Geophysical Research

Contains reports on two research projects.National Aeronautics and Space Administration (Grant NGR-22-009-131)National Aeronautics and Space Administration (Grant NGR-22-009-114)National Aeronautics and Space Administration (Contract NAS 12-436

Reciprocal and multiplicative relational reasoning with rational numbers

Abstract Developmental research has focused on the challenges that fractions pose to students in comparison to whole numbers. Usually the issues are blamed on children's failure to properly understand the magnitude of the fractional number because of its bipartite notation. However, recent research has shown that college-educated adults can capitalize on the structure of the fraction notation, performing more successfully with fractions than decimals in relational tasks, notably analogical reasoning. The present study examined whether this fraction advantage also holds in a more standard mathematical task, judging the veracity of multiplication problems. College students were asked to judge whether or not a multiplication problem involving either a fraction or decimal was correct. Some problems served as reciprocal primes for the problem that immediately followed it. Participants solved the fraction problems with higher accuracy than the decimals problems, and also showed significant relational priming with fractions. These findings indicate that adults can more easily identify relations between factors when rational numbers are expressed as fractions rather than decimals

Erraticity of Rapidity Gaps

The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may occur very rarely. Two moments of the gap distrubiton are suggested for characterizing an event. The fluctuations of those moments from event to event are then quantified by an entropy-like measure, which serves to describe erraticity. We use ECOMB to simulate the exclusive rapidity distribution of each event, from which the erraticity measures are calculated. The dependences of those measures on the order of $q$ of the moments provide single-parameter characterizations of erraticity.Comment: 10 pages LaTeX + 5 figures p

Critical Behavior of Hadronic Fluctuations and the Effect of Final-State Randomization

The critical behaviors of quark-hadron phase transition are explored by use of the Ising model adapted for hadron production. Various measures involving the fluctuations of the produced hadrons in bins of various sizes are examined with the aim of quantifying the clustering properties that are universal features of all critical phenomena. Some of the measures involve wavelet analysis. Two of the measures are found to exhibit the canonical power-law behavior near the critical temperature. The effect of final-state randomization is studied by requiring the produced particles to take random walks in the transverse plane. It is demonstrated that for the measures considered the dependence on the randomization process is weak. Since temperature is not a directly measurable variable, the average hadronic density of a portion of each event is used as the control variable that is measurable. The event-to-event fluctuations are taken into account in the study of the dependence of the chosen measures on that control variable. Phenomenologically verifiable critical behaviors are found and are proposed for use as a signature of quark-hadron phase transition in relativistic heavy-ion collisions.Comment: 17 pages (Latex) + 24 figures (ps file), submitted to Phys. Rev.

Congenital tumors and nonimmune hydrops fetalis

Peer Reviewe