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

Journal of Applied Mathematics and Physics 2024年第4期12卷 1134-1162页

作者： Declan Traill Melbourne Australia

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.

关键词： Electron Positron Wave Function Solution Electromagnetic Spin Mass Charge Proof Fundamental Particle Properties Quantum Mechanics Classical Physics Computer 3D Model Schrödinger Equation RMS Klein Gordon Electric Magnetic lorentz Invariant Hertzian Vector Point Potential Field Density Phase Flow Attraction Repulsion Shell Theorem Ehrenfest Virial Normalization Harmonic Oscillator

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Design,fabrication,characterization and reliability study of CMOS-MEMS lorentz-force magnetometers

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Microsystems & Nanoengineering 2022年第5期8卷 17-41页

作者： J.J.Valle J.M.Sánchez-Chiva D.Fernández J.Madrenas Department of Electronic Engineering Universitat Politècnica de CatalunyaJordi Girona 1 i 3Edifici C408034 BarcelonaSpain Sorbonne Université CNRSLaboratoire de Recherche en Informatique(LIP6)UMR76064 place Jussieu75005 ParisFrance Institut de Física d’Altes Energies(IFAE) The Barcelona Institute of Science and Technology(BIST)Edifici Cn.Facultat Ciències NordUniversitat Autónoma de Barcelona08193 Bellaterra(Barcelona)Spain

This article presents several design techniques to fabricate micro-electro-mechanical systems(MEMS)using standard complementary metal-oxide semiconductor(CMOS)processes.They were applied to fabricate high yield CMOS-MEMS shielded lorentz-force magnetometers(LFM).The multilayered metals and oxides of the back-end-of-line(BEOL),normally used for electronic routing,comprise the structural part of the MEMS.The most important fabrication challenges,modeling approaches and design solutions are discussed.Equations that predict the Q factor,sensitivity,Brownian noise and resonant frequency as a function of temperature,gas pressure and design parameters are presented and validated in characterization tests.A number of the fabricated magnetometers were packaged into Quad Flat No-leads(QFN)packages.We show this process can achieve yields above 95%when the proper design techniques are adopted.Despite CMOS not being a process for MEMS manufacturing,estimated performance(sensitivity and noise level)is similar or superior to current commercial magnetometers and others built with MEMS processes.Additionally,typical offsets present in lorentz-force magnetometers were prevented with a shielding electrode,whose efficiency is quantified.Finally,several reliability test results are presented,which demonstrate the robustness against high temperatures,magnetic fields and acceleration shocks.

关键词： lorentz magnetometer characterization

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lorentz Generators for the Maxwell Field and Gauge Fixing

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Communications in Theoretical Physics 2019年第4期71卷 403-409页

作者： V.Debierre Max Planck Institue for Nuclear Physics

We propose a direct derivation of the lorentz generators for the four-potential of electrodynamics on the basis of Wigner's theorem. The derivation relies on a study of the behaviour of polarisation vectors under k-space differentiation. The Coulomb and Lorenz gauges are discussed in that respect, and gauge invariance under Poincare′transformations is examined. The Poincar′e generators given by Bia lynicki-Birula and Bia lynicka-Birula are found to correspond to the Coulomb gauge case.

关键词： vector potential lorentz generators polarisation vectors gauge condition

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In-depth Study on Cylinder Wake Controlled by lorentz Force

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Chinese Physics Letters 2011年第12期28卷 163-166页

作者：张辉范宝春陈志华 Science and Technology on Transient Physics Laboratory Nanjing University of Science and TechnologyNanjing 210094

The underlying mechanisms of the electromagnetic control of cylinder wake are investigated and discussed.The effects of lorentz force are found to be composed of two parts,one is its direct action on the cylinder(the wall lorentz force)and the other is applied to the fluid(called the field lorentz force)near the cylinder surface.Our results show that the wall lorentz force can generate thrust and reduce the drag;the field lorentz force increases the drag.However,the cylinder drag is dominated by the wall lorentz force.In addition,the field lorentz force above the upper surface decreases the lift,while the upper wall lorentz force increases it.The total lift is dominated by the upper wall lorentz force.

关键词： surface force lorentz

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Differential programming enabled functional imaging with lorentz transmission electron microscopy

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npj Computational Materials 2021年第1期7卷 1268-1275页

作者： Tao Zhou Mathew Cherukara Charudatta Phatak Center for Nanoscale Materials Argonne National LaboratoryLemontILUSA Advanced Photon Source Argonne National LaboratoryLemontILUSA Materials Science Division Argonne National LaboratoryLemontILUSA

lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials.Information such as magnetization and electric potentials is carried by the phase of the electron wave,and is lost during image acquisition.Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images,most of which work only in the small defocus limit.Imaging at strong defoci not only carries more quantitative phase information,but is essential to the study of weak magnetic and electrostatic fields at the nanoscale.In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval.We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope.More importantly,our proposed method can go beyond recovering just the phase information.We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.

