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

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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

fundamental motor skills,screen-time,and physical activity in preschoolers

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Journal of Sport and Health Science 2019年第2期8卷 114-121页

作者： E.Kipling Webster Corby K.Martin Amanda E.Staiano School ofKinesiology Louisiana State University Pennington Biomedical Research Center Louisiana State University

Purpose: To examine the associations among preschoolers fundamental motor skills, screen-time, physical activity(PA), and sedentary behavior(SB).Methods: Children ages 3à4 years were enrolled in a prospective observational trial of PA. Trained assessors conducted the Test of Gross Motor Development-3 rd edition(TGMD-3), and the Movement Assessment Battery for Children-2 nd edition, and parent-reported child screen-time and sociodemographic information. Children wore an accelerometer for 7 days to examine SB and total PA(TPA). TPA was further characterized as moderateto-vigorous PA(MVPA) or vigorous PA(VPA). Mixed linear models were calculated, controlling for age(for TGMD-3), sex, household income, and accelerometer wear time(for accelerometry models), with childcare center as a random effect. The primary analysis reported on the cross-sectional baseline data of 126 children with complete fundamental motor skill and screen-time data; a subanalysis included 88 children with complete accelerometry data.Results: Children were 3.4 § 0.5 years of age(54% girls; 46% white, 42% African American, 12% other). A total of 48% lived in households at or below the federal poverty level. Children engaged in 5.1 § 3.6 h/day of screen-time. Children's screen-time was inversely related to the Movement Assessment Battery for Children-2 nd edition, manual dexterity skills percentile(b(SE) = ?1.7(0.8), p = 0.049). In the accelerometry subsample,children engaged in 5.9 § 0.9 h/day of TPA of which 1.7 § 0.6 h/day was MVPA. Boys engaged in more MVPA and VPA and less SB compared with girls(all p < 0.05). A higher TGMD-3, total score(b(SE) = 0.4(0.2), p = 0.017) and locomotor score(b(SE) = 0.7(0.3), p = 0.018) were associated with more VPA but not with TPA or MVPA. Screen-time and television in the bedroom were not related to SB, TPA, MVPA, or VPA.Conclusion: Children's motor skills were positively related to VPA but inversely related to screen-time. Further inquiry into the implications of high exposure to screen-time in young children i

关键词： fundamental motor skills Physical activity Preschool Screen-time

Beyond fundamental resonance mode:high-order multi-band ALN PMUT for in vivo photoacoustic imaging

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Microsystems & Nanoengineering 2022年第6期8卷 205-216页

作者： Junxiang Cai Yiyun Wang Daohuai Jiang Songsong Zhang Yuandong Alex Gu Liang Lou Fei Gao Tao Wu School of Information Science and Technology ShanghaiTech UniversityShanghaiChina Shanghai Institute of Microsystem and Information Technology ShanghaiChina University of Chinese Academy of Sciences BeijingChina School of Microelectronics Shanghai UniversityShanghaiChina Shanghai IndustrialμTechnology Research Institute ShanghaiChina Shanghai Engineering Research Center of Energy Efficient and Custom AI IC ShanghaiChina

This paper reports on an aluminum nitride(AlN)piezoelectric micromachined ultrasound transducer(PMUT)array for photoacoustic(PA)imaging,where the high-order resonance modes of the PMUT are utilized to improve imaging resolution.A flexural vibration mode(FVM)PMUT is fabricated and applied in a photoacoustic imaging(PAI)system.Specifically,the microelectromechanical system(MEMS)-based PMUT is suitable for PA endoscopic imaging of blood vessels and bronchi due to its miniature size and high sensitivity.More importantly,AlN is a nontoxic material,which makes it harmless for biomedical applications.In the PAI system,the AlN PMUT array is used to detect PA signals,and the acousto–mechanical response is designed and optimized at the PMUT’s fundamental resonance.In this work,we focus on the high-order resonance performance of the PMUT PAI beyond the fundamental resonance.The acoustic and electrical responses of the PMUT’s high-order resonance modes are characterized and analyzed.The fundamental and three high-order resonance bandwidths are 2.2,8.8,18.5,and 48.2 kHz.Compared with the resolution at the fundamental resonance mode,the resolutions at third-and fourth-order resonance modes increase by 38.7%and 76.9%in a phantom experiment.The high-order resonance modes of the AlN PMUT sensor array provide higher central frequency and wider bandwidth for PA signal detection,which increase the resolution of PAI compared to the PMUT working at the fundamental resonance mode.

关键词： resonance fundamental photoacoustic

fundamental solutions for transversely isotropic magneto-electro-elastic media and boundary integral formulation

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Science China(Technological Sciences) 2003年第6期46卷 607-619页

作者：丁皓江江爱民 Department of Civil Engineering Zhejiang University Hangzhou 310027 China West Branch of Zhejiang University of Technology Quzhou 324006 China

To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are de-rived and expressed in five harmonic functions from the governing equations and the strict differ-ential operator theorem. On the basis of these general solutions, the fundamental solution of infi-nite magneto-electro-elastic solid are obtained with the method of trial-and-error. Finally, the boundary integral formulation is derived and the corresponding boundary element method program is implemented to perform two numerical calculations(a column under uni-axial tension, uniform electric displacement or uniform magnetic induction, an annular plate simply-supported on outer and inner surfaces under axial loads). The numerical results agree well with the analytical ones.

