<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used togeth...<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.</span>展开更多
Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop q...Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.展开更多
It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This ...It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This is so because any macroscopic body—lo-cated in a high-energy quantum state—is in practice forced to change this state to a state having a lower energy. The rate of the energy decrease is usually extremely small which makes its effect uneasy to detect in course of the observations, or experiments. The energy of the harmonic oscillator is thoroughly examined as an example. Here our point is that not only the energy, but also the oscillator amplitude which depends on energy, are changing with time. In result, no constant positions of the turning points of the oscillator can be specified;consequently the well-known variational procedure concerning the calculation of the action function and its properties cannot be applied.展开更多
Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up t...Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.展开更多
The effects of isotope substitution on stereodynamic properties for the reactions C^+ + H_2/HD/HT →CH^+ + H/D/T have been studied applying a quasi classical trajectory method occurring on the new ground state CH_2^+ ...The effects of isotope substitution on stereodynamic properties for the reactions C^+ + H_2/HD/HT →CH^+ + H/D/T have been studied applying a quasi classical trajectory method occurring on the new ground state CH_2^+ potential energy surface [J. Chem. Phys. 142(2015) 124302]. In the center of mass coordinates applying the quasi classical trajectory method to investigate the orientation and the alignment of the product molecule. Differential cross section and three angle distribution functions P(θ_r), P(ф_r), P(θ_r, ф_r) on the potential energy surface that fixed the collision energy with a value is 40 kcal/mol have been studied. The isotope effect becomes more and more important with the reagent molecules H_2 changing into HD and HT. P(θ_r, ф_r) as the joint probability density function of both polar angles θ_r and ф_r, which can illustrate more detailed dynamics information. The isotope effect is obvious influence on the properties of stereodynamics in the reactions of C^+ + H_2/HD/HT → CH^+ + H/D/T.展开更多
文摘<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.</span>
基金Supported by the Algerian Ministry of Education and ResearchDGRSDT
文摘Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.
文摘It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This is so because any macroscopic body—lo-cated in a high-energy quantum state—is in practice forced to change this state to a state having a lower energy. The rate of the energy decrease is usually extremely small which makes its effect uneasy to detect in course of the observations, or experiments. The energy of the harmonic oscillator is thoroughly examined as an example. Here our point is that not only the energy, but also the oscillator amplitude which depends on energy, are changing with time. In result, no constant positions of the turning points of the oscillator can be specified;consequently the well-known variational procedure concerning the calculation of the action function and its properties cannot be applied.
基金Supported by the Natural Science Foundation of Henan Province(092300410150)the Key Youth Teacher Foundation of Department Education of Henan Province(2011GGJS-210)the Key Youth Teacher Foundation of Huanghuai University
文摘Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11474141,11274149,11544015the Program for Liaoning Excellent Talents in University under Grant No.LJQ2015040the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry(2014-1685)
文摘The effects of isotope substitution on stereodynamic properties for the reactions C^+ + H_2/HD/HT →CH^+ + H/D/T have been studied applying a quasi classical trajectory method occurring on the new ground state CH_2^+ potential energy surface [J. Chem. Phys. 142(2015) 124302]. In the center of mass coordinates applying the quasi classical trajectory method to investigate the orientation and the alignment of the product molecule. Differential cross section and three angle distribution functions P(θ_r), P(ф_r), P(θ_r, ф_r) on the potential energy surface that fixed the collision energy with a value is 40 kcal/mol have been studied. The isotope effect becomes more and more important with the reagent molecules H_2 changing into HD and HT. P(θ_r, ф_r) as the joint probability density function of both polar angles θ_r and ф_r, which can illustrate more detailed dynamics information. The isotope effect is obvious influence on the properties of stereodynamics in the reactions of C^+ + H_2/HD/HT → CH^+ + H/D/T.
