Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

An improved four-dimensional variation source term inversion model with observation error regularization

Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.

Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity

We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.

Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions

Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.

Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas

This paper investigates the solitary wave solutions of the (2+1)-dimensional regularized long-wave (2DRLG) equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas and (2+1) dimensional Davey-Stewartson (DS) equation which is governing the dynamics of weakly nonlinear modulation of a lattice wave packet in a multidimensional lattice. By using extended mapping method technique, we have shown that the 2DRLG-2DDS equations can be reduced to the elliptic-like equation. Then, the extended mapping method is used to obtain a series of solutions including the single and the combined non degenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear partial differential equations (NLPDEs).

Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor

Considering the uncertainty of the electrical axis for two-dimensional audo-magnetotelluric(AMT) data processing, an AMT inversion method with the Central impedance tensor was presented. First, we present a calculation expression of the Central impedance tensor in AMT, which can be considered as the arithmetic mean of TE-polarization mode and TM-polarization mode in the twodimensional geo-electrical model. Second, a least-squares iterative inversion algorithm is established, based on a smoothnessconstrained model, and an improved L-curve method is adopted to determine the best regularization parameters. We then test the above inversion method with synthetic data and field data. The test results show that this two-dimensional AMT inversion scheme for the responses of Central impedance is effective and can reconstruct reasonable two-dimensional subsurface resistivity structures. We conclude that the Central impedance tensor is a useful tool for two-dimensional inversion of AMT data.

Regularity and finite dimensionality of attractor for plate equation on R^n

This paper addresses the regularity and finite dimensionality of the global attractor for the plate equation on the unbounded domain. The existence of the attractor in the phase space has been established in an earlier work of the author. It is shown that the attractor is actually a bounded set of the phase space and has finite fractal dimensionality.

Seismic data reconstruction based on low dimensional manifold model

Seismic data reconstruction is an essential and yet fundamental step in seismic data processing workflow,which is of profound significance to improve migration imaging quality,multiple suppression effect,and seismic inversion accuracy.Regularization methods play a central role in solving the underdetermined inverse problem of seismic data reconstruction.In this paper,a novel regularization approach is proposed,the low dimensional manifold model(LDMM),for reconstructing the missing seismic data.Our work relies on the fact that seismic patches always occupy a low dimensional manifold.Specifically,we exploit the dimension of the seismic patches manifold as a regularization term in the reconstruction problem,and reconstruct the missing seismic data by enforcing low dimensionality on this manifold.The crucial procedure of the proposed method is to solve the dimension of the patches manifold.Toward this,we adopt an efficient dimensionality calculation method based on low-rank approximation,which provides a reliable safeguard to enforce the constraints in the reconstruction process.Numerical experiments performed on synthetic and field seismic data demonstrate that,compared with the curvelet-based sparsity-promoting L1-norm minimization method and the multichannel singular spectrum analysis method,the proposed method obtains state-of-the-art reconstruction results.

Dimensional Measurement of Complete-connective Network under the Condition of Particle’s Fission and Growth at a Constant Rate

We construct a complete-connective regular network based on Self-replication Space and the structural principles of cantor set and Koch curve. A new definition of dimension is proposed in the paper, and we also investigate a simplified method to calculate the dimension of two regular networks. By the study results, we can get a extension: the formation of Euclidean space may be built by the process of the Big Bang's continuously growing at a constant rate of three times.

Geologic body three-dimensional model generation and visualization method

The divergence three-dimensional millet-seed body model and the continuous distributing layer-imitating model were introduced, which were used to express geologic body, and the procedure of generating these two models and their merits and demerits were synthesized. Three methods of geologic body’s three-dimensional expression were separately introduced, and the merits of the continuous distributing layer imitating model were proposed as comparing with the divergence three-dimensional millet-seed body model. The three-dimensional cubes were observed from any direction and any tangle with the application of dealing methods such as peeling, hollowing out, transparent or half-transparent.

基于一维变分法的微波辐射计反演边界层温湿廓线

地基微波辐射计能够克服星载遥感对低层大气不敏感的缺点,在边界层大气探测方面更具优势.一维变分反演算法考虑了辐射传输过程等物理机制,在应用于微波辐射计的反演时具有很高的可信度.针对微波辐射计信息含量较低以及一维变分算法收敛率不高等问题,提出利用地面气象要素改进算法在近地面层的反演精度和引入正则化算子提升算法的收敛特性.利用探空数据对上述改进方法的提升效果进行验证,结果表明:地面气象要素的引入使得反演算法在地表温湿度的均方根误差分别降低了78.2%和55.5%,对于上层大气温湿廓线也有小幅提升;正则化算子对算法的反演时间和反演精度影响很小,但是可以显著地减少未收敛样本个数和提升反演廓线的质量.

