Four Algorithms for Boundary Control with Breaking in Space and Time

Typically, active control systems either have a priori complete information about the boundary-value problem and damped waves before switching on, or get it during the measurement process or accumulate and update information online (identification process in adaptive systems). In this case, the boundary problem is completely imprinted in the information arrays of the control system. However, very often complete information about a boundary-value problem is not available in principle or this info is changing in time faster than the process of its accumulation. The article considers examples of boundary control algorithms based almost without any information. The algorithms presented in the article cannot be obtained within the framework of the harmonic representation of the problem by complex amplitudes. And these algorithms carry out fast control in microstructured boundary problems. It is shown that in some cases it is possible to find simple solutions if we remove restrictions: 1) on the spatio-temporal resolution of controlling elements of a boundary-value problem;2) on the high-frequency radiation of the controlled boundary.

Oxidation Kinetics of Aluminum Powders in a Gas Fluidized Bed Reactor in the Potential Application of Surge Arresting Materials

In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.

In-situ observations on interphase boundary migration and grain growth during α/γ phase transformation in iron-4.2%Cr alloy

In-situ observations on α/γ phase transformation were made to study the effects of grain boundary microstructures on the formation of a new phase and the migration of α/γ interphase boundary in an iron4. 2%Cr alloy. It was found that triple junctions with more random boundaries could be the primary nucleation sites for a new phase, while triple junctions with low angle or low ∑ coincidence boundaries did not play any role as preferential sites. The migration of α/γ interphase boundary during heating over the transformation temperature range showed the two stage behaviour characterized by a stage with a migration velocity of 0. 33-0. 75 mm/s and secondly by a stage with 3. 7-7. 6 mm/s. It was also found that abnormal grain growth and a high density of ∑3 coincidence boundaries could occur in a phase with bcc structure after cycling of α/γ phase transformation. A new mechanism of nucleation and growth of a new phase in α/γ phase transformation is proposed on the basis of roles of plane-matching interphase boundaries, as previously discussed on the origin of anisotropy of grain growth due to the migration of {110} plane-matching boundaries in Fe-3z%Si alloy. The most recent theoretical work on the distribution of plane-matching boundaries in solids with different crystal structures was found to be useful for the understanding of nucleation and growth during α/γ phase transformation.

Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy

The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.

Origin of Magnetic Fields of Stellar Objects in the Universe Based on the 5D Projection Theory

Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D?void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping;these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B?−?log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).

Boundary Control Problem of Infinite Order Distributed Hyperbolic Systems Involving Time Lags

Various optimal boundary control problems for linear infinite order distributed hyperbolic systems involving constant time lags are considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

Analysis of Dynamics of Boundary Shape Perturbation of a Rotating Elastoplastic Radially Inhomogeneous Plane Circular Disk: Analytical Approach

For a rotating inhomogeneous circular disk a way of calculating dynamics of boundary shape perturbation and failure of bearing capacity is proposed in terms of small parameter method. Characteristic equation of plastic zone critical radius is obtained as a first approximation. A formula of critical angular velocity is derived which determines the stability loss of the disc according to the self-balanced form. Efficiency of the proposed method is shown by an illustrative example considered in Section 7. Values of critical angular velocity of rotation are found numerically for different parameters of the disc.

变系数三阶周期边值问题的正解(英文)

研究了变系数非线性三阶周期边值问题的正解.非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-selski不动点定理获得了1～2个正解的存在性.

奥陶纪-志留纪边界附近火山活动记录:来华南周缘钾质斑脱岩的信息

扬子地台内奥陶纪顶部的五峰组到志留纪底部的龙马溪组间存在着多个粘土岩层。前人研究结果认为这些粘土岩层为钾质斑脱岩,是火山喷发的凝灰质物质在海相环境沉积、蚀变的产物。这些斑脱岩广泛分布于扬子地台周缘,对理解奥陶纪-志留纪时华南所处的大地构造位置和相应的构造事件具有重要的意义。本文对采自扬子地台内湖北宜昌地区和贵州桐梓地区奥陶纪-志留纪界线剖面的斑脱岩层进行了矿物学及地球化学工作,旨在判定其形成的构造环境。矿物学研究表明上述岩石除了含有粘土矿物外,还含有石英、长石、黑云母、磷灰石、锆石等中酸性岩浆岩中的常见矿物,属典型的钾质斑脱岩。本文利用在风化过程中不活动元素对斑脱岩的原岩进行了恢复,结果也表明其原岩为中酸性火山岩,包括安山岩-英安岩-及流绞岩等。微量元素特征显示多数样品具有典型的岛弧火山岩的特征,很可能与北面早古生代秦岭洋的闭合过程中的板块俯冲有关,也可能是早古生代在华南板块东南缘外侧存在的一古老洋壳向华南板块的俯冲。有一个样品(YC0711)没有Nb的负异常,但是具有明显的Ti负异常,在Th/Yb-Nb/Yb判别图上落在岛弧区附近,其原岩可能是富铌玄武岩之类的特殊岛弧岩石。火山活动的峰期为晚奥陶世赫南特阶时代,与地质历史上第二大的生物大灭绝事件同时。前人认为该生物灭绝事件与冈瓦纳冰川有关。考虑到华南以及欧洲、北美等地均出现大规模晚奥陶世-早侏罗纪钾质斑脱岩,奥陶纪-志留纪边界的火山事件是具有全球规模的,所喷发的岩石多是富含挥发份的中酸性岩,对大气圈和生物圈具有十分重要的影响,本文认为火山活动很可能是造成晚奥陶世的生物大灭绝事件和冈瓦纳冰川的主要诱导因素。

