Some properties of the a+b → C reaction-diffusion system with initially separated components

We study some properties of the A+BC reaction-diffusion system with initially separated components, first analyzed by means of an asymptotic scaling argument by Gàlfi and Ràcz. We show that, in contrast to the asymptotic result that predicts that the rate of production of C goes liket ^–1, at early times it is shown to increase ast ^1/2. Deviations from this behavior appear at times inversely proportional to the reaction constant. Analogous crossover properties appear in the kinetic behavior of the reaction front. A second part of the study is concerned with the same chemical reaction on a fractal surface. When the substrate is a percolation cluster at criticality, both the maximum production rate and the width of the reaction zone differ considerably from those for the homogeneous space.     

The A+B→0 diffusion-limited reaction with correlated initial condition

We show some inaccuracies in recent arguments claiming that in the long-time limit the initially correlated A+B0 diffusion-limited reaction can be faster than the A+A0 one. With the errors corrected, these arguments seem to confirm the former theory of Toussant and Wilczek according to which the global rate of both reactions should ultimately be the same. This hypothesis is also supported by our numerical simulations of a two-dimensional lattice system.     

The diffusion-limited reaction A+B→0 on a fractal substrate

We show in this paper how the segregation of reactants in the diffusion-limited reaction A+B0 on a fractal substrate arises. For spectral dimensions d_s 2 we obtain segregation controlled by the source and/or the intrinsic lifetime of the particles.     

Large scale simulations of two-species annihilation,A+B→0, with drift

We present results of computer simulations of the diffusion-limited reaction process A+B→0, on the line, under extreme drift conditions, for lattices of up to 2²⁷ sites, and where the process proceeds to completion (no particles left). These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results allow us to resolve an existing controversy about the rate of growth of domain sizes, and about corrections to scaling of the concentration decay.     

A model of turbulent mixing in the A+B→0 reaction

The diffusion limited reaction A+B0 in sufficiently low dimensions results in macroscopically self-regregated systems with anomalous reaction rate laws. When the chemical mixture is embedded in a fluctuating velocity field having statistics mimicking turbulent diffusion the effects of spatial inhomogeneities are washed out and the classical global reaction rate laws in three dimensions result.     

Study ofA+A→0 with probability of reaction and diffusion in one dimension and in fractal substrata

We present Monte Carlo simulations of annihilation reactionA+A0 in one dimensional lattice and in three different fractal substrata. In the model, the particles diffuse independently and when two of them attempt to occupy the same substratum site, they react with a probabilityp. For different kinds of initial distributions and in the short an intermediate time regimes, the results for 0<p1 show that the density ofA particles approximately behaves as (t)=(t=0)f(t/t ₀), with the scaling functionf(x)1 forx1,f(x)x ^–y forx1. The crossover timet ₀, behaves ast _{0 0eff} ^–1y where theeffective initial density _0eff depends on (t=0) and on the kind of initial distribution. For a given substratum of spreading dimensiond _s, the exponenty(d _s/2<y<1) depends only onp and its value increases asp decreases (y1 whenp0). In the very long time regime it is expected thatp(t)t ^–ds/2 independently ofp.     

Stochastic simulation of the reaction-diffusion systemA+B→inert in integer and fractal dimensions

We present a stochastic simulation of the reaction-diffusion systemA+Binert based upon the algorithm of the minimal process method. In order to overcome the well known problems of this algorithm when selecting a reaction or diffusion event according to its rate contribution we introduce the concept of logarithmic classes which accelerates the algorithm by an order of magnitude. We simulate the systemA+Binert for integer dimensionsd=1,2,3,4 and confirm the predictions of the scaling theory by Kang and Redner. We extend our simulations to fractal structures, namely the Sierpinski carpet, triangle, the Menger sponge and HLA-clusters. Again we find agreement with the scaling theory if the fractal dimensions are defined as the spectral dimension.     

Investigation of isospin forbidden 0+ → 0+ Fermi beta decays with Pyatov method

In the present work, the matrix elements, isospin impurities and log ft values of the isospin forbidden 0⁺ → 0⁺ beta decays have been investigated. The calculated results have been compared with available experimental and another theoretical data. The isotopic invariance of the Hamiltonian has been restored by Pyatov method. Within the quasi-particle random phase approximation (QRPA), the computations have been performed both in presence and absence of the pairing interactions.     

Reversible A↔B reaction–diffusion process with initially mixed reactants: Boundary layer function approach

The reversible A?B reaction–diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is usually considered as a diffusion-limited process. In this work the reaction rate in such a process is investigated using the boundary layer function method. It was shown that the reaction–diffusion process can be considered as a quasi-equilibrium process. Despite this fact the contribution of the changes in the species concentration of the reaction is comparable to that of the diffusion. Moreover, the ratios of the reaction and diffusion contributions are independent of time and coordinate. The dependence of the reaction rate on the initial species distribution is analyzed. It was demonstrated, for the first time, that the number of the reaction zones is determined by the initial conditions and changes with time. Also the asymptotic long-time behavior of the reaction rate depends on the initial species distribution.     

