Lucky numbers: Choice strategies in the Pennsylvania Daily Number game

Examined the amount of money bet during a week of Pennsylvania's Daily Number game. In this game, players receive a predetermined payoff for picking the 3-digit number (000 to 999) drawn on that day. The betting distribution was distinctly nonuniform. Several betting patterns were identified, such as picking triples and avoiding double 9s. In addition, 121 adults and 215 students were asked to rate selected numbers for randomness, luckiness, and perceived history of winning; to categorize numbers; and to free associate to numbers. It is proposed that people seem to choose highly patterned, available, and/or "lucky" numbers. People apparently do not bet numbers that reflect the random process of the game (do not utilize a representativeness heuristic).

Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.