Analytical Solutions of Some Two-Point Non-Linear Elliptic Boundary Value Problems

Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

电磁检测中的开域电磁场数值计算

该文以涡流电缆偏心检测为例,针对电磁检测中开域涡流磁场难于求解这一问题,根据有限元和边界元的特点,对开域电磁场,采用设定虚拟边界的方法将无界场域分割成闭合的内部区域和开放的外部区域,在两个区域分别采用有限元法(FEM)和边界元法(BEM),在虚拟边界上采用直接耦合方法,使有限元方程和边界元方程得以成功组合,从而获得全域解。该方法避免了利用自然边界划分有限元区和边界元区,使开放的边界元区含有多种媒质及源,造成边界元方程组非对称满阵阶数过高,难于计算的缺点。得出了磁场的分布及其检测对象的涡流损耗。计算结果与偏心量变化的线性关系和实验结果与偏心量变化的线性关系在视在阻抗的物理意义上具有良好的一致性。

Use of the area of main influence to fix a relevant boundary for mining damages in Germany

In 2010, the fracking discussion in Germany caused a number of changes in German law, which came into force in 2016.Especially the production of gas had to be regulated.With the legislation amendment, the Subsidence-Area Mining Regulation has been revised, too.The changes expand the compensation of mining damages, especially to the extraction with drilling from the surface and underground storage.Although the Subsidence-Area Mining Regulation has been revised, the area of main influence(subsidence of 10 cm)remains to determine a relevant boundary for mining damages.The determination and prediction of this boundary above caverns are presented in this paper.In addition, further elements of ground movements and their relevance to mine damages are analyzed.The usage of the area of main influence to fix a relevant boundary for mining damages does not correspond to the relevant elements of ground movements.A limit for differences in subsidence(tilt) or horizontal changes in length should be preferred to describe the relevance of mining damages on buildings.Furthermore, this paper outlines the meaning of using the area of main influence to fix a relevant boundary for mining damages.

Key structure in laminar-turbulent transition of boundary layer with streaky structures

A numerical simulation is performed to find out a key vortical structure in the laminar-turbulent transition. A low-speed streak is generated inside a laminar boundary layer using an isolated cuboid roughness, aimed at providing an environment unstable to outer disturbances. Then, a short duration jet is issued into the boundary layer. When the jet velocity is low, some vortices appear in the boundary layer, but the transition of the boundary layer does not take place.However, when the jet velocity exceeds a certain threshold, two vortices newly appear above the elongated legs of a V-shaped vortex and only one of them is stretched and survives. After that,vortices are generated one after another around the survived one. By comparing the decayed and the survived vortices, it is found that the difference in their heights is the key characteristic which leads to the transition.

Existence of Solutions for Boundary Value Problems of Conformable Fractional Differential Equations

In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results.

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.

松辽盆地断陷期超层序界面的地质属性刻画及其油气地质意义

松辽盆地断陷期分为 1个超层序组、3个超层序、6个层序。从火石岭组到营城组构成一个完整的活动大陆边缘火山—断陷超层序组。三个超层序分别为同碰撞期火山—断陷超层序 (火石岭组 )、火山间歇期断陷超层序(沙河子组 )和后碰撞期火山—断陷超层序 (营城组 )。超层序组底界 T5界面是前三叠纪拼合基底与侏罗系火山岩—沉积岩互层序列之间的反射界面 ,界面上下层系之间的间断时限≥ 4 5 Ma;界面之下是古亚洲洋构造域时期形成的拼合基底 ,界面之上是鄂霍次克洋构造域形成的火山—沉积建造。超层序组顶界 T4 界面是断陷期火山岩—碎屑岩互层序列与上覆坳陷期正常沉积岩层序之间的反射界面 ,界面上下层系之间的间断时限为 3～ 5 Ma;界面之下是鄂霍次克洋构造域晚期形成的火山—沉积建造 ,界面之上是太平洋构造域早期形成的坳陷期沉积层序。层序对油气的控制作用十分明显。高产工业气藏主要见于超层序组的顶界面 ;工业气藏和低产气藏主要出现在层序界面附近 ;