LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

The Generalization and Proof of “Square Root of 2 Is Not a Rational Number” on the Integral Domain

In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if n is not a square, square root of n is not a rational number”. And then some conceptions of ring, integral domain, ideal, quotient ring in Advanced algebra, have been introduced. Integers can be regarded as an integral domain, the rational numbers can be regard as a fractional domain. Evens and odds are principal ideals in integral domain. The operations on evens and odds are operations on quotient ring. After introducing “the minimalist form” in fraction ring. The paper proves the main conclusion: in a integral domain, multiplicative subset S produces a fraction ring S−1R, and n is not a square element in R, then to every element a∈R, a2≠n.

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

Domain Decomposition for Wavelet Single Layer on Geometries with Patches

We focus on the single layer formulation which provides an integral equation of the first kind that is very badly conditioned. The condition number of the unpreconditioned system increases exponentially with the multiscale levels. A remedy utilizing overlapping domain decompositions applied to the Boundary Element Method by means of wavelets is examined. The width of the overlapping of the subdomains plays an important role in the estimation of the eigenvalues as well as the condition number of the additive domain decomposition operator. We examine the convergence analysis of the domain decomposition method which depends on the wavelet levels and on the size of the subdomain overlaps. Our theoretical results related to the additive Schwarz method are corroborated by numerical outputs.

DOMAIN DECOMPOSITION PRECONDITIONERS FOR SECOND-ORDER HYPERBOLIC EQUATIONS ON L-SHAPED REGIONS

Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.

How to Check If a Number Is Prime Using a Finite Definite Integral

In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will be commented on the paper, but a separate study will be needed to have detailed conclusions. Of course, the best would be that in the future, an analytical result (or at least an approximation) for the summation or for the integration is achieved.

Construct Protein-Protein Interaction Network by Mining Domain-Domain Interactions

Domain-domain interactions are important clues to inferring protein-protein interactions. Although about 8 000 domain-domain interactions are discovered so far,they are just the tip of the iceberg. Because domains are conservative and commonplace in proteins,domain-domain interactions are discovered based on pairs of domains which significantly co-exist in proteins. Meanwhile,it is realized that:( 1) domain-domain interactions may exist within the same proteins or across different proteins;( 2) only the domain-domain interactions across different proteins can mediate interactions between proteins;( 3) domains have biases to interact with other domains. And then,a novel method is put forward to construct protein-protein interaction network by using domain-domain interactions. The method is validated by experiments and compared with the state- of-art methods in the field. The experimental results suggest that the method is reasonable and effectiveness on constructing Protein-protein interactions network.

流动介质中板状结构辐射声功率研究

由对流波动方程和欧拉方程,本文推导了流动介质中区分传播波和倏逝波的辐射椭圆方程及板状结构辐射声功率计算公式。基于该公式,通过提取辐射椭圆内的传播波波数对应的表面法向振速波数域频谱,可实现流动介质中板状结构辐射声功率的计算。基于辐射椭圆方程,明确了介质流动对板状结构辐射声功率产生影响的机理。最后,以简支板为对象,通过数值仿真对比了不同流速下的辐射声功率,结果表明了考虑介质流动影响的必要性及其对声功率的影响规律。

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

多尺度曲率在渤海K油田断裂解释中的应用

复杂断裂系统是影响K油田开发的关键问题,常规属性(如相干属性、纹理属性等)在解释断层方面存在局限,特别是微小断层的识别和多尺度复杂断裂系统的成像效果较差,并且容易受噪音干扰。为了解决这些问题,本文采用保边平滑滤波(EPS)技术对地震资料进行预处理,既能有效压制随机噪音,提高信噪比,又保持地震数据的边缘结构信息。在此基础上,利用时频波数域多尺度算子实现多尺度曲率分析。这种组合创新方法在渤海K油田的断裂识别和解释中表现良好,为开发井位的顺利实施提供有力指导,帮助规避风险断层,提高了开发效率和成功率。

基于领域分析的结构线性静力软件串并行一致化方法

并行CAE软件的计算结果串并行一致性是其计算结果可信的必要条件。然而,软件研发时常引入串并行不一致缺陷,其形式众多,现象相互耦合,散布于海量代码中,成为实现CAE软件串并行一致性的挑战。文中以结构线性静力软件的串并行一致性需求为切入点,针对现有的“专家知识法”与“缺陷定位法”应用于CAE软件串并行一致化时存在的粒度粗、准度差、成本高和缺乏系统性问题,引入领域分析方法,并与专家知识和数据流状态比对结合,提出了一种适用于结构线性静力的串并行一致化方法,实现了结构线性静力软件串并行不一致缺陷的细粒度、高准度与低成本系统性识别与修复。基于前述方法形成相关工具,并将方法与工具应用于SSTA的串并行一致化,识别并修复其中8处串并行不一致缺陷,使其通过90余真实模型的串并行一致考核,并实现串并行结果严格一致;同时,该方法与工具还将串并行不一致缺陷定位耗时由平均大于两人天降低至数人时。

