Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach.Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction(SOI)arising from the curvature,as well as an effective scalar potential resulting from variations in thickness.Importantly,we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems,thus guaranteeing the robustness of spin interference measurements to thickness imperfection.Furthermore,we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios,which is crucial for its utilization in one-side etching systems.

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.

Analytic solution for a circular nano-inhomogeneity in a finite matrix

The Gurtin-Murdoch model has found wide applications in analyzing the mechanical behaviors of nanocomposites with surface/interface effect. In the existing literature, the matrix is usually assumed to be infinite and the surface/interface effect is considered only at the inhomogeneity-matrix interface. This assumption is indeed valid as the matrix is usually at macroscale rather than nanoscale. However, if the size of the matrix decreases to the nanoscale too, the surface/interface effect will have to be considered at the outer boundary of the matrix. In this paper, the plane deformation of a circular nano-inhomogeneity embedded inside a finite circular matrix (which implies the matrix is also at nanoscale) is investigated. The stress boundary conditions are given at the inhomogeneity-matrix interface and the outer boundary of the matrix by the G-M model. The analytic solution for the stress field is finally obtained through the complex variable method. The results show that the stress field inside the inhomogeneity is still uniform (size-dependent) when the surface/interface effect is considered. In addition, the stress field inside the bulk (including the inhomogeneity and the matrix) can be influenced not only by the size and elastic constant of the inhomogeneity, but also by those of the matrix.

Inhomogeneous Shadowing Effect in High-Energy p-A Drell-Yan Process:

Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this paper.We find thatthe inhomogeneous shadowing effect does amend the rate of energy loss per unit path length,-dE/dz.Finally,thetheoretical results for the Drell-Yan differential cross-section ratios are compared with the E772 and E866 data.It isfound that the theoretical results are in good agreement with the experimental data.

MULTIPLE SCATTERING THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF INHOMOGENEOUS MEDIA

The rate of hydrothermal reaction of SiO_2 and/or A1_2O_3 in the system of CaO-Al_2O_3-SiO_2-H_2O at 200℃ and the factors which influence the reactions are investigated by determining the reaction ratio.The rate of reactions depends on the reactive activities of raw materials, initial composition of mixture and relative activity of SiO_2 and A12O3. The hydrothermal reaction can be accelerated by sodium hydroxide,in the case of silica,which has low activity, this is quite obvious.

A Numerical Study of the Effect of Disorder on Optical Conductivity in Inhomogeneous Superconductors

We present the effect of disorder on the optical conductivity of two-dimensional inhomogeneous superconductors by applying the kernel polynomial method to solve the Bogoliubov-de Gennes equations. By means of the lattice size scaling of the generalized inverse participation ratio, we find that the localization length of the quasiparticle decreases significantly with the increase of the disorder strength. Meanwhile, the weak disorder can readily restrain the Drude weight, while the superconducting gap has the tendency to suppress the low-energy optical conductivity. We also employ the Lanczos exact diagonalization method to study the competition between the on-site repulsive interactions and disorder. It is shown that the screening effect of repulsive interactions significantly enhances the Drude weight in the normal phase.

非均匀强激光场下正负电子对的产生

随着强激光技术领域的不断突破,使得能量转化成物质的施温格过程的实验指日可待.在这样的背景下,在接近实际强激光的模型中理论研究施温格效应至关重要.本文采用量子场论模拟方法在非均匀电场中研究施温格效应的空间特性.首先,发现在能量保持不变的情况下电场的空间尺度显著影响正负电子对的产生率、动量和空间分布.正负电子对的动量和空间分布显示,当电场的空间尺度增大时,因为电场强度变小,所以产生的正负电子对无法及时被分开,抑制正负电子对的产生.最后,用连续性方程研究正负电子对的产生位置分布,发现正负电子对的产生位置分布与电场强度分布是对应的,电子和正电子的产生位置分离一个康普顿波长.此研究结果展示了施温格效应的空间特性,同时解释了弱电场下施温格效应的抑制机制.这些结论在人们常采用的均匀电场近似研究中无法得到.我们的研究对检测施温格实验中的正负电子对具有重要的指导意义.

