Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

The hydrothermal wave of large-Prandtl-number fluid in a shallow cavity

The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite to the surface flow (upstream) in the case of zero gravity when the applied temperature difference grows and over the critical value. The phase relationships of the disturbed velocity,temperature and pressure demonstrate that the traveling wave is driven by the disturbed tem-perature,which is named hydrothermal wave. The hydrothermal wave is so weak that the oscillatory flow field and temperature distribution can hardly be observed in the liquid layer. The exciting mechanism of hydrothermal wave is analyzed and discussed in the present paper.

Why Gravitational Waves Cannot Exist

The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear systems of ordinary or partial differential equations, using new methods from Differential Geometry (D.C. Spencer, 1970), Differential Algebra (J.F. Ritt, 1950 and E. Kolchin, 1973) and Algebraic Analysis (M. Kashiwara, 1970). The main idea is to identify the differential indeterminates of Ritt and Kolchin with the jet coordinates of Spencer, in order to study Differential Duality by using only linear differential operators with coefficients in a differential field K. In particular, the linearized second order Einstein operator and the formal adjoint of the Ricci operator are both parametrizing the 4 first order Cauchy stress equations but cannot themselves be parametrized. In the framework of Homological Algebra, this result is not coherent with the vanishing of a certain second extension module and leads to question the proper origin and existence of gravitational waves. As a byproduct, we also prove that gravitation and electromagnetism only depend on the second order jets (called elations by E. Cartan in 1922) of the system of conformal Killing equations because any 1-form with value in the bundle of elations can be decomposed uniquely into the direct sum (R, F) where R is a section of the Ricci bundle of symmetric covariant 2-tensors and the EM field F is a section of the vector bundle of skew-symmetric 2-tensors. No one of these purely mathematical results could have been obtained by any classical approach. Up to the knowledge of the author, it is also the first time that differential algebra in a modern setting is applied to study the specific algebraic feature of most equations to be found in mathematical physics, particularly in GR.

Development of Magnetic Compound Fluid Rubber Sensor for Practical Usage on γ-Irradiation and Energy Harvesting for Broad-Band Electromagnetic Waves

We have performed sequential studies on new types of soft rubber for their application as artificial skin in robots and haptic sensors. Based on a proposed electrolytic polymerization method and novel adhesion technique for rubber and a metal that utilizes a metal complex hydrate, we have developed an MCF rubber sensor. This sensor uses a magnetic compound fluid (MCF), natural rubber (NR-latex) or chloroprene rubber latex (CR-latex), and requires the application of a magnetic field. The potential application of the developed sensor in various engineering scenarios and our daily lives is significant. In this regard, we investigated the effects of γ-irradiation, infrared radiation, microwaves, and a thermal source on the MCF rubber sensor. We established that the MCF rubber is effective enough to be used for power generation of broadband electro-magnetic waves from γ-rays to microwaves, including the range of the solar spectrum, which is the typical characteristic obtained in the present investigation. The remarkable attribute is that the MCF rubber sensor dose is not degraded by γ-irradiation. We also demonstrated the effectiveness of the MCF rubber sensor in energy harvesting.

If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox

We start from a minimal number of generally accepted premises, in particular Hartle-Hawking quantum wave of the universe and von Neumann-Connes’ pointless and self referential spacetime geometry. We then proceed from there to show, using Dvoretzky’s theorem of measure concentration, that the total energy of the universe is divided into two parts, an ordinary energy very small part which we can measure while most of the energy is concentrated as the second part at the boundary of the holographic boundary which we cannot measure in a direct way. Finally the results are shown to imply a resolution of the black hole information paradox without violating the fundamental laws of physics. In this way the main thrust of the two opposing arguments and views, namely that of Hawking on the one side and Susskind as well as tHooft on the other side, is brought to a consistent and compatible coherent unit.