关键词： materials programming lorentz

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The effect of lorentz-like force on collective flows of K+in Au+Au collisions at 1.5 Ge V/nucleon

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Science China(Physics,Mechanics & Astronomy) 2018年第6期61卷 24-29页

作者： YuShan Du YongJia Wang QingFeng Li Ling Liu School of Science Huzhou University School of Physics science and Technology Shenyang Normal University Institute of Modern Physics Chinese Academy of Sciences

Producing kaon mesons in heavy-ion collisions at beam energies below their threshold energy is an important way to investigate the properties of dense nuclear matter. In this study, based on the newly updated version of the ultrarelativistic quantum molecular dynamics model, we introduce the kaon-nucleon(KN) potential, including both the scalar and vector(also dubbed lorentz-like)aspects. We revisit the influence of the KN potential on the collective flow of K+mesons produced in Au+Au collisions at Elab= 1.5 Ge V/nucleon and find that the contribution of the newly included lorentz-like force is very important, particulary for describing the directed flow of K+. Finally, the corresponding Kao S data of both directed and elliptic flows can be simultaneously reproduced well.

关键词： lorentz 流动能碰撞集体动力学模型介子重离子椭圆形

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Preliminary experimental study on applicability of lorentz force velocimetry in an external magnetic field

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Nuclear Science and Techniques 2018年第6期29卷 28-35页

作者： Yan-Qing Tan Run-Cong Liu Shang-Jun Dai Xiao-Dong Wang Ming-Jiu Ni Juan-Cheng Yang Nataliia Dubovikova Yurii Kolesnikov Christian Karcher College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Sciences The Fifth Electronics Research Institute Ministry of Industry and Information Technology School of Engineering Science University of Chinese Academy of Sciences Institute of Thermodynamics and Fluid Mechanics Ilmenau University of Technology

lorentz force velocimetry(LFV) is a noncontact technique for measuring electrically conducting fluids based on the principle of electromagnetic induction. This work aims to answer the open and essential question of whether LFV can work properly under a surrounding external magnetic field(ExMF). Two types of Ex MFs with different magnetic intensities were examined: a magnetic field with a typical order of 0.4 T generated by a permanent magnet(PM) and another generated by an electromagnet(EM) on the order of 2 T. Two forces, including the magnetostatic force between the Ex MF and PM in the LFV, and the lorentz force generated by the PM in LFV were measured and analyzed in the experiment. In addition,Ex MFs of varying strengths were added to the LFV, and the location of the LFV device in the iron cores of the EM was considered. The experimental outcomes demonstrate that it is possible for a LFV device to operate normally under a moderate Ex MF. However, the magnetostatic force will account for a high proportion of the measured force,thus inhibiting the normal LFV operation, if the Ex MF is too high.

关键词： lorentz 外部磁场试验性适用性学习设备操作永久磁铁测量基

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Krein space representation and lorentz groups of analytic Hilbert modules

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Science China Mathematics 2018年第4期61卷 745-768页

作者： Yue Wu Michio Seto Rongwei Yang School of Insurance Central University of Finance and EconomicsBeijing 100081China National Defense Academy Yokosuka 239-8686Japan Department of Mathematics State University of New York at AlbanyAlbanyNY 12222USA

This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the lorentz group is a complete invariant for congruence relation. Furthermore, the lorentz group contains an interesting abelian subgroup(called little lorentz group) which turns out to be a finer invariant for M.

关键词： lorentz Hilbert 空间模块度量标准操作员不可分多信息

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Effects of lorentz Breaking on the Accretion onto a Schwarzschild-like Black Hole

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Communications in Theoretical Physics 2019年第5期71卷 568-572页

作者：杨荣佳高贺郑瑶光吴琴 College of Physical Science and Technology Hebei University Hebei Key Lab of Optic-Electronic Information and Materials Hebei University National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices Hebei University School of Information Engineering Guangdong Medical University

We formulate and solve the problem of spherically symmetric, steady state, adiabatic accretion onto a Schwarzschild-like black hole obtained recently. We derive the general analytic expressions for the critical points, the critical velocity, the critical speed of sound, and subsequently the mass accretion rate. The case for polytropic gas is discussed in detail. We find the parameter characterizing the breaking of lorentz symmetry will slow down the mass accretion rate, while has no effect on the gas compression and the temperature profile below the critical radius and at the event horizon.

关键词： accretion mass accretion rate lorentz breaking Schwarzschild-like black hole

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Bidirectional and Unidirectional Negative Differential Thermal Resistance Effect in a Modified lorentz Gas Model

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Chinese Physics Letters 2021年第1期38卷 58-62页

作者：杨宇李秀玲张力发 NNU-SULI Thermal Energy Research Center(NSTER)and Center for Quantum Transport and Thermal Energy Science(CQTES) School of Physics and TechnologyNanjing Normal UniversityNanjing 210023China

Recently,the negative differential thermal resistance effect was discovered in a homojunction made of a negative thermal expansion material,which is very promising for realizing macroscopic thermal transistors.Similar to the Monte Carlo phonon simulation to deal with grain boundaries,we introduce positive temperature-dependent interface thermal resistance in the modified lorentz gas model and find negative differential thermal resistance effect.In the homojunction,we reproduce a pair of equivalent negative differential thermal resistance effects in different temperature gradient directions.In the heterojunction,we realize the unidirectional negative differential thermal resistance effect,and it is accompanied by the super thermal rectification effect.Using this new way to achieve high-performance thermal devices is a new direction,and will provide extensive reference and guidance for designing thermal devices.

关键词： resistance thermal lorentz

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