随机数编码融合长脉冲级联调制提升Φ-OTDR定位性能

为解决随机数编码造成相位敏感光时域反射系统振动定位差的问题,设计了一种随机数编码融合长脉冲的级联调制方法,分别利用声光调制器和半导体光放大器实现随机数编码和长脉冲的融合调制,提升消光比。使用自相关的随机数编码生成脉冲序列,设计数字正交解调算法获得拍频信号幅值与相位信息。实验结果表明,在4km长度传感光纤上,脉冲宽度为40ns时,方案可将消光比提升13.7dB;当振动信号频率为200Hz时,振动信号定位均方根误差为2.1m,最大绝对误差为3.8m,提升了振动信号定位精度,为编码相位敏感光时域反射系统定位性能提升提供了新方法。

基于频域介电谱油纸结构对变压器绝缘的影响研究

为研究油纸层数对频域介电特性的影响,进而评估油纸结构对变压器绝缘特性的影响。在实验室内制备不同油纸层数的试品进行FDS测试。通过对得到FDS试验结果深入分析后提出以特征频率f=0.1mHz、f=0.01Hz、f=10Hz处的复电容实部C′为频域介电特征参量。将油纸层数与频域介电特征参量进行拟合,通过两者的拟合关系评估油纸绝缘结构对变压器绝缘性能的影响。研究结果表明:油纸层数与频域介电特征参量具有高拟合优度的函数关系,证明该方法评估油纸层数对频域介电特性的影响具有很高的可行性,该方法还为应用FDS法评估油纸结构对油纸绝缘性能提供了一定依据。

采用波数域方法分析细长柱壳的振动与声辐射特性

采用波数域方法对细长柱壳进行振动与辐射噪声分析。在获得细长柱壳表面振动后,法向振动在波数域展开为波数谱,结构振动波数特征由此得以直观展现,与辐射噪声相关的有效振动量得以定量给出。对细长柱壳的波数谱分析表明:低阶周向波数振动是其参与有效声辐射的主要成分,通过不等间距分舱可以在一定程度上控制有效声辐射振动级,从而控制结构的噪声辐射,但对整体呼吸运动的振动则效果不显著。

利用重力归一化总梯度及相位法研究断裂构造

用波数域的位场转换和快速傅立叶变换理论研究重力归一化总梯度和归一化相位;在波数域向下延拓和导数计算的滤波算子中,分别引入圆滑滤波因子,抑制了向下延拓计算中对噪声干扰的放大作用,增加了计算的稳定性;利用改进的方法,计算并阐述了4种断裂构造GH场等值线和相位曲线的变化特征;别列兹金重力归一化总梯度法中极大值理论在研究断裂构造中具有局限性,对于无限延伸断裂构造,应根据GH场等值线的走向、形状的特点,结合归一化相位曲线的转折点确定断裂空间位置。

基于波场延拓的变换坐标转换波静校正

常规的转换波静校正的基本思想都是从地震波的运动学特征出发,基于地表一致性假设.在地表条件复杂和地表高程相差较大的地区,它不仅无法解决严重的静校正问题,反而会带来新的畸变.本文基于频率波数域波动方程偏移原理,采用波场延拓方法实现转换波静校正,其关键点在于时间空间域和频率波数域的相对应.文中通过坐标变换将起伏地表转化为新坐标系下的水平地表,把炮点和检波点映射到同一水平面上,然后在新坐标系下推导频率域波动方程延拓公式,接着对下行波P和上行转换波SV分别利用近地表速度向上延拓到基准面,恢复起伏地表到基准面之间的真实波场,最后转换到原始坐标系取出基准面数据完成转换波静校正.通过对模拟和实际数据处理,证明该方法是正确和有效的.

蒙特卡罗区域分解并行计算中确保串并行结果一致的伪随机数应用

物理建模的精细化和三维模拟给蒙特卡罗粒子输运计算的规模成千上万倍的增加,甚至超过单核内存的最大规模,仅仅依靠传统的粒子并行蒙特卡罗计算无法实现对模型模拟,区域分解并行是可能的解决方法之一.然而区域分解带来了粒子在各区域间进行迁移,导致现有的伪随机数应用方式无法确保串行计算和并行计算的结果一致.针对这种现象,本文提出赋予粒子随机数属性和动态派生次级粒子随机数的技巧来确保区域分解并行计算的串并行结果一致.

双基地逆合成孔径雷达成像分析

在波数域对双基地逆合成孔径雷达(ISAR)模型进行分析。双基雷达ISAR的特殊性主要体现在双基地角和等效视线方位角这两个参数中。前者会影响径向波数的大小而后者会影响波数的方向。利用双基地角等值线将观测区域进行了分类。对各类区域内双基地角和等效视线方位角变化规律进行了讨论,从而可以确定各区域内的双基ISAR成像算法。仿真结果验证了分析的正确性。

高速列车作用下板式轨道引起的地面振动

根据波数域内分层大地波动方程的求解理论,建立高速列车作用下板式轨道—大地耦合振动分析模型。利用Fourier变换,在频率—波数域内求解振动微分方程,再通过Fourier逆变换得到大地表面的振动位移响应。通过算例分析列车运行速度对板式轨道周围地面振动的影响。结果表明:列车运行速度越高,线路周围地面的振动响应越大。当列车速度大于200 km.h-1时,路基表面位移的幅值随车速提高迅速增大;然而当列车速度增至350 km.h-1时,位移幅值最大值又出现了回落。距离板式轨道中心线越近,行车速度的变化对地面振幅的影响越显著。尤其当列车速度接近地基的Rayleigh波波速时,由于引发共振而使地面振动位移出现峰值。