Generation-channel interference of high-order harmonics of an anharmonic oscillator driven by bi-chrime laser fields and its mechanism

A method to describe the generation channels of high-order harmonics is proposed. According to this method, the mechanism of generation-channel interference of high-order harmonics is revealed clearly. We take the anharmonic oscillator driven by bi-chrome fields as an example to illustrate that this method can be used to understand the effect of generation-channel interference.

A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization

Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.

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.

Surface second harmonic generation of chiral molecules using three-coupled-oscillator model

Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized secondharmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.

A SINGLE-CAVITY MULTIPLE-DEVICE HARMONIC OSCILLATOR AT W-BAND

The equivalent circuit of single-cavity multiple-device fundamentaloscillator(SCMDFO)and that of single-device harmonic oscillator(SDHO)proposed byK.Kurokawa and K.Solbach,respectively,are extended and applied to a single-cavitymultiple-device harmonic oscillator(SCMDHO).By means of describing the functions ofnonlinearity of Gunn diodes,the performances of the SCMDHO are analyzed.It is foundthat the voltage amplitudes are similar to those of SDHO,and the ratio of maximum pow-er of harmonic to that of fundamental is identical to that in SDHO when the devices havesame parameters.The harmonic injection locking behavior is also investigated.The injec-tion locking range is greater than that of SDHO if locking gain remains constant.A2-Gunn diode harmonic oscillator was designed.It delivers 30mW output power at103GHz.The mechanical tuning range is 4.15GHz when the output power remains morethan 10mW.The desired operation mode is stable.

THE LARGE-SIGNAL DESIGN FOR FET FUNDAMENTAL AND HARMONIC OSCILLATORS

A Large-signal model for GaAs FET is derived based on its small-signal S parame-ters and DC characteristics. The harmonic balance algorithm is applied to analyze and optimizethe FET fundamental and harmonic oscillators, and the values of steady current are obtained.In the solving process, a simplified CAD approach is used to obtain the parameters of matchingnetwork when the output power is maximum. Finally, a fundamental oscillator and a harmonicoscillator of Q-band are fabricated. The measurements show that the theoretical analysis andexperimental results are in good agreement.

Possible Modular Structure of Matter Based on the “YY Model” Approach —An Overview of the Construction Rules for Quarks and Atomic Nuclei with Configurative Examples for Neutron, Proton, Deuteron and Dineutron

The newly developed YY model contains a set of constitutive rules to describe the structures of atomic nuclei and subatomic particles, by using two elementary sub-quark particles, the Yin and Yang fermions of charge 1/3 forming all the particles of the Standard Model. This model suggests a modular structure of the universe, in which two elementary constituents recursively form all the matter. The advantage of this hypothesis is that it provides a total symmetry and a noticeably clear conceptual understanding. Moreover, it justifies the cosmological formation of a limited number of atoms, e.g., H and Li with their isotopes, considering that matter can be produced as a free agglomerate of semi-stable neutrons, which would lead to the feeding of baryonic matter in the universe. In this current article, some further theoretical aspects are proposed as an evolution of the YY model. They cover correlation paths between interacting quarks, the considerations of color forces between yin-yang elementary elements. Moreover, an agreement of the YY model with the Teplov approach based on harmonic quarks and oscillators is established, and the mass of Yin and Yang is considered. Two example nuclei are used for the analysis: a radioactively stable deuteron (containing a neutron and a proton) and a possible semi-stable dineutron (roughly “consisting of two neutrons”), which is purely theoretical, represent a very natural and legal nuclear state within YY model. Based on the results obtained here, some indications are given for a possible simple experimental verification providing proof for the stability or instability of the dineutron.

Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.

The Association of the Neutron, and the Quantum Properties of Hydrogen, with the Prime Numbers 2, 3, 5, 7, 11

The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants are associated with quantum integers, n, within a classic integer and partial harmonic fraction system, and follow a known two-dimensional, 2D, power law geometry. These are exponents of a fundamental frequency, vF, the basis of which is the annhilation frequency of the neutron, vn0. Our goal to a first approximation is to derive the frequency equivalents of the Rydberg constant, vR, the Bohr radius, va0, the electron, ve-, and the reciprocal fine structure constant, 1/α all from vn0, π, and a small set of prime integers only. The primes used in the derivations are respectively 2, 3, 5, 7, and 11. This is possible since it is known that the number 3 is associated with R, 5 with a0, 7 with e-, and 11 with 1/α. In addition, the interrelationships of the frequency ratio equivalents of these natural units with 2 and π are known, thus allowing for the derivation of any one from the others. Also the integer and partial fractions of a0, e-, and n0 define Planck time squared, tP2. An accurate estimate of tP2 from vF alone is also related to the integer 2 since gravity is a kinetic force. Planck time squared, tP2 scales the Y-axis, and vF scales the X-axis. In conclusion the quantum properties of hydrogen are derived from only the natural unit physical data of the neutron, to a relative precision ranging from 2.6 × 10-3 to 6.7 × 10-4. This supports the hypothesis that many of the fundamental constants are related to vn0.

CAD OF MILLIMETER WAVE OSCILLATORS WITH THE FDHB TECHNIQUE

In this paper the modelling, analysis and optimization of millimeter wave oscillatorsare investigated by using the a frequency-domain harmonic balance technique (FDHB), where theexternal-circuit impedances looking outside from the active device are calculated with a combinedtechnique of modes expansion, Galerkin, and collocation methods. The optimization results arein agreement with the experimental ones, which show the reliability of the presented model andoptimization.

