Centrifuge impact cratering experiments: Scaling laws for non-porous targets

This research is a continuation of an ongoing program whose objective is to perform experiments and to develop scaling relationships for large body impacts onto planetary surfaces. The development of the centrifuge technique has been pioneered by the present investigator and is used to provide experimental data for actual target materials of interest. With both powder and gas guns mounted on a rotor arm, it is possible to match various dimensionless similarity parameters, which have been shown to govern the behavior of large scale impacts. Current work is directed toward the determination of scaling estimates for nonporous targets. The results are presented in summary form

Laboratory simulation of cratering on small bodies

A new technique using external pressure was developed to simulate the lithostatic pressure due to self-gravity of small bodies. A 13-in. diameter cylindrical test chamber with L/D of 1 was fabricated to accommodate firing explosive charges with gas overpressures of up to 6000 psi. The chamber was hydrotested to 9000 psi. The method allows much larger scale factors that can be obtained with existing centrifuges and has the correct spherical geometry of self gravity. A simulant for jointed rock to be used in this fixture was developed using weakly cemented basalt. Various strength/pressure scaling theories can now be examined and tested

Centrifuge impact cratering experiments: Scaling laws for non-porous targets

A geotechnical centrifuge was used to investigate large body impacts onto planetary surfaces. At elevated gravity, it is possible to match various dimensionless similarity parameters which were shown to govern large scale impacts. Observations of crater growth and target flow fields have provided detailed and critical tests of a complete and unified scaling theory for impact cratering. Scaling estimates were determined for nonporous targets. Scaling estimates for large scale cratering in rock proposed previously by others have assumed that the crater radius is proportional to powers of the impactor energy and gravity, with no additional dependence on impact velocity. The size scaling laws determined from ongoing centrifuge experiments differ from earlier ones in three respects. First, a distinct dependence of impact velocity is recognized, even for constant impactor energy. Second, the present energy exponent for low porosity targets, like competent rock, is lower than earlier estimates. Third, the gravity exponent is recognized here as being related to both the energy and the velocity exponents

Crater size estimates for large-body terrestrial impact

Calculating the effects of impacts leading to global catastrophes requires knowledge of the impact process at very large size scales. This information cannot be obtained directly but must be inferred from subscale physical simulations, numerical simulations, and scaling laws. Schmidt and Holsapple presented scaling laws based upon laboratory-scale impact experiments performed on a centrifuge (Schmidt, 1980 and Schmidt and Holsapple, 1980). These experiments were used to develop scaling laws which were among the first to include gravity dependence associated with increasing event size. At that time using the results of experiments in dry sand and in water to provide bounds on crater size, they recognized that more precise bounds on large-body impact crater formation could be obtained with additional centrifuge experiments conducted in other geological media. In that previous work, simple power-law formulae were developed to relate final crater diameter to impactor size and velocity. In addition, Schmidt (1980) and Holsapple and Schmidt (1982) recognized that the energy scaling exponent is not a universal constant but depends upon the target media. Recently, Holsapple and Schmidt (1987) includes results for non-porous materials and provides a basis for estimating crater formation kinematics and final crater size. A revised set of scaling relationships for all crater parameters of interest are presented. These include results for various target media and include the kinematics of formation. Particular attention is given to possible limits brought about by very large impactors

Resource Allocation Contests: Experimental Evidence

Across many forms of rent seeking contests, the impact of risk aversion on equilibrium play is indeterminate. We design an experiment to compare individuals’ decisions across three contests which are isomorphic under risk-neutrality, but are typically not isomorphic under other risk preferences. The pattern of individual play across our contests is not consistent with a Bayes-Nash equilibrium for any distribution of risk preferences. We show that replacing the Bayes-Nash equilibrium concept with the quantal response equilibrium, along with heterogeneous risk preferences can produce equilibrium patterns of play that are very similar to the patterns we observe.rent seeking, experiments, risk aversion, game theory

History and Logic Model NASA Goddard Space Flight Center Instrument Project Division (IPD) Schedule and Cost Study

No abstract availabl

A model for orientation effects in electron‐transfer reactions

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells

Modeling Institutional Production of Higher Education

This study examines the input-output relationship for private undergraduate education. The objective s to identify the relative contributions of human and physical resources in the production of quality undergraduate education. The research methods are noteworthy in three general respects. First, the theoretical orientation emphasized interdependence among inputs and outputs in higher education. The significance of simultaneity is demonstrated in an empirical model estimated via a three-stage least-squares technique. Second, the study introduces an original and promising data set for research in higher educational production. Of special note is an index of output reflecting the quantity and quality of institutional production. Finally, the exclusive emphasis on private undergraduate institutions offers a well focused perspective for policy decisions in higher education. The report is organized as follows. Section 1 discusses the focus and contribution of this research in relation to the economics literature. Section 2 specifies a simultaneous model of educational production. Section 3 describes the data, variables, and estimation procedures. Empirical results appear in Section 4. Section 5 presents concluding remarks and suggestions for future research

Assessing the Impact of Expenditure on Achievement in Virginia Public Education

The strength of the relationship between student achievement and school resources has important implications for public policy in general, and for the appropriate role of state funding in local education in particular. It is well known that, to the extent that higher expenditures render improved educational performance, vexing issues of legal and economic equity arise. Of course, it is also well known that the findings of extensive empirical analysis suggest that the expenditure-achievement nexus is, at best, of secondary importance among the factors affecting education. This paper examines the relationship between achievement and expenditure in Virginia public schools. Our focus falls in the category of education production studies which have taken an essentially macro orientation. These studies use cross-sectional and/or longitudinal observations aggregated at a school or school district level. This method thus relates average achievement by district to the level of physical and financial resources (class-size, library volumes, instructional expenditure, etc.). While the policy inferences which can flow from this approach are straightforward, there is concern whether more highly aggregated data are able to capture important details of the educational process. This is the most common explanation offered for the failure of the more highly aggregated studies in demonstrating a significant link between school resources and achievement

Modeling Institutional Production of Higher Education

This paper follows an earlier article in which we examined the production process of higher education. Two aspects of the original study serve as the basis for this paper and thus warrant brief review. First, we have argued that educational production does not lend it self to analysis as a production function in the classic sense. A simple production rendering ignores the fact that two of the more important factors, students and faculty, enter the process upon considerable self-selection, especially among the more highly qualified of these inputs. This reasoning led us to model educational production as a three-equation simultaneous system in which the quality of students , faculty, and college output were treated endogenously. The results of that research confirmed the strength of interdependencies existing among the endogenous variables, thus recommending simultaneous estimation as the appropriate methodology for evaluating factors in educational production