Gradient Transformation of Momentum and Single-Valued Vector Potential in Nonrelativistic Dynamics

A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.

A THEORY OF DETERMINING MASS TRANSFERPARAMETERS FOR WOOD PARTICLE MATERIALS

The transient mass transter processes in the natural drying of wood particle materials were experimental;y studied A new theory tio determme the mass transfer parameters in the Materials was developed in terms of gradient transformation method(GTM).By making use of GTM.Thewater vapour diffusion coefficient and the surtaee emission coefficent of wood chip were expermentally determined both in air phase and in solid phase.It Was found that the internal resistance to water vapour diffusion in the air phase of wood partiele aggregates is around ten to the third power as large as that in common air The drag coefficient was given to quantify the effect The phenomenon of undersurface diffusion in wood partiele bed was quantitatively modelled.The dimensionless Fourier snumber and the Biot's number for mass transfer were theoretically derived.The study showed that Biot's number for the problem investigated was the ratio of the characteristie length of wood partiele bed to the penetrating depth of the undersurface.An analytical solution of the nonlinear goveming equation for water transport process in the aggregates of wood chip was obtained by introducing the variable coefficients measured in the study into the governing equation.The comparison between the analytical solution and the observed moisture content of wood chip showed that the deviation was less than ±7%.The thermophysieal properties of wood particle materials are little known at present.The knowledge provided in the paper will be and in the handling.researeh or engineering application of wood chip.wood shavingsete.

An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media

Boundary integral equations provide a powerful tool for the solution of scattering problems.However,often a singular kernel arises,in which case the standard quadratures will give rise to unavoidable deteriorations in numerical precision,thus special treatment is needed to handle the singular behavior.Especially,for inhomogeneous media,it is difficult if not impossible to find out an analytical expression for Green’s function.In this paper,an efficient fourth-order accurate Cartesian grid-based method is proposed for the two-dimensional Helmholtz scattering and transmission problems with inhomogeneous media.This method provides an alternative approach to indirect integral evaluation by solving equivalent interface problems on Cartesian grid with a modified fourth-order accurate compact finite difference scheme and a fast Fourier transform preconditioned conjugate gradient(FFT-PCG)solver.A remarkable point of this method is that there is no need to know analytical expressions for Green’s function.Numerical experiments are provided to demonstrate the advantage of the current approach,including its simplicity in implementation,its high accuracy and efficiency.