point dislocation in a SNREI earth and those generated by external forces, such as tidal force, surface loading and surface shear forces. Coseismic deformations can be rewritten as follows: (1) potential change in terms of the tide deformation field, (2) radial displacement in terms of the load and tidal deformation fields, and (3) tangential displacement in terms of shear and torsional deformation fields. The relations greatly reduce the effort to compute the coseismic crustal deformation in a spherically symmetric earth.     

NWP 模式热量系统误差的动力诊断分析

文章证明了模式在预报时段的位温误差，是由于在模式大气和真实大气中，该时段内位温变化过程的不同而造成的。还证明了原始方程的无加速定理对各强迫因子的线性分解同样适用于研究NWP模式热量误差的成因。对国家气象中心T42L9模式1992年1月和7月预报结果的动力诊断表明，模式对纬向位温分布具有较好的预报能力，但在各纬带也存在明显的误差。通过无加速定理的分解分析，研究了这些误差的成因及改善模式的可能途径。     

Numerical simulations of katabatic jumps in coats land,Antartica

A non-hydrostatic numerical model, the Regional Atmospheric Modeling System (RAMS), has been used to investigate the development of katabatic jumps in Coats Land, Antarctica. In the control run with a 5 m s^-1downslope directed initial wind, a katabatic jump develops near the foot of the idealized slope. The jump is manifested as a rapid deceleration of the downslope flow and a change from supercritical to subcritical flow, in a hydraulic sense, i.e., the Froude number (Fr) of the flow changes from Fr > 1 to Fr> 1. Results from sensitivity experiments show that an increase in the upstream flow rate strengthens the jump, while an increase in the downstream inversion-layer depth results in a retreat of the jump. Hydraulic theory and Bernoulli's theorem have been used to explain the surface pressure change across the jump. It is found that hydraulic theory always underestimates the surface pressure change, while Bernoulli's theorem provides a satisfactory estimation. An analysis of the downs balance for the katabatic jump indicates that the important forces are those related to the pressure gradient, advection and, to a lesser extent, the turbulent momentum divergence. The development of katabatic jumps can be divided into two phases. In phase I, the t gradient force is nearly balanced by advection, while in phase II, the pressure gradient force is counterbalanced by turbulent momentum divergence. The upslope pressure gradient force associated with a pool of cold air over the ice shelf facilitates the formation of the katabatic jump.