577 research outputs found
Cluster approximation solution of a two species annihilation model
A two species reaction-diffusion model, in which particles diffuse on a
one-dimensional lattice and annihilate when meeting each other, has been
investigated. Mean field equations for general choice of reaction rates have
been solved exactly. Cluster mean field approximation of the model is also
studied. It is shown that, the general form of large time behavior of one- and
two-point functions of the number operators, are determined by the diffusion
rates of the two type of species, and is independent of annihilation rates.Comment: 9 pages, 7 figure
Exponents appearing in heterogeneous reaction-diffusion models in one dimension
We study the following 1D two-species reaction diffusion model : there is a
small concentration of B-particles with diffusion constant in an
homogenous background of W-particles with diffusion constant ; two
W-particles of the majority species either coagulate ()
or annihilate () with the respective
probabilities and ; a B-particle and a
W-particle annihilate () with probability 1. The
exponent describing the asymptotic time decay of
the minority B-species concentration can be viewed as a generalization of the
exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D
-state Potts model starting from a random initial condition : the
W-particles represent domain walls, and the exponent
characterizes the time decay of the probability that a diffusive "spectator"
does not meet a domain wall up to time . We extend the methods introduced by
Derrida, Hakim and Pasquier ({\em Phys. Rev. Lett.} {\bf 75} 751 (1995); Saclay
preprint T96/013, to appear in {\em J. Stat. Phys.} (1996)) for the problem of
persistent spins, to compute the exponent in perturbation
at first order in for arbitrary and at first order in
for arbitrary .Comment: 29 pages. The three figures are not included, but are available upon
reques
Autonomous models solvable through the full interval method
The most general exclusion single species one dimensional reaction-diffusion
models with nearest-neighbor interactions which are both autonomous and can be
solved exactly through full interval method are introduced. Using a generating
function method, the general solution for, , the probability that
consecutive sites be full, is obtained. Some other correlation functions of
number operators at nonadjacent sites are also explicitly obtained. It is shown
that for a special choice of initial conditions some correlation functions of
number operators called full intervals remain uncorrelated
Reaction Kinetics of Clustered Impurities
We study the density of clustered immobile reactants in the
diffusion-controlled single species annihilation. An initial state in which
these impurities occupy a subspace of codimension d' leads to a substantial
enhancement of their survival probability. The Smoluchowski rate theory
suggests that the codimensionality plays a crucial role in determining the long
time behavior. The system undergoes a transition at d'=2. For d'<2, a finite
fraction of the impurities survive: ni(t) ~ ni(infinity)+const x log(t)/t^{1/2}
for d=2 and ni(t) ~ ni(infinity)+const/t^{1/2} for d>2. Above this critical
codimension, d'>=2, the subspace decays indefinitely. At the critical
codimension, inverse logarithmic decay occurs, ni(t) ~ log(t)^{-a(d,d')}. Above
the critical codimension, the decay is algebraic ni(t) ~ t^{-a(d,d')}. In
general, the exponents governing the long time behavior depend on the dimension
as well as the codimension.Comment: 10 pages, late
Coherent State path-integral simulation of many particle systems
The coherent state path integral formulation of certain many particle systems
allows for their non perturbative study by the techniques of lattice field
theory. In this paper we exploit this strategy by simulating the explicit
example of the diffusion controlled reaction . Our results are
consistent with some renormalization group-based predictions thus clarifying
the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference
correcte
Exactly solvable models through the empty interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions, which is exactly-solvable through the empty
interval method, has been introduced. Assuming translationally-invariant
initial conditions, the probability that consecutive sites are empty
(), has been exactly obtained. In the thermodynamic limit, the large-time
behavior of the system has also been investigated. Releasing the translational
invariance of the initial conditions, the evolution equation for the
probability that consecutive sites, starting from the site , are empty
() is obtained. In the thermodynamic limit, the large time behavior of
the system is also considered. Finally, the continuum limit of the model is
considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
The Swift Surge of Perovskite Photovoltaics
The breakthrough early 1990s dye sensitization of mesoscopic TiO2 films along with a regenerative iodide redox couple led to the explosive growth of dye-sensitized solar cell (DSC) research. The pioneering work of Grätzel and colleagues also made it possible to develop a solid-state DSSC with spiro-oMETAD as the hole conductor and thus replace the liquid electrolyte in the cell. Research efforts of Konenkamp and others further initiated the search for the “extremely thin absorber” (ETA) nanostructured solar cell, using TiO2 as the electron conductor, an inorganic absorber, and a hole conductor. Another major research thrust was by Weller, Kamat, Zaban, Nozik, Hodes, and others, who employed inorganic quantum dots (e.g., CdS and CdSe) as sensitizers. While discussing developments in sensitized solar cells, it is important to note the contributions of early visionaries like Gerischer, Sutin, and Bard, who were first to establish the concepts of sensitization using dye molecules and semiconductor nanostructures
Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and A+A A and the
annihilation dynamics A+A -> 0 for particles moving subdiffusively in one
dimension. This scenario combines the "anomalous kinetics" and "anomalous
diffusion" problems, each of which leads to interesting dynamics separately and
to even more interesting dynamics in combination. Our analysis is based on the
fractional diffusion equation
Solution of a one-dimensional stochastic model with branching and coagulation reactions
We solve an one-dimensional stochastic model of interacting particles on a
chain. Particles can have branching and coagulation reactions, they can also
appear on an empty site and disappear spontaneously.
This model which can be viewed as an epidemic model and/or as a
generalization of the {\it voter} model, is treated analytically beyond the
{\it conventional} solvable situations. With help of a suitably chosen {\it
string function}, which is simply related to the density and the
non-instantaneous two-point correlation functions of the particles, exact
expressions of the density and of the non-instantaneous two-point correlation
functions, as well as the relaxation spectrum are obtained on a finite and
periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical
Review E (September 2001
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