In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate ...In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.展开更多
This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state repre...This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.展开更多
By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energ...The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters （amplitude and pitch） of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.展开更多
A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal （NLC） cell manufactured with t...A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal （NLC） cell manufactured with two pre-treated grating surface substrates may realize the vertical display, parallel display and twist display. In this paper, the threshold property of this NLC cell is investigated systematically. With the Frank elastic theory and the equivalent anchoring energy formula of grating surface substrate, the analytic expressions of the threshold voltage related to three displays are obtained, which are dependent on their geometrical parameters such as amplitude ~ and pitch A of the grating surface substrate. For a certain anchoring strength, the threshold voltage increases or decreases with the increase of the value δ/λ of the different displays.展开更多
文摘In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Natural Science Foundation of Liaocheng University (Grant No. X071049)
文摘This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.
基金supported by the Special Funds of the National Natural Science Foundation of China (Grant No.10947017/A05)
文摘By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
文摘The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters （amplitude and pitch） of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.
基金Project supported by the Key Subject Construction Project of Hebei Province University of Chinathe National Natural Science Foundation of China (Grant Nos 10704022 and 60736042)
文摘A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal （NLC） cell manufactured with two pre-treated grating surface substrates may realize the vertical display, parallel display and twist display. In this paper, the threshold property of this NLC cell is investigated systematically. With the Frank elastic theory and the equivalent anchoring energy formula of grating surface substrate, the analytic expressions of the threshold voltage related to three displays are obtained, which are dependent on their geometrical parameters such as amplitude ~ and pitch A of the grating surface substrate. For a certain anchoring strength, the threshold voltage increases or decreases with the increase of the value δ/λ of the different displays.
