This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued potential function...This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued potential function. Gradient fields are irrotational, as in the curl in all conservative vector fields is zero, by Clairaut’s Theorem. Additionally, line integrals in conservative vector fields are path-independent, and line integrals over closed paths are always equal to zero, properties proved by the Gradient Theorem of multivariable calculus. Gradient fields represent conservative forces, and the associated potential function is analogous to potential energy associated with said conservative forces. The Intersect Rule provides a new, unique shortcut for determining if a vector field is conservative and deriving potential functions, by treating the indefinite integral as a set of infinitely many functions which satisfy the integral.展开更多
[Objective] The aim was to study the rainstorm process in a single station on July 19, 2010. [Method] Based on MICAPS conventional data and Doppler radar data, the rainstorm process in Dagang station in Tianjin on Jul...[Objective] The aim was to study the rainstorm process in a single station on July 19, 2010. [Method] Based on MICAPS conventional data and Doppler radar data, the rainstorm process in Dagang station in Tianjin on July 19, 2010 was analyzed systematically by means of weather dynamic diagnosis analysis. [Result] From physical vector diagnostic analysis, the dynamic effect provided by southwest vortex and warm shear line, water vapor transported by warm and wet flow at the edge of subtropical high and upper and lower jet and unstable convection of atmospheric stratification were the main causes of rainstorm formation on July 19, 2010. In addition, rainfall area was located in the big convergence area of vapor flux, and there was a negative center of vapor flux divergence before rainfall, with obvious accumulation of water vapor, which provided better water vapor condition for this rainstorm. [Conclusion] The study could provide theoretical foundation for the forecast of rainstorm in Tianjin.展开更多
文摘This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued potential function. Gradient fields are irrotational, as in the curl in all conservative vector fields is zero, by Clairaut’s Theorem. Additionally, line integrals in conservative vector fields are path-independent, and line integrals over closed paths are always equal to zero, properties proved by the Gradient Theorem of multivariable calculus. Gradient fields represent conservative forces, and the associated potential function is analogous to potential energy associated with said conservative forces. The Intersect Rule provides a new, unique shortcut for determining if a vector field is conservative and deriving potential functions, by treating the indefinite integral as a set of infinitely many functions which satisfy the integral.
文摘[Objective] The aim was to study the rainstorm process in a single station on July 19, 2010. [Method] Based on MICAPS conventional data and Doppler radar data, the rainstorm process in Dagang station in Tianjin on July 19, 2010 was analyzed systematically by means of weather dynamic diagnosis analysis. [Result] From physical vector diagnostic analysis, the dynamic effect provided by southwest vortex and warm shear line, water vapor transported by warm and wet flow at the edge of subtropical high and upper and lower jet and unstable convection of atmospheric stratification were the main causes of rainstorm formation on July 19, 2010. In addition, rainfall area was located in the big convergence area of vapor flux, and there was a negative center of vapor flux divergence before rainfall, with obvious accumulation of water vapor, which provided better water vapor condition for this rainstorm. [Conclusion] The study could provide theoretical foundation for the forecast of rainstorm in Tianjin.
