A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

A new type of boundary integral-equation for plane problems of elasticity including rotational forces

Based on the idea proposed by Hu [Scientia Sinica Series A XXX, 385-390 (1987)], a new type of boundary integral equation for plane problems of elasticity including rotational forces is derived and its boundary element formulation is presented. Numerical results for a rotating hollow disk are given to demonstrate the accuracy of the new type of boundary integral equation.

On dilatational plastic constitutive equation of ductile materials and plastic loading paths at bifurcation

The dilatational plastic constitutive equation presented in this paper is proved to be in a form of generality. Based on this equation, the constitutive behaviour of materials at the moment of bifurcation is demonstrated to follow a loading path with the response as "soft" as possible.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.

Measures of Plant Surface-areas for Eurasian Watermilfoil and Water Stargrass

Plant surface areas were measured from samples of two common submersed aquatics with widely diverging morphologies: Eurasian watermilfoil ( Myriophyllum spicatum L.) and water stargrass ( Heteranthera dubia (Jacq.) MacM.). Measures for the highly dissected leaves of Eurasian watermilfoil involved development of a regression equation relating leaf length to direct measures of a subsample of leaf parts. Measures for the simple leaves of the stargrass were sums of measured triangles. Stem surfaces for both species were calculated as measured cylinders. Though the means of the stem length and leaf length were larger for stargrass samples, their mean surface area was 95 cm 2 which was less than the 108 cm 2 recorded for Eurasian watermilfoil samples. Relating surface area to dry weight for the stargrass was straightforward, with 1 mg of dry weight yielding an average 0.678 cm 2 of surface area. Biomass measures for the water milfoil were confounded by the additional weight of epiphytic algae persisting on cleaned samples. The results suggest that a lesstime consuming method for surface area measures of plants with highly dissected leaves and a caveat for using biomass measures to estimate surface area in such plants.

Seasonal Biomass and Carbohydrate Allocation Patterns in Southern Minnesota Curlyleaf Pondweed Populations

Four southern Minnesota populations of curlyleaf pondweed ( Potamogeton crispus L.) were sampled monthly from January 2001 to November 2002 to determine seasonal phenological, biomass, and carbohydrate allocation patterns. Low periods of carbohydrate storage in the seasonal phenological cycle indicate potentially vulnerable periods in the plant’s life cycle and may be the ideal time to initiate management and control efforts.

Estimating above-ground biomass of Melaleuca quinquenervia in Florida, USA

One hundred and thirty-eight Melaleuca quinquenervia (Cav.) S. T. Blake (broad-leaved paperbark) trees were harvested from six sites in South Florida to formulate regression equations for estimating tree above-ground dry weight.