关键词： transversely isotropic magneto-electro-elastic media, fundamental solution, boundary integral formulation.

fundamental solutions for plane problem of piezoelectric materials

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Science China(Technological Sciences) 1997年第3期40卷 331-336页

作者：丁皓江王国庆陈伟球 Department of Civil Engineering Zhejiang University Hangzhou 310027 China

Based on the basic equations of two-dimensional, transversely isotropic, piezoelectric elasticity, a group of general solutions for body force problem is obtained. And by utilizing this group of general solutions and employing the body potential theory and the integral method, the closed-form solutions of displacements and electric potential for an infinite piezoelectric plane loaded by point forces and point charge are acquired. Therefore, the fundamental solutions, which are very important and useful in the boundary element method (BEM), are presented.

关键词： piezoelectric materials plane problem potential theory fundamental solution.

Social-ecological correlates of fundamental movement skills in young children

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Journal of Sport and Health Science 2019年第2期8卷 122-129页

作者： Nan Zeng Susan L.Johnson Richard E.Boles Laura L.Bellows Department of Food Science and Human Nutrition Colorado State University Department of Pediatrics University of Colorado Anschutz Medical Campus

Purpose: To identify the social-ecological correlates associated with fundamental movement skills at the child, family, and environment levels in young children.Methods: Preschool children from 4 Colorado Head Start/preschool centers were recruited from 2010 to 2012. Two hundred twenty-eight children(128 girls; age = 56.08 § 4.09 months; body mass index(BMI) z-score = 0.53 § 1.12(mean § SD); 42.1% Hispanic/Latino) and 159 families were included in the final analysis. Children's perceived competence and fundamental movement skills were assessed via the Pictorial Scale of Perceived Competence and Social Acceptance and the Bruininks-Oseretsky Test of Motor Proficiency, 2 nd edition. Data on the number of children in the family, parent age, BMI, education, employment status, family income, perception of child coordination, and home physical activity environment were collected via a questionnaire. Linear regressions adjusted for child BMI, age, sex, and school site were performed at each level.Results: Child perceived cognitive competence was positively associated with locomotor skills(p = 0.04; adjusted R2= 0.035) and object-control skills(p = 0.003; adjusted R2= 0.083) at the child level. Parent education, BMI, and perception of child coordination were positively associated with locomotor skills and explained 8.8% of variance, but only parent education was significant(p = 0.04) at the family level. In addition, physical environment was positively associated with locomotor skills(p = 0.02) and explained 5.5% of variance at the environment level.Conclusion: Social-ecological correlates associated with young children's fundamental movement skills are multidimensional and differ according to skill category at the child, family, and environment levels.

关键词： Activity environment fundamental movement skills Parent education Perceived cognitive competence Preschool children

fundamental SOLUTION OF BI-MATERIAL ELASTIC SPACE

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Science China Mathematics 1991年第3期34卷 309-315页

作者：黄克服王敏中 Department of Mechanics Peking University Beijing 100871 PRC

In this paper, the fundamental solution of the bi-material elastic space is studied. Usingthe Papkovich-Neuber solution and the Kelvin state of the 3-dimensional elasticity, thedisplacement field of the bi-material elastic space where a concentrated body force is appliedin the interior, is obtained. As several special cases, the solutions of the Lorentz problemand Mindlin problem in the elastic half space, and the solution of the analogue problem inthe Stokes flow can all be deduced from our results.

关键词： fundamental solution harmonic function composite material linear elasticity.

fundamental cycles and graph embeddings

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Science China Mathematics 2009年第9期52卷 1920-1926页

作者： REN Han ZHAO HongTao LI HaoLing Department of Mathematics East China Normal UniversityShanghai 200062China

In this paper, we investigate fundamental cycles in a graph G and their relations with graph embeddings. We show that a graph G may be embedded in an orientable surface with genus at least g if and only if for any spanning tree T , there exists a sequence of fundamental cycles C1, C2, . . . , C2g with C2i-1 ∩ C2i≠ф for 1≤ i ≤g. In particular, among β(G) fundamental cycles of any spanning tree T of a graph G, there are exactly 2γM (G) cycles C1, C2, . . . , C2γM (G) such that C2i-1 ∩ C2i≠ф for 1 ≤i≤γM (G), where β(G) and γM (G) are the Betti number and the maximum genus of G, respectively. This implies that it is possible to construct an orientable embedding with large genus of a graph G from an arbitrary spanning tree T (which may have very large number of odd components in G\E(T )). This is different from the earlier work of Xuong and Liu, where spanning trees with small odd components are needed. In fact, this makes a common generalization of Xuong, Liu and Fu et al. Furthermore, we show that (1) this result is useful for locating the maximum genus of a graph having a specific edge-cut. Some known results for embedded graphs are also concluded; (2) the maximum genus problem may be reduced to the maximum matching problem. Based on this result and the algorithm of Micali-Vazirani, we present a new efficient algorithm to determine the maximum genus of a graph in O((β(G)) 25 ) steps. Our method is straight and quite different from the algorithm of Furst, Gross and McGeoch which depends on a result of Giles where matroid parity method is needed.

关键词： fundamental cycle maximum genus upper-embedded

Complete Space-like λ-surfaces in the Minkowski Space R1^3 with the Second fundamental Form of Constant Length

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Acta Mathematica Sinica,English Series 2020年第5期36卷 559-577页

作者： Xing Xiao LI Yang Yang LIU Rui Na QIAO School of Mathematics and Information Sciences Henan Normal UniversityXinxiang 453007P.R.China

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R1^3.As the result,we obtain a complete classification theorem for all the complete space-like λ-surfaces x:M^2→R1^3 with the second fundamental form of constant length.This is a natural extension to the λ-surfaces in R1^3 of a recent interesting classification theorem by Cheng and Wei forλ-surfaces in the Euclidean space R^3.

关键词： Mean curvature second fundamental form space-likeλ-surfaces classification