Size effects on plastic deformation behavior in micro radial compression of pure copper

Micro radial compression tests were carried out on cylindrical specimens of pure copper polycrystals with different grain sizes. Experimental results indicated that phenomena of decreasing forming force, increasing scatter of forming force and more irregular surface topography occurred with the increase of grain size. A modified surface model based on dislocations pile-up in surface layer grains, and a flow stress scattering formulation based on standard deviation and grain size distribution were proposed to analyze size effects on forming force in micro compression. The inhomogeneous deformation of surface layer grains was discussed by the main deformation manner of rotation. A good agreement with the experimental results was achieved.

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir includ- ing the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.

Large-scale two-dimensional nonlinear FE analysis on PGA amplification effect with depth and focusing effect of Fuzhou Basin

Based on the explicit finite element(FE) method and platform of ABAQUS,considering both the inhomogeneity of soils and concave-convex fluctuation of topography,a large-scale refined two-dimensional(2D) FE nonlinear analytical model for Fuzhou Basin was established.The peak ground motion acceleration(PGA) and focusing effect with depth were analyzed.Meanwhile,the results by wave propagation of one-dimensional(1D) layered medium equivalent linearization method were added for contrast.The results show that:1) PGA at different depths are obviously amplified compared to the input ground motion,amplification effect of both funnel-shaped depression and upheaval areas(based on the shape of bedrock surface) present especially remarkable.The 2D results indicate that the PGA displays a non-monotonic decreasing with depth and a greater focusing effect of some particular layers,while the 1D results turn out that the PGA decreases with depth,except that PGA at few particular depth increases abruptly; 2) To the funnel-shaped depression areas,PGA amplification effect above 8 m depth shows relatively larger,to the upheaval areas,PGA amplification effect from 15 m to 25 m depth seems more significant.However,the regularities of the PGA amplification effect could hardly be found in the rest areas; 3) It appears a higher regression rate of PGA amplification coefficient with depth when under a smaller input motion; 4) The frequency spectral characteristic of input motion has noticeable effects on PGA amplification tendency.

A Theoretical Study on Van Der Pauw Measurement Values of Inhomogeneous Compound Semiconductor Thin Films

The influence of intermixing heterogeneous regions that have different electrical properties from the base materials on van der Pauw measurement values was theoretically studied by computer simulation using the finite-element method. The measurement samples selected were thin films of inhomogeneous semiconductors. Calculated electrical properties, such as resistivity, carrier density, and mobility of the thin films, varied in predictable ways when heterogeneous regions were dispersed in wide ranges over the samples. On the other hand, the mobility of the thin films showed a different change when heterogeneous regions were locally concentrated in the measurement samples.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Two methods to deal with an inhomogenous Rabi frequency in microwave transition

We analyse the influence of an inhomogenous microwave field on the coherence of atom ensembles. Two methods are proposed to suppress the dephasing generated by the inhomogenous Rabi frequency. One of them is realized by using a spin echo, and the other one is based on the identical spin rotation effect. The calculation results show that the contrast of a signal acquired in experiment can be improved by using the two methods. Their advantages and drawbacks are discussed. We hope they can be used to improve the contrast of experimental signals in situations where microwave fields are very inhomogenous. Finally, we discuss the case of a continuous working microwave field and show that the dipole force raised with the inhomogeneitv can be eased by slain flip.

Applications of fluid substitution effect analysis on seismic interpretation

The root mean square(RMS) difference of time-lapse seismic amplitudes is routinely used to identify the substituted fluid type in a reservoir during oil field production and recovery. By a time-lapse seismic method, we study the effects of fluid substitution in a physical model, which is an analogy of the three-dimensional inhomogeneous reservoir. For a weak inhomogeneous medium, gas/oil substitution results in positive anomalies in the reservoir layers, and negative anomalies below the bottom of the reservoir layers; while water/oil substitution causes only weak variations in the reservoir layers, but positive anomalies below the bottom of the reservoir layers. For the strong inhomogeneous medium, no matter what kind of fluid substitution(gas/oil or water/oil), there are significant anomalies in seismic amplitude difference attributes both in and below the reservoir layers. Therefore, for weak inhomogeneous media, such as tight sandstone or thin interbedded layers, the RMS amplitude difference attributes can be used to monitor fluid changes and predict the drilling direction; for inhomogeneous medium with karst carves or fractures, it is difficult to accurately determine the distribution of fluids with the RMS amplitude difference attributes.

