Gravitational radiation of angular－momentum from general covariant conservation law

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Discovering exact,gauge-invariant,local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (X) -MASTER BALANCE LAW

Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)--SURFACE COUSERVATION LAWS

The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .

Solar System. Angular Momentum. New Physics

The most widely accepted model of Solar System formation, known as the Nebular hypothesis, does not solve the Angular Momentum problem—why is the orbital momentum of Jupiter larger than rotational momentum of the Sun? The present manuscript introduces a Rotational Fission model of creation and evolution of Macrostructures of the World (Superclusters, Galaxies, Extrasolar Systems), based on Overspinning Cores of the World’s Macroobjects, and the Law of Conservation of Angular Momentum. The Hypersphere World-Universe model is the only cosmological model in existence that is consistent with this Fundamental Law.

Decisive Role of Dark Matter in Cosmology

Hypersphere World-Universe Model (WUM) is an alternative to the prevailing Big Bang Model (BBM). WUM and BBM are principally different Models: 1) Instead of the Initial Singularity with the infinite energy density and the extremely rapid expansion of the space (Inflation) in BBM;in WUM, there was a Fluctuation (4D Nucleus of the World with an extrapolated radius equals to a basic unit of size a) in the Eternal Universe with a finite extrapolated energy density (four orders of magnitude less than the nuclear density) and a finite expansion of the Nucleus in its fourth spatial dimension with speed c that is the gravitodynamic constant;2) Instead of the Infinite Homogeneous and Isotropic Universe around the Initial Singularity in BBM;in WUM, the 3D Finite Boundless World (the Hypersphere of the 4D Nucleus) presents a Patchwork Quilt of different Luminous Superclusters (≳103), which emerged in various places of the World at different Cosmological times. The Medium of the World is Homogeneous and Isotropic. The distribution of Macroobjects in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous. The Absolute Age of the entire World (determined by the parameters of the Medium) is 14.22 Gyr.

Hypersphere World-Universe Model: Centre of Our Galaxy

In 1937, Paul Dirac proposed: the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”;and later added the notion of continuous creation of Matter in the World. The developed Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics, and it can already serve as a basis for a New Cosmology proposed by Paul Dirac. In 2013, WUM predicted the values of the following Cosmological parameters: gravitational, concentration of intergalactic plasma, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020) made by Prof. R. Genzel and A. Ghez is a confirmation of one of the most important predictions of WUM in 2013: “Macroobjects of the World have cores made up of the discussed DM particles. Other particles, including DM and baryonic matter, form shells surrounding the cores”.

Hypersphere World-Universe Model: Evolution of the World

The main objective of this paper is to discuss the Evolution of a 3D Finite World (that is a Hypersphere of a 4D Nucleus of the World) from the Beginning up to the present Epoch in frames of World-Universe Model (WUM). WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) when only Dark Matter (DM) Macroobjects (MOs) existed, and Luminous Epoch (ever since for 13.77 billion years) when Luminous MOs emerged due to Rotational Fission of Overspinning DM Superclusters’ Cores and self-annihilation of Dark Matter Particles (DMPs). WUM envisions that DM is created by the Universe in the 4D Nucleus of the World. Dark Matter Particles (DMPs) carry new DM into the 3D Hypersphere World. Luminous Matter is a byproduct of DMPs self-annihilation. By analogy with 3D ball, which has two-dimensional sphere surface (that has surface energy), we can imagine that the 3D Hypersphere World has a “Surface Energy” of the 4D Nucleus. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Missing Baryon problem related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements. In 2013, WUM predicted the values of the following Cosmological parameters: gravitational, concentration of intergalactic plasma, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020) made by Prof. R. Genzel and A. Ghez is a confirmation of one of the most important predictions of WUM in 2013: “Macroobjects of the World have cores made up of the discussed DM particles. Other particles, including DM and baryonic matter, form shells surrounding the cores”.

