Prof John Cardy FRS

Abstract:

The A+B→{circled division slash} diffusion-limited reaction, with equal initial densities a(0)=b(0)=n0, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension d>2 an effective theory is derived, from which the density and correlation functions call be calculated. We find the density decays in time as {Mathematical expression} for d<4, with Δ=n0-C′n0^d/2+..., where C is a universal constant and C′ is nonuniversal. The calculation is extended to the case of unequal diffusion constants DA≠DB, resulting in a new amplitude but the same exponent. For d≤2 a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an ε=2-d expansion. Finally, we address reaction zones formed in the steady state by opposing currents of A and B particles, and derive scaling properties. © 1995 Plenum Publishing Corporation.

Abstract:

The mean area of two-dimensional unpressurized vesicles, or self-avoiding loops of fixed length N, behaves for large N as A0N3/2, while their mean square radius of gyration behaves as R02N3/2. The amplitude ratio A0/R02 is computed exactly and found to equal 4π/5. The physics of the pressurized case, in both the inflated and collapsed phases, may be usefully related to that of a complex O(n) field theory coupled to a U(1) gauge field, in the limit n→0. © 1994 The American Physical Society.