4 research outputs found
Nontrivial Polydispersity Exponents in Aggregation Models
We consider the scaling solutions of Smoluchowski's equation of irreversible
aggregation, for a non gelling collision kernel. The scaling mass distribution
f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now,
only be computed by numerical simulations. We develop here new general methods
to obtain exact bounds and good approximations of . For the specific
kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles
moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R
is the particle radius), perturbative and nonperturbative expansions are
derived.
For a general kernel, we find exact inequalities for tau and develop a
variational approximation which is used to carry out the first systematic study
of tau(d,D) for KdD. The agreement is excellent both with the expansions we
derived and with existing numerical values. Finally, we discuss a possible
application to 2d decaying turbulence.Comment: 16 pages (multicol.sty), 6 eps figures (uses epsfig), Minor
corrections. Notations improved, as published in Phys. Rev. E 55, 546