Adaptive Fuzzy Sliding Mode Controller for Grid Interface Ocean Wave Energy Conversion

This paper presents a closed-loop vector control structure based on adaptive Fuzzy Logic Sliding Mode Controller (FL-SMC) for a grid-connected Wave Energy Conversion System (WECS) driven Self-Excited Induction Generator (SEIG). The aim of the developed control method is to automatically tune and optimize the scaling factors and the membership functions of the Fuzzy Logic Controllers (FLC) using Multi-Objective Genetic Algorithms (MOGA) and Multi-Objective Particle Swarm Optimization (MOPSO). Two Pulse Width Modulated voltage source PWM converters with a carrier-based Sinusoidal PWM modulation for both Generator- and Grid-side converters have been connected back to back between the generator terminals and utility grid via common DC link. The indirect vector control scheme is implemented to maintain balance between generated power and power supplied to the grid and maintain the terminal voltage of the generator and the DC bus voltage constant for variable rotor speed and load. Simulation study has been carried out using the MATLAB/Simulink environment to verify the robustness of the power electronics converters and the effectiveness of proposed control method under steady state and transient conditions and also machine parameters mismatches. The proposed control scheme has improved the voltage regulation and the transient performance of the wave energy scheme over a wide range of operating conditions.

The de Broglie Waves and Joule-Lenz Law Applied in Examining the Electron Transitions in Small Quantum Systems

A transformation of the electron states—say those enclosed in a potential box—into the de Broglie waves done in the paper, enabled us to calculate the energy change between two quantum levels as a function of the specific heat and difference of the temperature between the states. In consequence, the energy difference and that of entropy between the levels could be examined in terms of the appropriate classical parameters. In the next step, the time interval necessary for the electron transition between the levels could be associated with the classical electrodynamical parameters like the electric resistance and capacitance connected with the temporary formation of the electric cell in course of the transition. The parameters characterizing the mechanical inertia of the electron were next used as a check of the electrodynamical formulae referring to transition.

Interpreting the Shortwave Infrared &Thermal Infrared Regions of Remote Sensed Electromagnetic Spectrum with Application for Mineral-Deposits Exploration

The ASTER (Advanced Space-borne Thermal Emission and Reflection radiometer) data, including all the 3 parts: VNIR (Visible and Near-Infrared), SWIR (Short Wave Infrared), TIR (Thermal Infrared), were applied for extraction of mineral deposits, such as the Ni-Cu deposit in eastern Tianshan, the gypsum in western Tianshan, and the borax in Tibetan. This paper discusses the extraction methodology using the ASTER remote sensing data and reveals the good extraction results. This paper bravely represents the summary of the main achievement for this field by the scientists in other countries and gives a comparison with the works by others. The new achievements, described in this paper, comprise the extraction of anomalies for Ni-Cu deposit, gypsum, and borax.

Exact Traveling Wave Solutions of Nano-Ionic Solitons and Nano-Ionic Current of MTs Using the exp(-φ (ξ ))-Expansion Method

In this work, the exp(-φ (ξ )) -expansion method is used for the first time to investigate the exact traveling wave solutions involving parameters of nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. The validity and reliability of the method are tested by its applications to Nano-ionic solitons wave’s propagation along microtubules in living cells and Nano-ionic currents of MTs which play an important role in biology.

What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse

We reason that in quantum cosmology there are two kinds of energy. The first is the ordinary energy of the quantum particle which we can measure. The second is the dark energy of the quantum wave by quantum duality. Because measurement collapses the Hawking-Hartle quantum wave of the cosmos, dark energy cannot be detected or measured in any conventional manner. The quantitative results are confirmed using some exact solutions for the hydrogen atom. In particular the ordinary energy of the quantum particle is given by E(0) = (/2)(mc2) where is Hardy’s probability of quantum entanglement, =( - 1)/2 is the Hausdorff dimension of the zero measure thin Cantor set modeling the quantum particle, while the dark energy of the quantum wave is given by E(D) = (5/2)(mc2) where is the Hausdorff dimension of the positive measure thick empty Cantor set modeling the quantum wave and the factor five (5) is the Kaluza-Klein spacetime dimension to which the measure zero thin Cantor set D(0) = (0,) and the thick empty set D(-1) = (1,) must be lifted to give the five dimensional analogue sets namely and 5 needed for calculating the energy density E(0) and E(D) which together add to Einstein’s maximal total energy density E(total) = E(0) + E(D) = mc2 = E(Einstein). These results seem to be in complete agreement with the WMAP, supernova and recent Planck cosmic measurement as well as the 2005 quantum gravity experiments of V. V. Nesvizhersky and his associates. It also confirms the equivalence of wormhole solutions of Einstein’s equations and quantum entanglement by scaling the Planck scale.

