Plane strain problem of growing crack for a perfectly plastic solid

In this paper, fundamental equations of the plane strain problem based on the 3-dimensional plastic flow theory are presented for a perfectly-plastic solid The complete governing equations for the growing crack problem are developed. The formulae for determining the velocity field are derived.The asymptotic equation consists of the premise equation and the zero-order governing equation. It is proved that the Prandtl centered-fan sector satisfies asymptotic equation but does not meet the needs of hlgher-order governing equations.

Second-best tax policy in a growing economy with externalities

This paper investigates the exploitation of environmental resources in a growing economy within a second-best scal policy framework. Agents derive utility from two types of consumption goods one which relies on an environmental input and one which does not as well as from leisure and from environmental amenity values. Property rights for the environmental resource are potentially incomplete. We connect second best policy to essential components of utility by considering the elasticity of substitution among each of the four utility arguments. The results illustrate potentially important relationships between environmental amentity values and leisure. When amenity values are complementary with leisure, for instance when environmental amenities are used for recreation, taxes on extractive goods generally increase over time. On the other hand, optimal taxes on extractive goods generally decrease over time when leisure and environmental amenity values are substitutes. Unders some parameterizations, complex dynamics leading to nonmonotonic time paths for the state variables can emerge.

Fast growing mode of stimulated Raman scattering in a pure three-wave process

Stimulated Raman scattering (SRS) of a relativistic laser in plasmas is studied in the framework of the standard equation set of a three-wave process. As far as every wave involved in the process is concerned, its evolution has two aspects: time-dependent amplitude and time-dependent frequency. These two aspects affect each other. Strict analysis and numerical experiment on the full three-wave equation set reveal that a fast growing mode of the instability, which could reach a balance or saturation point during a period far shorter than an estimation based on conventional analysis, could take place in a standard three-wave process without coupling with a fourth wave. This fast growing mode is found to stem from the constraint set by the background density on the amplitude of the driven Langmuir wave. The effect of various parameters on the development of the SRS instability is studied by numerical calculation of the history of the instability in different cases. (c) 2007 American Institute of Physics.

The production of algae growing on gravel in a chalk-stream

Epilithic algae, ie that growing on the surface of stones, was studied as part of the work on the energy flow of the chalk-stream ecosystem, by the River Laboratory. The study area was on Bere Stream and 2 neighbouring streams. The algal biomass was estimated from analysis of chlorophyll a. In Bere Stream the peak chlorophyll a cover occurred in April, while in the neighbouring streams, which have considerably lower nutrient levels, there was on peak. Assuming that 2% of a diatoms dry wt is chlorophyll a, then even in mid-April the biomass of epilithic algae amounted to no more than 15 g dry wt m Super(-2) of exposed gravel. Annual production was calculated to be > 15 times greater than biomass. The estimation of net primary production is always difficult for benthic floras and comparisons are especially difficult when different methods are used. But these figures contrast sharply with those for Ranunculus (water crowfoot) which has a ratio of annual production to maximal seasonal biomass of 1:16. The accumulation of algal biomass is apparently being prevented. Some organic matter may be excreted; some algae will be washed off the bed of the stream by current and grazing by herbivorous invertebrates will also tend to prevent algal accumulation.