Numerical simulation of the trapping reaction with mobile and reacting traps.

We study a variation of the trapping reaction, A+B→A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A→0 or A. This two-species reaction-diffusion system is known to exhibit a nontrivial decay exponent for the B particles, and recently renormalization group methods have predicted an anomalous dimension in the BB correlation function. To test these predictions, we develop a computer simulation method, motivated by the technique of Mehra and Grassberger [Phys. Rev. E 65, 050101(R) (2002)1063-651X10.1103/PhysRevE.65.050101], that determines the complete probability distribution of the B particles for a given realization of the A-particle dynamics, thus providing a significant increase in the quality of statistics. Our numerical results indeed reveal the anomalous dimension predicted by the renormalization group, and compare well quantitatively to precisely known values in cases where the problem can be related to a four-walker problem.

On Ramanujan's definition of mock theta function.

In his famous "deathbed" letter, Ramanujan "defined" the notion of a mock theta function and offered some examples of functions he believed satisfied his definition. Very recently, Griffin et al. established for the first time that Ramanujan's mock theta functions actually satisfy his own definition. On the other hand, Zwegers' 2002 doctoral thesis [Zwegers S (2002) Mock theta functions. PhD thesis (Univ Utrecht, Utrecht, The Netherlands)] showed that all of Ramanujan's examples are holomorphic parts of harmonic Maass forms. This has led to an alternate definition of a mock theta function. This paper shows that Ramanujan's definition of mock theta function is not equivalent to the modern definition.