Theoretical Quantization of Exact Wave Turbulence in Exponential Oscillons and Pulsons

In a preceding paper, the theoretical and experimental, deterministic and random, scalar and vector, kinematic structures, the theoretical and experimental, deterministic-deterministic, deterministic-random, random-deterministic, random-random, scalar and vector, dynamic structures have been developed to compute the exact solution for wave turbulence of exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. The rectangular, diagonal, and triangular summations of matrices of the turbulent kinetic energy and general terms of numerous sums have been used in the current paper to develop theoretical quantization of the kinetic energy of exact wave turbulence. Nested structures of a cumulative energy pulson, a deterministic energy pulson, a deterministic internal energy oscillon, a deterministic-random internal energy oscillon, a random internal energy oscillon, a random energy pulson, a deterministic diagonal energy oscillon, a deterministic external energy oscillon, a deterministic-random external energy oscillon, a random external energy oscillon, and a random diagonal energy oscillon have been established. In turn, the energy pulsons and oscillons include deterministic group pulsons, deterministic internal group oscillons, deterministic-random internal group oscillons, random internal group oscillons, random group pulsons, deterministic diagonal group oscillons, deterministic external group oscillons, deterministic-random external group oscillons, random external group oscillons, and random diagonal group oscillons. Sequentially, the group pulsons and oscillons contain deterministic wave pulsons, deterministic internal wave oscillons, deterministic-random internal wave oscillons, random internal wave oscillons, random wave pulsons, deterministic diagonal wave oscillons, deterministic external wave oscillons, deterministic-random external wave oscillons, random external wave oscillons, random diagonal wave oscillons. Consecutively, the wave pulsons and oscillons are composed of deterministic elementary pulsons, deterministic internal elementary oscillons, deterministic-random internal elementary oscillons, random internal elementary oscillons, random elementary pulsons, deterministic diagonal elementary oscillons, deterministic external elementary oscillons, deterministic-random external elementary oscillons, random-deterministic external elementary oscillons, random external elementary oscillons, and random diagonal elementary oscillons. Symbolic computations of exact expansions have been performed using experimental and theoretical programming in Maple.

Dispersion Dynamical Magnetic Radius in Intrinsic Spin Equals the Compton Wavelength

Because magnetic moment is spatial in classical magnetostatics, we progress beyond the axiomatic concept of the point particle electron in physics. Orbital magnetic moment is well grounded in spherical harmonics in a central field. There, quantum numbers are integral. The half-integral spinor moment appears to be due to cylindrical motion in an external applied magnetic field;when this is zero , the spin states are degenerate. Consider lifting the degeneracy by diamagnetism in the cylindrical magnetic field: a uniquely derived electronic magnetic radius shares the identical value to the Compton wavelength.

Development of a Post Quantum Encryption Key Generation Algorithm Using Electromagnetic Wave Propagation Theory

In today’s rapid widespread of digital technologies into all live aspects to enhance efficiency and productivity on the one hand and on the other hand ensure customer engagement, personal data counterfeiting has become a major concern for businesses and end-users. One solution to ensure data security is encryption, where keys are central. There is therefore a need to find robusts key generation implementation that is effective, inexpensive and non-invasive for protecting and preventing data counterfeiting. In this paper, we use the theory of electromagnetic wave propagation to generate encryption keys.

Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography

The aim of the present paper is to explain and accurately calculate the missing dark energy density of the cosmos by scaling the Planck scale and using the methodology of the relatively novel discipline of cosmic crystallography and Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following this road we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with the WMAP and supernova measurements and analysis. We develop non-constructively what may be termed super symmetric Penrose fractal tiling and find that the isomorphic length of this tiling is equal to the self affinity radius of a universe which resembles an 11 dimensional Hilbert cube or a fractal M-theory with a Hausdorff dimension where. It then turns out that the correct maximal quantum relativity energy-mass equation for intergalactic scales is a simple relativistic scaling, in the sense of Weyl-Nottale, of Einstein’s classical equation, namely EQR = (1/2)(1/) moc2 = 0.0450849 mc2 and that this energy is the ordinary measurable energy density of the quantum particle. This means that almost 95.5% of the energy of the cosmos is dark energy which by quantum particle-wave duality is the absolute value of the energy of the quantum wave and is proportional to the square of the curvature of the curled dimension of spacetime namely where and is Hardy’s probability of quantum entanglement. Because of the quantum wave collapse on measurement this energy cannot be measured using our current technologies. The same result is obtained by involving all the 17 Stein spaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group which gives the number of the first level of massless particle-like states in Heterotic string theory. All these diverse subjects find here a unified view point leading to the same result regarding the missing dark energy of the universe, which turned out to by synonymous with the absolute value of the energy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation while ordinary energy is the energy of the quantum particle into which the Hawking-Hartle wave collapse at cosmic energy measurement. In other words it is in the very act of measurement which causes our inability to measure the “Dark energy of the quantum wave” in any direct way. The only hope if any to detect dark energy and utilize it in nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.

