George Bulman

Stability of an elastic rod buckling into a soft wall

The conjugate point theory of the calculus of variations is extended to apply to the buckling of an elastic rod in an external field. We show that the operator approach presented by Manning (Manning et al. 1998 Proc. R. Soc. A 454, 3047–3074) can be used when the second-variation operator is an integrodifferential operator, rather than a differential operator as in the classical case. The external field is chosen to model two parallel ‘soft’ walls. We consider the examples of two-dimensional buckling under both pinned–pinned and clamped–clamped boundary conditions, as well as the three-dimensional clamped–clamped problem, where we consider the importance of the rod cross-section shape as it ranges from circular to extreme elliptical. For each of these problems, we find that in the appropriate limit, the soft-wall solutions approach a ‘hard-wall’ limit, and thus we make conjectures about these hard-wall contact equilibria and their stability. In the two-dimensional pinned–pinned case, this allows us to assign stability to the configurations reported by Holmes (Holmes et al. 1999 Comput. Methods Appl. Mech. Eng. 170, 175–207) and reconsider the experimental results discussed therein.

The Returns to the Federal Tax Credits for Higher Education

Three tax credits benefit households who pay tuition and fees for higher education. The credits have been justified as an investment by generating more educated people and thus more earnings and externalities associated with education. The credits have also been justified purely as tax cuts to benefit the middle class. In 2009, the generosity of and eligibility for the tax credits expanded enormously so that their 2011 cost was

Technology and Education: Computers, Software, and the Internet

25 billion. Using selected, de-identified data from the population of potential filers, we show how the credits are distributed across households with different incomes. We estimate the causal effects of the federal tax credits using two empirical strategies (regression kink and simulated instruments), which we show to be strong and very credibly valid for this application. The latter strategy exploits the massive expansion of the credits in 2009. We present causal estimates of the credits’ effects on postsecondary attendance, the type of college attended, the resources experienced in college, tuition paid, and financial aid received. We discuss the implications of our findings for society’s return on investment and for the tax credits’ budget neutrality over the long term (whether higher lifetime earnings generate sufficient taxes to recoup the tax expenditures). We assess several explanations as to why the credits appear to have negligible causal effects.

The Effect of Access to College Assessments on Enrollment and Attainment

A substantial amount of money is spent on technology by schools, families and policymakers with the hope of improving educational outcomes. This chapter explores the theoretical and empirical literature on the impacts of technology on educational outcomes. The literature focuses on two primary contexts in which technology may be used for educational purposes: i) classroom use in schools, and ii) home use by students. Theoretically, ICT investment and CAI use by schools and the use of computers at home have ambiguous implications for educational achievement: expenditures devoted to technology necessarily offset inputs that may be more or less efficient, and time allocated to using technology may displace traditional classroom instruction and educational activities at home. However, much of the evidence in the schooling literature is based on interventions that provide supplemental funding for technology or additional class time, and thus favor finding positive effects. Nonetheless, studies of ICT and CAI in schools produce mixed evidence with a pattern of null results. Notable exceptions to this pattern occur in studies of developing countries and CAI interventions that target math rather than language. In the context of home use, early studies based on multivariate and instrumental variables approaches tend to find large positive (and in a few cases negative) effects while recent studies based on randomized control experiments tend to find small or null effects. Early research focused on developed countries while more recently several experiments have been conducted in developing countries.