基于磁场分割法的EE型电感器磁路参数计算

开关电源电感器设计中,磁路参数的计算具有重要意义。首先,针对EE型磁芯中柱开气隙的电感器,结合有限元仿真,通过理论分析,利用磁场分割的方法将总磁通量分为7个等效磁通,提出无效匝数的概念,在充分考虑扩散磁通、旁路磁通及磁芯磁通分布不均匀影响的基础上,求得主气隙磁导等效面积的解析表达式,根据等效磁路模型,从而求得电感系数AL的解析表达式。提出磁密分布不均匀系数的概念,根据单位电流最大磁通密度,求得饱和电流IA的解析表达式。然后,采用编制Excel表的方式对磁路参数进行精确计算。最后,通过实验测量,验证了所建公式的准确性,可为设计人员提供有益参考。

Semi-analytical Modeling of the Influence of Macro Bending Effects on Micro Contact-Inhomogeneity Problems

This study examines the effects of macroscopic bending and microscopic contact loading in inhomogeneous materials using a semi-analytical model based on Eshelby’s equivalent inclusion method.The model accounts for bending effects through the beam theory,with bending stress included in the Eshelby’s equivalent inclusion equations.The macroscopic displacement resulting from bending effects is incorporated into the microscopic contact solver,and the final displacement is determined using the conjugate gradient method in an iterative solution.Computational efficiency can be improved by incorporating the discrete convolution and fast Fourier transform.The core scheme is validated using the finite element method,yielding accurate and efficient results for bending-contact problems in inhomogeneous materials.Simulations reveal the interplay between bending,contact loading,and inhomogeneity,as stress around the inhomogeneity alters and the stress concentration area expands under increasing bending moments.Conversely,low-magnitude negative bending moments reduce both contact pressure and stress around the inhomogeneity.The position where inhomogeneities are least affected shifts from the neutral surface depending on the coupling effect.The model provides a valuable bridge for connecting the macroscopic bending effect and microscale contact-inhomogeneity problems by visualizing stress fields and assessing pressure distributions.

Polycrystalline model for FE-simulation of micro forming processes

A new polycrystal model was presented from the viewpoint of polycrystal structure of the billets considering free surface effects.In the model,the billet was divided into three portions,such as free surface portion,transition portion and internal portion.The grains in free surface portion were considered the single grains,and the anisotropy of the grains was taken into account by introducing grain orientation to explain the inhomogeneous deformation.In the transition portion,the effects of the neighbouring grains were adopted in the model.The grains in the internal portion were considered the polycrystalline material.With the developed model,the upsetting deformation process was simulated by the MSC Superform software.The scatter of the flow stress and inhomogeneous deformation was observed by analysis of the model.The comparisons show that the computational results are good agreed with the experimental results.This means that the presented model is effective.

岩石的非均质性对其材料强度尺寸效应的影响

采用非均质数值试验的方法,研究了非均质参数m对岩石材料强度尺寸效应的影响,提出尺寸效应影响参数η,其值越大尺寸效应越明显.研究表明:随着非均质参数m的增加,尺寸效应影响参数η的值先增加后减小,当m→+∞时η→0.在m=2附近时η达到最大值,此时的强度尺寸效应最明显.η在1.65≤m≤3范围内变化最为剧烈,所以当非均质参数m在此范围内时,岩石材料的强度尺寸效应在明显和不明显之间变化幅度最大.

瓦斯压力对非均质煤岩抗压强度尺寸效应的影响

通过非均质固、气耦合数值试验的方法,研究不同瓦斯压力作用下非均质煤岩抗压强度尺寸效应的影响规律及其作用机理.研究表明:含瓦斯煤岩的抗压强度随着瓦斯压力的增加而呈非线性降低,其降低的幅度随着瓦斯压力的增加而增大;在煤岩裂纹萌生、扩展、演化过程中,通过渗流场与应力场的耦合作用,瓦斯压力降低了煤岩的有效应力,促使裂纹不同方向发育,导致应力局部集中和变形的局部化;增加煤岩的非均质性,促使煤岩均质度动态演化,使得同一均质度煤岩,瓦斯压力越大,抗压强度尺寸效应越明显,瓦斯压力对非均质煤岩抗压强度尺寸效应有显著影响.

电磁波在非均匀等离子体中的吸收

研究了电磁波在非均匀碰撞等离子体中的传播和吸收。提出了一种计算电磁波在非均匀等离子体层中反射和透射功率的模型。对几种典型的非均匀密度剖面 ,计算了在不同的碰撞频率和层边缘密度下电磁波衰减率与电磁波频率的关系。结果表明 ,对于给定的密度剖面和有效吸收频宽 。