Nature of segregation of reactants in diffusion controlled A+B reactions: Role of mobility in forming compact clusters

We investigate the A+B=0 bimolecular chemical reaction taking place in low-dimensional spaces when the mobilities of the two reacting species are not equal. While the case of different reactant mobilities has been previously reported as not affecting the scaling of the reactant densities with time, but only the pre-exponential factor, the mechanism for this had not been explained before. By using Monte-Carlo simulations we show that the nature of segregation is very different when compared to the normal case of equal reactant mobilities. The clusters of the mobile species are statistically homogeneous and randomly distributed in space, but the clusters of the less mobile species are much more compact and restricted in space. Due to the asymmetric mobilities, the initial symmetric random density fluctuations in time turn into asymmetric density fluctuations. We explain this trend by calculating the correlation functions for the positions of particles for the several different cases

Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.Comment: 19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-0

Vibrational excitons, resonant energy transfer, and local structure in liquid benzene

The presence of vibrational excitons in liquid benzene has been tested by the method of isotopic dilution. A C6H6/C6D6 concentration study on the infrared and Raman fundamental modes reveals that the umbrella (A2u) vibrational exciton in solid benzene retains its characteristics upon melting and at room temperature. The total liquid exciton bandwidth is about 40 cm−1, practically the same as in the solid. This indicates an instantaneous local liquid structure similar to that of the solid (the Ci crystal site symmetry is also nearly preserved), in general agreement with indications from other methods. The fastest nearest neighbor vibrational resonant transfer takes about 1 psec. The residual linewidth at isotopic dilution is 3–4 cm−1, which is due to inhomogeneous and/or homogeneous broadening. The respective overall reorientational and/or translational relaxation takes about 2 psec or longer. The exciton linewidth is proportional to the square root of the isotopic concentration except for a sudden break at some critical concentration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70052/2/JCPSA6-66-11-5035-1.pd

Front localization in a ballistic annihilation model

We study the possibility of localization of the front present in a one-dimensional ballistically-controlled annihilation model in which the two annihilating species are initially spatially separated. We construct two different classes of initial conditions, for which the front remains localized.Comment: Using elsart (Elsevier Latex macro) and epsf. 12 Pages, 2 epsf figures. Submitted to Physica

Quasiresonant excitation transfer in molecular aggregates@fa@f)

Excitation transfer in finite molecular aggregates is analyzed in the context of the Haken–Strobl model. Explicit solutions are presented for a trimer and a rectangular tetramer. Special emphasis is placed upon population transfer among subunits (monomers, dimers) and its relationship to energy transfer, and upon the problems associated with coherence of this transfer process. These aggregates serve as models for the problem of excitation transfer in disordered media, where partial coherence resulting from short‐range interactions has been largely ignored. Our most intriguing result is the greatly diminished effectiveness of the longer‐ranged transfer in the presence of short‐range clusters. Under some conditions the ensuing energetic mismatches may well dominate the overall energy transport and render invalid the usual description in terms of hopping among individual sites. An application to triplet energy transport in isotopic mixed naphthalene crystals is given; it is seen that the reduced efficiency of non‐nearest‐neighbor transfer processes reinforces the two‐dimensional characteristics of the energy transport.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70614/2/JCPSA6-79-3-1444-1.pd

Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension

We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact solution of the same process with infinite reaction rate. The approximation becomes exact in the very early time regime (or the reaction-controlled limit) and in the long time (diffusion-controlled) asymptotic limit. For the intermediate time regime, we obtain a simple interpolative behavior between these two limits. We also study the coalescence process (with finite reaction rates) with the back reaction $A\to A+A$, and in the presence of particle input. In each of these cases the system reaches a non-trivial steady state with a finite concentration of particles. Theoretical predictions for the concentration time dependence and for the IPDF are compared to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j 05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0

Small Solutions for Big Problems: The Application of Nanoparticles to Brain Tumor Diagnosis and Therapy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109842/1/cptclpt2008296.pd

Exciton transport in disordered crystals: velocity correlation functions

The two-particle coherent-potential approximation is used to calculate Frenkel-exciton group-velocity correlation functions for substitutionally disordered crystals. Most of the results can be described by a relaxation-time approximation, provided that k-dependent and complex relaxation times are allowed; however, some evidence for long-time tails, associated with the finite frequency range of the scattering potentials, is found. The probable accuracy of the approximation and its relationships with localization and kinetic theory are discussed, as is its relevance to experimental systems (triplet excitons in isotopic mixed naphthalene and anthracene crystals).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24699/1/0000118.pd