Derivation of Maxwell’s Equations via the Covariance Requirements of the Special Theory of Relativity, Starting with Newton’s Laws

The purpose of this paper is to establish a connection between Maxwell’s equations, Newton’s laws, and the special theory of relativity. This is done with a derivation that begins with Newton’s verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and Maxwell’s equations for free space emerge with the assumption that the tensor and its dual must both satisfy first-order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton’s third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that both can be assigned the same units. Requiring covariance under either spatial inversions or time reversals precludes magnetic charge being a source of electromagnetic fields that exert forces on electric charges.

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

This paper investigates the computational solution to the problem of projectile motion under a significant linear drag effect. The drag force acting on the particle within the medium of propagation is proportional to the cross-section area of the projectile, the velocity of the particle, and the medium’s density. From zero air resistance force (vacuum) the problems are well known with solutions, but with air resistance (drag force) the problems have no exact analytical solutions which lead to most of the significant scientific research works using numerical methods. Therefore, this study aims to present the analysis of the computational modelling of drag force exerted by the surrounding medium on the linear motion. However, the horizontal and vertical components of differential equations of motion were derived and characterized from the solutions governed by Newton’s 2nd law of motion. The baseball features were presented as the projectile (object) in this work. In addition, the numerical computational results were received from FreeMat. The results were discussed and compared with those from the vacuum. Moreover, the displacements, velocities, range, and trajectories of the projectile were all discussed and a conclusion was made.

The Research of the Flow of Bodies with Use of the Vector Form of the Newton’s Law for the Viscous Liquid

On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.

Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, qpl, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where ζ(3) equals Apery’s constant, 1.202 …, and, n+(0)=n_(0), is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, n+(0) equals, 7.848E54 m-3, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, l+(0)=l_(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, g=9.81m/s2, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

New Interpretation of Newton’s Law of Universal Gravitation

Elliptical motions of orbital bodies are treated here using Fourier series, Fortescue sequence components and Clarke’s instantaneous space vectors, quantities largely employed on electrical power systems analyses. Using this methodology, which evidences the analogy between orbital systems and autonomous second-order electrical systems, a new theory is presented in this article, in which it is demonstrated that Newton’s gravitational fields can also be treated as a composition of Hook’s elastic type fields, using the superposition principle. In fact, there is an identity between the equations of both laws. Furthermore, an energy analysis is conducted, and new concepts of power are introduced, which can help a better understanding of the physical mechanism of these quantities on both mechanical and electrical systems. The author believes that, as a practical consequence, elastic type gravitational fields can be artificially produced with modern engineering technologies, leading to possible satellites navigation techniques, with less dependency of external sources of energy and, even, new forms of energy sources for general purposes. This reinterpretation of orbital mechanics may also be complementary to conventional study, with implications for other theories such as relativistic, quantum, string theory and others.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

The Natural Law of Transition of a Charged Particle into a Compound State under the Action of an Electroscalar Field

This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.

On the Physical Nature of Einstein’s Gravitational Lensing Effect

Gravitational lensing has become a powerful research tool for exploring the distribution of matter and energy in the universe nowadays, as glare phenomena around the Sun and massive galaxies are indeed observed on the Earth. What is the physical nature of gravitational lensing effect? Both Newton’s law of gravitation and Einstein’s theory of relativity are difficult to physically explain these glare phenomena. This study points out that the observed glare around the Sun and large galaxies is a result or product of the orthogonal interaction of high-energy particles emitted from different star light sources. It shows a new physical state associated with abnormal high mass-energy density.

The Quantization of Space

In the present work, it will be shown that the dimensionless number 137 of the fine-structure constant α demands a quantization of space. For this purpose, we refer to a volume constant of electromagnetic processes, which takes effect as a volume quantum. This involves not only a re-evaluation of the Dirac equation but also, and above all, a determination of Einstein’s velocity vector as the fundamental property of these processes. A prerequisite is the linking of the hydrogen spectrum with the hydrogen nucleus.

不可逆空间太阳能动力Braysson循环的生态学优化

基于生态学优化判据对一种不可逆空间太阳能Braysson循环的性能参数进行优化计算。生态学目标函数定义为火用输出率减去火用损失率,而火用损失率等于环境温度乘以循环熵产率。空间太阳能动力系统由太阳能收集器和不可逆的Braysson循环两部分组成。该Braysson循环与高温热源的换热满足牛顿传热规律,与低温热源的换热则满足热辐射换热规律。推导出包括循环的效率、输出功率、生态学函数等在内的性能参数的具体表达式,进一步在最优生态学函数的条件下,对热机的各种性能参数进行了优化分析,获得了一些有意义的结论。

分数布朗运动的局部Strassen重对数律

应用[1]中方法,研究了分数布朗运动局部Strassen重对数律,将[1]的结果推广到了分数布朗运动情形,也将[2]的结果推广到了局部情形。

Brown运动在Hlder范数下的拟必然局部Strassen重对数律

为推广Strassen重对数律,研究了Brown运动在抽象Wiener空间下的局部极限性质。应用(r,p)-容度及Hlder范数意义下的Schilder定理,证明了拟必然局部Strassen重对数律,为研究多参数Brown运动的极限性质提供方法。

New Dynamic Equations of Aerosol in Air of Certain Type

A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theorem and supplemented by corresponding scientific laws for related properties of air and aerosols. This new dynamic equation of aerosol in air is a set of non-linear partial differential equations involved six unknown functions of mass densities, pressure, air and aerosol speeds and temperature. It has features: 1, it belongs to certain type;2, it emphases the effect of buoyancy in equilibrium and potential energy, and the Archimedes principle of buoyancy is firstly extended to lateral directions based on logical deduction, the phenomenon of stirring a glass of oil-water mixture and the recorded of Hurricane Isabel (2003) from space station. The later shows the evidence of existence of lateral buoyancy;3, the mass densities of air and aerosol of a point in our model are varied in different directions due to traction and are treated as vectors, and they have been used in the calculation of lateral buoyancy.

For Propulsion Applications It Is Possible to Utilize Both the Torque Output of the Rotor and the Reactional Torque Acting on the Stator of the Driving Electric Motor by Linearizing the Stator

This paper presents a novel idea of utilizing the reactional torque of the conventional electric motor as a linear output for propulsion in addition to the conventional torque output of the rotor. The idea is demonstrated by a theoretical proposal of linearizing the stator of one of the most used motors in Electrical Vehicles and Hybrid Vehicles. The proposed Linear Stator Motor is a simple modification without involving any functional change of the conventional motor. Though theoretical, the indicated possible input energy saving of more than 75% as compared to the conventional motor is no surprise, as by linearizing the stator, an almost equal linear propulsion output is added to the conventional rotor output. In addition to this remarkable saving in input energy, the proposed Linear Stator Motor that suits all types of vehicles, can maintain propulsion without the need for a mechanical transmission system. Also, in the case of watercraft and aircraft vehicles, no external mechanical propulsion drive system is required. It is just an internal force that can push the vehicle forward, backward, or laterally, while the conventional rotor output can be utilized for energy recovery by driving a DC generator.

EFFECT OF VISCOSITY OF LUBRICANT IN FRICTION

The movement of lubricated fibres in a fibre assembly is investigated theoretically and aviscous sliding model of friction is proposed.Previous work and experimental results are discussedin relation to the model.Results of drawing experiments carried out on wool slivers are also pres-ented and discussed.