Self-consistent kinetic theory with nonlinear wave-particle resonances

We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.

Exact Traveling Wave Solutions for Nano-Solitons of Ionic Waves Propagation along Microtubules in Living Cells and Nano-Ionic Currents of MTs

In this work, the extended Jacobian elliptic function expansion method is used as the first time to evaluate the exact traveling wave solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to nano-solitons of ionic waves propagation along microtubules in living cells and nano-ionic currents of MTs which play an important role in biology.

基于D-Wave Advantage的量子退火公钥密码攻击算法研究

D-Wave专用量子计算机的原理量子退火凭借独特的量子隧穿效应可跳出传统智能算法极易陷入的局部极值,可视为一类具有全局寻优能力的人工智能算法.本文研究了两类基于量子退火的RSA公钥密码攻击算法(分解大整数N=pq):一是将密码攻击数学方法转为组合优化问题或指数级空间搜索问题,通过Ising模型或QUBO模型求解,提出了乘法表的高位优化模型,建立新的降维公式,使用D-Wave Advantage分解了 200万整数2269753.大幅度超过普渡大学、Lockheed Martin和富士通等实验指标,且Ising模型系数h范围缩小了 84%,系数J范围缩小了 80%,极大地提高了分解成功率,这是一类完全基于D-Wave量子计算机的攻击算法;二是基于量子退火算法融合密码攻击数学方法优化密码部件的攻击,采用量子退火优化CVP问题求解,通过量子隧穿效应获得比Babai算法更近的向量,提高了 CVP问题中光滑对的搜索效率,在D-Wave Advantage上实现首次50比特RSA整数分解.实验表明,在通用量子计算机器件进展缓慢情况下,D-Wave表现出更好的现实攻击能力,且量子退火不存在NISQ量子计算机VQA算法的致命缺陷贫瘠高原问题:算法会无法收敛且无法扩展到大规模攻击.

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

Investigation of Wave-Structure Interaction Using State of the Art CFD Techniques

The suitability of computational fluid dynamics (CFD) for marine renewable energy research and development and in particular for simulating extreme wave interaction with a wave energy converter (WEC) is considered. Fully nonlinear time domain CFD is often considered to be an expensive and computationally intensive option for marine hydrodynamics and frequency-based methods are traditionally preferred by the industry. However, CFD models capture more of the physics of wave-structure interaction, and whereas traditional frequency domain approaches are restricted to linear motions, fully nonlinear CFD can simulate wave breaking and overtopping. Furthermore, with continuing advances in computing power and speed and the development of new algorithms for CFD, it is becoming a more popular option for design applications in the marine environment. In this work, different CFD approaches of increasing novelty are assessed: two commercial CFD packages incorporating recent advances in high resolution free surface flow simulation;a finite volume based Euler equation model with a shock capturing technique for the free surface;and meshless Smoothed Particle Hydrodynamics (SPH) method. These different approaches to fully nonlinear time domain simulation of free surface flow and wave structure interaction are applied to test cases of increasing complexity and the results compared with experimental data. Results are presented for regular wave interaction with a fixed horizontal cylinder, wave generation by a cone in driven vertical motion at the free surface and extreme wave interaction with a bobbing float (The Manchester Bobber WEC). The numerical results generally show good agreement with the physical experiments and simulate the wave-structure interaction and wave loading satisfactorily. The grid-based methods are shown to be generally less able than the meshless SPH to capture jet formation at the face of the cone, the resolution of the jet being grid dependent.