To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
Three(2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by different transformation of variables respectively. Since the single sol...Three(2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the Kd V equation have been known already, substituting the solutions of the Kd V equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three(2+1)-dimensional equations can be obtained successfully.展开更多
This article presents further experimental results of the Magnetization-LAST mode in magnetically assisted gas-fluidized tapered beds, including external transverse magnetic field control of solid phase movement, cent...This article presents further experimental results of the Magnetization-LAST mode in magnetically assisted gas-fluidized tapered beds, including external transverse magnetic field control of solid phase movement, central channel formation, spout depth and the pressure drop across the bed. Phase diagrams similar to those recently reported for the Magnetization-FIRST mode were also developed. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number pertinent to particle aggregate formation was applied to develop the scaling relationships.展开更多
The article presents an effort to create dimensionless scaling correlations of the overall bed porosity in the case of magnetically assisted fluidization in a tapered vessel with external transverse magnetic field. Th...The article presents an effort to create dimensionless scaling correlations of the overall bed porosity in the case of magnetically assisted fluidization in a tapered vessel with external transverse magnetic field. This is a stand of portion of new branch in the magnetically assisted fluidization recently created concerning employment of tapered vessels. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number has been applied to develop scaling relationships of dimensionless groups representing ratios of pressures created by the fluid flow, gravity and the magnetic field over an elementary volume of the fluidized bed. Special attention has been paid on the existing data correlations developed for non-magnetic beds and the links to the new ones especially developed for tapered magnetic counterparts. A special dimensionless variable Xp = （Ar△Dbt）1/3√RgMQ combining Archimedes and Rosensweig numbers has been conceived for porosity correlation. Data correlations have been performed by power-law, exponential decay and asymptotic functions with analysis of their adequacies and accuracies of approximation.展开更多
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金Supported by the National Natural Science Foundation of China under Grant No.11301153the Doctoral Foundation of Henan University of Science and Technology under Grant No.09001562the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No.2015XPT001
文摘Three(2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the Kd V equation have been known already, substituting the solutions of the Kd V equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three(2+1)-dimensional equations can be obtained successfully.
文摘This article presents further experimental results of the Magnetization-LAST mode in magnetically assisted gas-fluidized tapered beds, including external transverse magnetic field control of solid phase movement, central channel formation, spout depth and the pressure drop across the bed. Phase diagrams similar to those recently reported for the Magnetization-FIRST mode were also developed. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number pertinent to particle aggregate formation was applied to develop the scaling relationships.
文摘The article presents an effort to create dimensionless scaling correlations of the overall bed porosity in the case of magnetically assisted fluidization in a tapered vessel with external transverse magnetic field. This is a stand of portion of new branch in the magnetically assisted fluidization recently created concerning employment of tapered vessels. Dimensional analysis based on ＂pressure transform＂ of the initial set of variables and involving the magnetic granular Bond number has been applied to develop scaling relationships of dimensionless groups representing ratios of pressures created by the fluid flow, gravity and the magnetic field over an elementary volume of the fluidized bed. Special attention has been paid on the existing data correlations developed for non-magnetic beds and the links to the new ones especially developed for tapered magnetic counterparts. A special dimensionless variable Xp = （Ar△Dbt）1/3√RgMQ combining Archimedes and Rosensweig numbers has been conceived for porosity correlation. Data correlations have been performed by power-law, exponential decay and asymptotic functions with analysis of their adequacies and accuracies of approximation.
