Optimal Explicit Strong Stability Preserving Runge--Kutta Methods with High Linear Order and optimal Nonlinear Order

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge--Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge--Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge--Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may be still be worthwhile to use methods with higher nonlinear order

Labor Market Competition among Youths, White Women, and Others

We estimate substitution possibilities among a set of age-race-sex groups in the labor force. The estimates are based on cross-section data from SMSAs in 1969,and they allow us to consider how substitutable adult women are for young women or young men. The estimates are used, along with assumptions about the extent of wage rigidity and elasticities of labor supply, to simulate the direct and indirect effects of the growth of the female labor force on job opportunities for youth, assuming rigid wages for young workers, and on the wage rates of adult males, assuming these wages are flexible.

Diablo Canyon power plant site ecological study Annual Report July 1, 1976 - June 30, 1977 and Quarterly Report no. 16 April 1, 1977 - June 30, 1977

More stations were surveyed during this report period than during any previous period. A total of 818 mandays was spent surveying 18 permanent and 67 random subtidal stations, 19 permanent and 50 random intertidal stations, and 64 sportfish catch-per-unit-of-effort stations, as well as conducting corollary laboratory work. In the subtidal areas, Laminaria dentigera and Pterygophora californica, both important subsurface kelp species, increased in their combined total numbers from the 1976 survey. However, Nereocystis luetkeana, the bull kelp, declined substantially in all study areas. Population trends of many of the dominant subtidal macro-invertebrates have varied depending on the species and on the type of method utilized. Regression analyses have been performed on selected species for numbers versus depth. Red algal abundance and diversity appear to have increased in both subtidal study areas. Of the three observation areas, sea otters were observed least frequently in Diablo Cove. However, there continues to be fresh evidence of otter foraging within Diablo Cove. Several seasons' data for intertidal algae and invertebrates have been summarized for one study area. While the algae biomass shows a fairly clear seasonality of abundance, the trends in numbers of the six invertebrate species considered are not as well defined. Because of high variability in the data, the sportfish catch-per-unit-of-effort and hook-and-line study was cancelled in December. Populations of intertidal red and black abalones, Haliotis rufescens and H. cracherodii, respectively, appear to have remained fairly stable during the 1976-77 period. Two other ancillary studies were also terminated during this period: interviews of commercial abalone and urchin fishermen, and observations of foam in Diablo Cove. (107pp.

Diablo Canyon power plant site ecological study Quarterly Report no. 22: October 1 - December 31, 1978

Field work for this quarter consisted of completion of random 1/4-m2 subtidal stations from the summer sampling season. In addition, one permanent subtidal station was surveyed. No intertidal stations were surveyed. Sea otters, Enhydra lutris, remained scarce in the vicinity of the power plant. Lab work was comprised of processing subtidal algae samples and sorting and identifying invertebrates from intertidal samples. Analysis of preoperational data for final report proceeded apace. (7pp.

Diablo Canyon power plant site ecological study Quarterly Report no. 19: January 1 - March 31, 1978

Field work was limited to monitoring permanent intertidal and subtidal stations. Only a few stations were surveyed due to a long series of winter storms which produced large seas. Office and laboratory work was devoted to completing computer data sheets for keypunching, completing the 1976/77 annual report and several quarterly reports, and processing the remaining algae samples collected at subtidal and intertidal stations in 1977. Sea otter activity increased in South Cove and Diablo Cove where sea otters were observed on five out of 20 observation days. (11pp.

Diablo Canyon power plant site ecological study Quarterly Report no. 18; October 1 - December 31, 1977

Large storm-generated swells prevented us from completing the random stations in the North Control. The project has shifted to a low level of field work to allow for analysis of all data and preparation of the final report. Field work during the next year will be confined to monitoring permanent stations. Four permanent subtidal stations were surveyed during the quarter, including a new station located at the entrance of Diablo Cove. Nine random 30m2 stations and 32 - 1/4m2 quadrats were also completed. It appears, from this year's subtidal studies, that there has been a decline in the abundance of lingcod, Ophiodon elongatus, and kelp greenling, Hexagrammos decagrammus, in the Diablo Canyon area since our studies began in 1974. A few sea otters continue to raft and forage in Lion Rock Cove. (12pp.

Diablo Canyon power plant site ecological study Quarterly Report No. 21: July 1 - September 30, 1978

Rough seas and the hiring freeze further delayed completion of our field and laboratory work. All random 1/4-m2 stations were completed in Diablo Cove but ten stations remain in the North Control. Nine random fish species counts were conducted in Diablo Cove. Very few sea otters, Enhydra lutris, were observed during this quarter, none in Diablo Cove. (10pp.

Diablo Canyon power plant site ecological study Quarterly Report no. 20: April 1 - June 30, 1978

Although we continue to monitor permanent stations on a regular basis, we have suspended our 30-m2 random subtidal and 1/4-m2 random intertidal studies during this interim year. The 1/4-m2 random subtidal study is being continued and we have added a new subtidal method of determining fish abundance. Giant red sea urchin, Strongylocentrotus franciscanus, numbers continue to decline at their last "stronghold" in our subtidal study area, permanent station 15. The recruitment of juvenile blue rockfish, Sebastes mystinus, appears to be either late or low this year in our study areas. The most abundant fish, so far, from the new method of assessment, are adult blue rockfish, kelp greenling, Hexagrammos decagrammus, and gopher rockfish, Sebastes carnatus. Various trends of abalone abundance at the permanent intertidal stations, increasing at some, decreasing at others, were observed during this quarter. Sea otters, Enhydra lutris, seem to have reached their annual springtime peak in abundance during April and May. Several otters were seen rafting and foraging around and near the intake cove breakwaters, apparently becoming emboldened to human presence. (18pp.