The Fundamental Relationship between Harmonic Quark Masses and Reduced Max Planck Constant

O. A. Teplov developed an approach to describe the meson quark model by establishing a mathematical quark series (harmonic quark series). With respect to the physical mesons, he made some basic hypotheses of his own and used the well-known theory of harmonic oscillation to construct a numerical mass series that obeys a rigid multiplicative pattern and allows the physical meson masses to be calculated accurately. We have found that his numerical quark series, i.e., their masses, has a fundamental relation to the reduced Max Planck constant ħand report on it in the present paper. This discovery is obviously a theoretical contribution to the correctness of Teplov’s harmonic quark model approach and at the same time a confirmation of the importance of this simple and powerful research work.

Mathematical Modeling of Peat Self-ignition at Ambient Temperature Oscillations

In the classical formulation, the problem of thermal explosion in a finite volume of the reacting material in the presence of harmonic oscillations of the ambient temperature has been solved. It is shown that in the oscillation periods, commensurate with the adiabatic induction period of thermal explosion, implement a kind of resonance which corresponding with average ambient temperature. At both high and very low frequencies oscillations at ambient temperature, their influence on the critical condition and on the induction period of thermal explosion is negligible. However, at low-frequencies influence of ambient temperature oscillations, even a relatively low amplitude, on critical condition and especially on induction period of thermal explosion, can be very strong.

Harmonic Oscillations in a Grid-connected PV Generation Farm Caused by an Increased Number of Parallel-connected PV Generating Units and Damping Controllers

This paper examines the harmonic oscillations in a grid-connected PV generation farm(PVGF)caused by the parallel connection of an increased number of PV generation units(PVGUs).An equivalent model of the grid-connected PVGF is derived,which clearly explains why there are internal and external oscillation modes in the grid-connected PVGF.An indicator of impedance multiplication(IIM)is proposed to quantitatively estimate the impact of the increased number of PVGUs in parallel connection.The analysis in this paper reveals the mechanism about why the damping of external oscillation modes may decrease when more PVGUs are in parallel connection under the condition that the IIM is positive.An example grid-connected PVGF is presented in this paper to demonstrate and evaluate the derived analysis and conclusions.A method for designing the damping controllers to ensure a negative IIM is proposed.With the damping controllers being installed,the risk of growing harmonic oscillations caused by the increased number of the PVGUs in parallel connection can be effectively eliminated.

Anharmonic oscillator model of overtone spectra for D_(3h) symmetry molecules

The bond stretching vibrations of XF_5 molecules with D_(3h)symmetry are treated computa- tionally on the Morse oscillator model in which the bond oscillators are coupled harmonically.Each calculation involves four parameters for two types of Morse potential and three parameters for the kinetic-energy,potontial coupling terms.The eigenvalue formula for overtone and combination states up to three are presented and can be used to predict all the vibrational energylevels from local mode molecules through normal mode molecules.For PF_5,AsF_5 and VF_5,the coupled Morse oscillator model gives a prediction in good agreement with the experimental data.

Structure of Halo Nuclei

A self-similar-structure shell modct （SSM） is proposed to extend the conven-tional shell model （SM） calculation to study halo nuclei.The exotic structures of 11Liand 6He nuclei are reproduced by means of SSM.The neutron halo of 11Li comes fromthe spin-orbit term and the thick neutron skin of 6He arises from the different quantumnumbers Nn and Np（N=2n+1） in SSM.

Computer Simulation Study of Thermal Conduction in 1D Chains of Anharmonic Oscillators

In this work thermal conduction in one-dimensional （1D） chains of anharmonic oscillators are studied using computer simulation. The temperature profile, heat flux and thermal conductivity are investigated for chain length N = 100, 200, 400, 800 and 1600. In the computer simulation anharmonicity is introduced due to Fermi-Pasta- U1am-β （FPU-β） model For substrate interaction, an onsite potential due to Frenkel-Kontorova （FK） model has been used. Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N. For the thermal conductivity K, KN to N obey the linear relation of the type KN = 0.8805N. It is shown that thermal transport is dependent on phonon-phonon interaction as web as phonon-lattice interaction. The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ =0.133 ＋ 0.804β. It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.

The Harmonic Approximation in Heavy-Ion Reaction Study

The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.

Lifetime of Doubly Charmed Baryons

In this work, we evaluate the lifetimes of the doubly charmed baryons Ξcc^＋ ,Ξcc^＋＋, and Ωcc^＋. We carefully calculate the non-spectator contributions at the quark level, where the Cabibbo-suppressed diagrams are also included. The hadronic matrix elements are evaluated in the simple non-relativistic harmonic oscillator model. Our numerical results are generally consistent with that obtained by other authors who used the diquark model. However, all the theoretical predictions on the lifetimes are one order larger than the upper limit set by the recent SELEX measurement. This discrepancy would be clarified by the future experiment. If more accurate experiment still confirms the value of the SELEX collaboration, there must be some unknown mechanism to be explored.

Decay Rate of Energy Eigenfunctions in Classically Energetically Inaccessible Regions in more than One-Dimensional Configuration Spaces

An approximate formula is proposed for the decay rate of energy eigenfunctions in classically energetically inaccessible regions in more than one-dimensional configuration spaces. This is achieved by generalizing an approach proposed recently for energy eigenfunctions in the one-dimensional configuration space. The formula is tested numerically in the Pullen-Edmonds model.

Option Pricing beyond Black-Scholes Model:Quantum Mechanics Approach

Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.