We calculate the average speed of a projectile in the absence of air resistance, a quantity that is missing from the treatment of the problem in the literature. We then show that this quantity is equal to the time-ave...We calculate the average speed of a projectile in the absence of air resistance, a quantity that is missing from the treatment of the problem in the literature. We then show that this quantity is equal to the time-average instantaneous speed of the projectile, but different from its space-average instantaneous speed. It is then shown that this behavior is shared by general motion of all particles regardless of the dimensionality of motion and the nature of the forces involved. The equality of average speed and time-average instantaneous speed can be useful in situations where the calculation of one is more difficult than the other. Thus, making it more efficient to calculate one by calculating the other.展开更多
Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge fiel...Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.展开更多
文摘We calculate the average speed of a projectile in the absence of air resistance, a quantity that is missing from the treatment of the problem in the literature. We then show that this quantity is equal to the time-average instantaneous speed of the projectile, but different from its space-average instantaneous speed. It is then shown that this behavior is shared by general motion of all particles regardless of the dimensionality of motion and the nature of the forces involved. The equality of average speed and time-average instantaneous speed can be useful in situations where the calculation of one is more difficult than the other. Thus, making it more efficient to calculate one by calculating the other.
基金Supported by the National Natural Science Foundation of China(No.62175144,No.61773249)the Science and Technology on Near-Surface Detection Laboratory(No.TCGZ2020C003)Shanghai Science and Technology Innovation Action Plan(No.20142200100)。
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10773002,10875012,and 11175019supported by the Fundamental Research Funds for the Central Universities under Grant No. 105116
文摘Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.