三维大地电磁测深阶段式自适应正则化反演

如何合理地确定正则化因子是地球物理正则化反演领域的研究热点。阶段式自适应算法可以充分发挥模型稳定器的作用,提高反演结果的稳定性,但是该算法仅在一维、二维大地电磁测深(Magnetotelluric,MT)反演中得以实现。目前,三维MT反演正在快速发展,基于此,本文将阶段式自适应正则化算法引入三维MT正则化反演,按照“阶段”而不是“迭代次数”自适应地调整正则化因子的取值,进而观察反演结果的变化。本文设计单块体和双块体模型试验,并特意设置了较大的迭代次数,进而观察反演结果随反演进程的变化情况。模型试验表明:阶段式自适应算法是适用于三维MT正则化反演的,该算法在反演的后期可以更好地保持解的稳定,故此,从解的稳定性这个角度去考量正则化因子的选择是一种值得探索的方向。

基于结合先验信息的最小支撑稳定器的三维重力正则化反演

如何将先验信息融入地球物理反演,进而改善反演的不适定性,一直是地球物理反演领域的研究热点。将先验信息直接融入目标函数的方法通常会增加目标函数的复杂性。为了不在目标函数上增加约束项,更加简单、方便地实现先验信息的融入,本文以三维重力正则化反演为例,将先验信息融入最小支撑稳定器,实现了对最小支撑稳定器的重构,并设计了单块体和双块体模型,进行对比试验。试验结果表明:相较于基于最小支撑稳定器的三维重力反演结果,基于结合先验信息的最小支撑稳定器的三维重力正则化反演更好地还原了异常体的几何形态和物性分布;此外,基于新方法反演的误差迭代曲线收敛更快,拟合精度更高。故此,通过最小支撑稳定器的重构实现先验信息的融入是可行的,该方法适用于三维重力反演,具有实现方便且不额外增加约束项的优点。

具Robin条件的高维扩散方程反问题正则化算法

初始热场和热源同时识别问题是一类热传导方程反问题.通过两个固定时刻的温度测量数据同时反演初始温度和热源项,提出了改进的正则化方法,获得了稳定化算法,给出了正则化参数的选取策略及正则化解的误差估计,对带噪声干扰的测量数据进行预处理以提高数据精度.数值算例验证了算法的有效性.

斜激波与内凹半圆柱面无粘相互作用

针对三维内转式进气道流动中激波入射内凹壁面主导的复杂波系干扰问题,采用斜激波入射内凹半圆柱面的简化构型,在来流马赫数为6的条件下,通过无粘数值模拟结合理论分析,研究了激波角β_(i)=14°~29°的斜激波在内凹半圆柱面反射形成的三维流场。结果表明,流场对称面均会出现显著高于二维情况的逆压梯度。当β_(i)≤25°时,从侧壁到对称面,斜激波经历了从马赫反射(MR)到规则反射(RR)的转变,形成了MR-RR型流场,转变点处产生的桥激波向对称面延伸,桥激波在对称面反射后产生的压力峰值高于二维斜激波反射;当β_(i)≥25°时,斜激波在侧壁和对称面均发生马赫反射,形成了MR-MR型流场,两种马赫反射分界点处产生的桥激波向侧壁发展,侧壁气流在对称面相撞后产生的压力峰值高于正激波后的压力;当β_(i)=25°时,流场存在MR-RR型和MR-MR型双解现象。通过降维分析理论,揭示了两类流场中转变点和分界点的形成机制,并厘清了桥激波的产生原因和初期演化特征。当β_(i)≥18°时,无粘激波干扰所主导的侧壁气流加剧向对称面汇聚,并在对称面附近产生流向涡对。无粘分析获得的认识,有助于揭示内转式进气道中流动汇聚和流向涡对等现象的形成机理。

基于正则化SVD算法的660MW机组煤粉加热炉炉膛三维温度场重建

针对现有加热炉炉膛内三维温度场重建方法存在的重建误差较大、重建消耗时间较长的问题,提出基于正则化SVD算法的660MW机组煤粉加热炉炉膛三维温度场重建方法。根据人眼视觉二维图像特征点提取原理,提取温度场立体图像特征点;利用小波变换方法计算子线段端点,获取特征点匹配结果;通过声学测温方法以及射线成像理论,重建声波传播速度分布形式,凭借正则化SVD算法构建声学测量系统模型,对声波飞行值进行修正,结合特征点匹配结果和对称轴,得到实现660MW机组煤粉加热炉炉膛三维温度场重建。实验结果表明,所提方法的最低AER、MER、RMSE分别为4.11、0.98、1.21,重建时间始终保持在0.6s以内,重建误差较小、重建消耗时间较短,抗噪声能力强,温度场重建效果好。

基于机载LiDAR点云数据的建筑物三维模型重建方法

以机载LiDAR点云数据为研究对象,提出一套建筑物三维模型重建方法。首先使用渐进三角网滤波算法分类地面点与非地面点,通过训练完成的随机森林模型完成建筑物点云提取;其次将方向作为约束条件,使用随机抽样一致(Random Sample Consensus,RANSAC)算法完成建筑物轮廓线提取并获取屋顶关键点信息;最后使用SharpGL工具包,以建筑物轮廓线与屋顶关键点信息为框架重建建筑物三维模型。以实测机载LiDAR点云数据为例进行实验,结果表明,本文方法能够提取得到完整的建筑物轮廓信息,并具有较高的建筑物模型重建精度。

无人机航测在弃土场合规性监测中的应用

线性工程中经常会设置弃土场,其是水土保持监测的重要对象。无人机有明显的高效、全面和准确等优势,已成为弃土场水土保持监测的重要手段。以某铁路项目水泉村2号弃土场为例,通过无人机航测建立三维模型的方法,对弃土场扰动范围、堆置方案和水土保持措施进行合规性监测,并解译发现了错车平台边坡缺乏防护、弃土场边坡形成冲沟等水土流失问题,旨在探讨无人机航测在弃土场合规性监测中的应用思路,为水土保持信息化监督和监测提供依据。

Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..