Effect of nonequilibrium charge screening in A + B → 0 bimolecular reactions in condensed matter

The formalism of many-particle densities developed earlier by the present authors is applied to the study of the cooperative effects in the kinetics of bimolecular A + B 0 reactions between oppositely charged particles (reactants). It is shown that unlike the Debye-Hückel theory in statistical physics, here charge screening has essentially a nonequilibrium character. For the asymmetric mobility of reactants (D _A = 0,D _B 0 the joint spatial distribution of similar immobile reactants A reveals at short distances a singular character associated with their aggregation. The relevant reaction rate does not approach a steady state (as it does in the symmetric case,D _A =D _B, but increases infinitely in time, thus leading to a concentration decay which is quicker than the algebraic law generally accepted in chemical kinetics,n t _–1.     

Search for B(s)(0) → μ+ μ- and B(0) → μ+ μ- decays with CDF II

A search has been performed for B(s)(0) → μ+ μ- and B(0) → μ+ μ- decays using 7 fb(-1) of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of B(0) candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of B(B(0) → μ+ μ-) < 6.0 × 10(-9) at 95% confidence level. We observe an excess of B(s)(0) candidates. The probability that the background processes alone could produce such an excess or larger is 0.27%. The probability that the combination of background and the expected standard model rate of B(s)(0) → μ+ μ- could produce such an excess or larger is 1.9%. These data are used to determine B(B(s)(0)→ μ+ μ-) = (1.8(-0.9) (+1.1)) × 10(-8) and provide an upper limit of B(B(s)(0) → μ+ μ-) < 4.0 × 10(-8) at 95% confidence level.     

Effects of Final State Interactions in Pure Annihilation Decay of B+ → D+K0*

The decay of the B ⁺ meson to the D ⁺ and K ⁰* mesons is a pure annihilation decay. For this reason, in the framework of the quantum chromodynamics factorization (QCDF) approach, this decay has a small amplitude and a small branching ratio. In this research we find that, before the D ⁺ and K ⁰* mesons are produced in the final states, pair mesons such as D _s ⁺* and D _s ⁺ρ⁰ are produced. The intermediate-state mesons via the exchange of K ⁰(K ⁰*) and D ⁺(D ⁺*) go to the D ⁺ and K ⁰* final state mesons. However we calculate the B ₊ → D ⁺ K ⁰* decay in two different frameworks. The first framework is the QCDF method and the second one is final state interaction (FSI). The experimental branching ratio of B ₊ → D ₊ K ⁰* decay is less than 3 × 10^–6, and our results obtained by the QCDF method and FSI are (0.35 ± 0.04) × 10^–6 and (2.94 ± 0.10) × 10^–6, respectively.     

Effects of final-state interactions in pure annihilation decay of B s 0 → π+π −

The hadronic decay of B _s ⁰ → π ⁺ π ^? is analyzed by using “QCD factorization” (QCDF) method and final-state interaction (FSI). First, the B _s ⁰ → π ⁺ π ^? decay is calculated via QCDF method and the annihilation graphs only exist in this method. Hence, the FSI must be seriously considered to solve the B _s ⁰ → π ⁺ π ^? decay and the K ^+(*) K ^?(*) and \(K^{0(*)} K^{\bar 0(*)}\) via the exchange of K ^0(*) and K ^?(*) mesons are chosen for the intermediate states. To estimate the intermediate state amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of B _s ⁰ → π ⁺ π ^? decay is less than 1.2 × 10^?6 and our results according to the QCDF method and FSI are 0.68 × 10^?8 and 1.18 × 10^?6, respectively.     

Erratum: Renormalization group study of the A+B→Φ diffusion-limited reaction

A recent argument of Oerding shows that our calculation of the quantity , which determines the amplitude of the asymptotic decay of the particle density in 2<d<4, was in error. Instead it is simply given by =n ₀, the initial density, for uncorrelated initial conditions.     

Differential branching fraction and angular analysis of the decay B0 → K*0 μ+ μ-

The angular distributions and the partial branching fraction of the decay B0 → K*0 μ+ μ- are studied by using an integrated luminosity of 0.37 fb(-1) of data collected with the LHCb detector. The forward-backward asymmetry of the muons, A(FB), the fraction of longitudinal polarization, F(L), and the partial branching fraction dB/dq2 are determined as a function of the dimuon invariant mass. The measurements are in good agreement with the standard model predictions and are the most precise to date. In the dimuon invariant mass squared range 1.00-6.00 GeV2/c4, the results are A(FB)=-0.06(-0.14)(+0.13)±0.04, F(L)=0.55±0.10±0.03, and dB/dq2=(0.42±0.06±0.03)×10(-7) c4/GeV2. In each case, the first error is statistical and the second systematic.