Solar System. Angular Momentum. Dark Matter Reactors

The developed Hypersphere World-Universe Model (WUM) is consistent with all Concepts of the World [1]. In WUM, we postulate the principal role of Angular Momentum and Dark Matter in Cosmological theories of the World. The most widely accepted model of Solar System formation, known as the Nebular hypothesis, does not solve the Angular Momentum problem—why is the orbital momentum of Jupiter larger than rotational momentum of the Sun? WUM is the only cosmological model in existence that is consistent with this Fundamental Law. The Nebular hypothesis does not solve Internal Heating and Diversity problems for all Planets and Moons in Solar system—why the actual mean surface temperature of them is higher than their effective temperature calculated based on the Sun’s heat for them and how could each one be so different if all of them came from the same nebula? The proposed concept of Dark Matter Reactors in Cores of all gravitationally-rounded Macroobjects successfully resolves these problems.

From the Beginning of the World to the Beginning of Life on Earth

Hypersphere World-Universe Model (WUM) is, in fact, a Paradigm Shift in Cosmology [1]. In this paper, we provide seven Pillars of WUM: Medium of the World;Inter-Connectivity of Primary Cosmological Parameters;Creation of Matter;Multicomponent Dark Matter;Macroobjects;Volcanic Rotational Fission;Dark Matter Reactors. We describe the evolution of the World from the Beginning up to the birth of the Solar System and discuss the condition of the Early Earth before the beginning of life on it.

Influence of the Delay and Dispersion in Mechanics

The aim of this work is to clarify the new mathematical model describing the mechanics of continuous media and rarefied gas. The present study is associated with the formulation of conservation laws as conditions of equilibrium of angular momentums, while usually formulated in terms of balance of force. The equations for gas are found from the modified Boltzmann equation and the phenomenological theory. For a rigid body, the equations used the phenomenological theory, but changed their interpretation. We elucidate the contribution of cross-effects in the conservation laws of continuum mechanics, including the self-diffusion, thermal diffusion, etc., which indicated S. Wallander. The paradox of Hilbert in the solution of the Boltzmann equation by the Chapman-Enskog method was resolved. Refined model of the boundary conditions for rarefied gas flows and transient flow were near the moving surfaces. We establish conditions for the existence of the A. N. Kolmogorov inertial range on the basis of the proposed theory. Based on the theory, derivation of the Prandtl formula for boundary layer was received. Delay in mechanics plays an important role on commensurability of relaxation times and lateness. New accounting delay option is proposed to consider the difference between the time derivative as a limit and end values of the mean free path in a rarefied gas. The role of individual time delay for each particle velocity and the average time is debated. The Boltzmann equation is written with an additional term. This situation is typical for discrete medium. The transition from discrete to continuous environment is a key issue mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The role of the time has similar problems in quantum mechanics. Some examples are suggested.

Velocity Distribution of Slurry in Horizontal Pipe WhenSolid Particles Sliding

Based on the laws of momentum conservation and impulse in accelerating process, the distribution on speed of ununiform slurry flow in a horizontal pipe was studied. According to the momentum change of solid particles and conveying liquid of slurry flow during accelerating, and some effect factors, the relationship between the speed of solid particles and the speed of conveying liquid was obtained. When dealing with the friction between sliding solid particles and pipe, it is pivotal to reasonably distribute component of friction to each solid particle. The friction coefficient between solid particles was obtained by forces analysis and theoretic calculation, and can be used to calculate the friction force on every solid particle. The effect of friction on speed of every solid particle was investigated through the impulse law. The result is more accurate than that by using uniform friction on solid particles. It is completely new method to use above theory to get solid particles speed distribution, conveying liquid speed distribution and slurry speed distribution.

General covariant conservative angular momentum as internal charges

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Effect of Mathematical Models on Experimental Data for the Gas and Liquids

The new analysis of the influence the method of calculating macro-parameters to experimental data is made for the mixture a rarefied gas and gas with internal degrees of freedom. The delay process is counted, which is important in describing of the discrete space and in describing the relaxation of the complicated molecules. The analysis of the recording the Lagrangian function for the collective interaction of the particles is made with counting of changing position of the inertia center. This equation should have a modified Liouville equation and the Boltzmann equation. General consideration of all effects gives us cumbrous system of equations. New another definition of temperature is obtained for molecules with vibration and rotation degree of freedom and for mixture. This is making another value for pressure of the mixture a rarefied gas and gas with internal degrees of freedom. Probably, exactly, these values are measured in all experiments. The simplest interaction of two homogeneous flows is studied which move in the same direction at different speeds.

