1,774 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
Fluctuation-driven insulator-to-metal transition in an external magnetic field
We consider a model for a metal-insulator transition of correlated electrons
in an external magnetic field. We find a broad region in interaction and
magnetic field where metallic and insulating (fully magnetized) solutions
coexist and the system undergoes a first-order metal-insulator transition. A
global instability of the magnetically saturated solution precedes the local
ones and is caused by collective fluctuations due to poles in electron-hole
vertex functions.Comment: REVTeX 4 pages, 3 PS figure
Effects of in-chain and off-chain substitutions on spin fluctuations in the spin-Peierls compound CuGeO_3
The effect of in-chain and off-chain substitutions on 1D spin fluctuations in
the spin-Peierls compound CuGeO_3 has been studied using Raman scattering in
order to understand the interplay between defect induced states, enhanced
spin-spin correlations and the ground state of low dimensional systems.
In-chain and off-chain substitutions quench the spin-Peierls state and induce
3D antiferromagnetic order at T\leq 5 K. Consequently a suppression of a 1D
gap-induced mode as well as a constant intensity of a spinon continuum are
observed at low temperatures. A 3D two-magnon density of states now gradually
extends to higher temperatures T\leq 60K compared with pure CuGeO_3. This
effect is more pronounced in the case of off-chain substitutions (Si) for which
a N\'eel state occurs over a larger substitution range, starting at very low
concentrations. Besides, additional low energy excitations are induced. These
effects, i.e. the shift of a dimensional crossover to higher temperatures are
due to an enhancement of the spin-spin correlations induced by a small amount
of substitutions. The results are compared with recent Monte Carlo studies on
substituted spin ladders, pointing to a similar instability of coupled,
dimerized spin chains and spin ladders upon substitution.Comment: 14 pages, 6 eps figures, to be published in PR
Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation
We study the dynamic scaling properties of an aggregation model in which
particles obey both diffusive and driven ballistic dynamics. The diffusion
constant and the velocity of a cluster of size follow
and , respectively. We determine the dynamic exponent and
the phase diagram for the asymptotic aggregation behavior in one dimension in
the presence of mixed dynamics. The asymptotic dynamics is dominated by the
process that has the largest dynamic exponent with a crossover that is located
at . The cluster size distributions scale similarly in all
cases but the scaling function depends continuously on and .
For the purely diffusive case the scaling function has a transition from
exponential to algebraic behavior at small argument values as changes
sign whereas in the drift dominated case the scaling function decays always
exponentially.Comment: 6 pages, 6 figures, RevTeX, submitted to Phys. Rev.
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