角动量演示仪的教具制作及其教学研究

角动量和角动量守恒定律是大学物理教学中的重点和难点。文章介绍了一套自制的集定性演示角动量的矢量性、定性演示和定量验证角动量守恒定律为一体的便携式角动量演示教具,探讨了其在研究型课堂演示实验教学过程中的应用。该教具主要由旋转圆盘、穿珠圆盘、电动机、变速控制器等部分组成。教具整体结构紧凑,方便携带,操作简便,现象十分明显,可将角动量矢量性和角动量守恒定律可视化,有利于突破角动量相关概念和规律的教学难点,实现高效课堂的生成。

电磁场角动量守恒定律的四维协变形式

导出了电磁场角动量守恒定律的四维协变形式,并讨论了其物理意义:该形式是一个四维二阶张量方程,一共有6个非零独立分量,其中3个分量给出电磁场的角动量守恒定律,另外3个分量同时给出电磁场的能量和动量守恒定律.

Angular momentum of a brane-world model

In this paper we discuss the properties of the general covariant angular momentum of a fivedimensional brane-world model. Through calculating the total angular momentum of this model, we are able to analyze the properties of the total angular momentum in the inflationary RS model. We show that the space-like components of the total angular momentum of the inflationary RS model are all zero while the others are non-zero, which agrees with the results from ordinary RS model.

散粒体斜坡上滚石法向碰撞恢复系数研究

国内外在研究滚石碰撞问题时多将碰撞目标假设为弹塑性体,从而推导出恢复系数计算公式。但是对于散粒体斜坡,由于具有结构松散、高压缩、低黏结力等物理力学特性,如果将其完全考虑为弹塑性体,那么低估了其自身的耗能潜力。为此,我们考虑了松散介质的孔隙压密特征,改进提出了散粒体斜坡上滚石法向碰撞恢复系数的计算式,并探讨了滚石碰撞再回弹的临界条件。同时以西藏昌都察达隧道进口散粒体斜坡为算例进行数值模拟,分析了5种影响因素下滚石法向碰撞恢复系数变化规律,并与改进公式、已有相关公式计算结果进行了对比分析。结果表明改进公式与数值模拟结果较为吻合,优于假设为弹塑性体的公式计算值。研究思路及成果可为类似区域性问题提供参考。

The Basic Concepts and Basic Laws Relating to Matter and Gravitational Fields in Physics

In this work, the author applied the universal gauge field theory and Noether theorem to prove that universality exists for the Lorentz and Levi-Civita law of conservation of energy momentum tensor density. We also found that this conservation law has profound implications in physics. For example, based on this law, one can explore the origin of the matter field, and propose a new view about what is “dark energy” and what is “dark matter”.

基于角动量轮控制的无人驾驶自行车的实现

针对无人驾驶自行车自平衡问题,提出了一种通过角动量守恒定律设计的角动量轮来使无人驾驶自行车能够长久地保持静态平衡。对自行车倾侧时进行动力学分析,确定角动量轮的最终控制方案。驱动系统方面,本文采用了M4内核32位的STM32F407ZGT6芯片,使用Odrive直接控制角动量轮转速。使用由三轴加速度计、三轴陀螺仪和一款微控制器集成的CH100姿态传感器获取自行车姿态信息;使用一阶低通滤波减少电机抖动对CH100陀螺仪测量数值的影响;使用二阶巴特沃斯滤波和卡尔曼滤波融合滤波将高频抖动滤波除去。最终调试的角动量轮静止平衡参数KP、KI、KD、最大输出、最大积分分别为-120、-1.0、-3000、28、10;直线行进参数KP、KI、KD、最大输出、最大积分分别为-100、0、-500、28、10;舵机控制参数KP、KI、KD、最大输出、最大积分分别为90、0、0、80、0。在Odrive参数中,角动量角轮的vel_ramp_rate为40,电机的vel_ramp_rate为8;角动量轮的vel_gain为0.035、电机的vel_gain为0.15。