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

Time evolution of the reaction front in a subdiffusive system

Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result is derived for the system where the subdiffusion coefficients of reactants differ from each other. It includes the case of one static reactant. As an application of our results, we compare the time evolution of reaction front extracted from experimental data with the theoretical formula and we find that the transport process of organic acid particles in the tooth enamel is subdiffusive.Comment: 18 pages, 3 figure

Equilibrium First-Order Melting and Second-Order Glass Transitions of the Vortex Matter in Bi2_2Sr2_2CaCu2_2O8_8

The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.Comment: 5 pages, 4 figures. To be published in Phys. Rev. Let

Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A

Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the distribution of distances between nearest particles. However, a full characterization of a particle system is only provided by the infinite hierarchy of multiple-point density correlation functions. We derive an exact description of the full hierarchy of correlation functions for the diffusion-limited irreversible coalescence process A + A -> A.Comment: 4 pages, 2 figures (postscript). Typeset with Revte

Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to drift do not fall into a limited number of universality classes.Comment: 10 pages, tex, 3 figures, also available upon reques

Annihilation of Immobile Reactants on the Bethe Lattice

Two-particle annihilation reaction, A+A -> inert, for immobile reactants on the Bethe lattice is solved exactly for the initially random distribution. The process reaches an absorbing state in which no nearest-neighbor reactants are left. The approach of the concentration to the limiting value is exponential. The solution reproduces the known one-dimensional result which is further extended to the reaction A+B -> inert.Comment: 12 pp, TeX (plain

Investigating Open-World Person Re-identification Using a Drone

Abstract. Person re-identification is now one of the most topical and intensively studied problems in computer vision due to its challenging na-ture and its critical role in underpinning many multi-camera surveillance tasks. A fundamental assumption in almost all existing re-identification research is that cameras are in fixed emplacements, allowing the explicit modelling of camera and inter-camera properties in order to improve re-identification. In this paper, we present an introductory study push-ing re-identification in a different direction: re-identification on a mobile platform, such as a drone. We formalise some variants of the standard formulation for re-identification that are more relevant for mobile re-identification. We introduce the first dataset for mobile re-identification, and we use this to elucidate the unique challenges of mobile re-identification. Finally, we re-evaluate some conventional wisdom about re-id models in the light of these challenges and suggest future avenues for research in this area.

Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents

We introduce a model of three-species two-particle diffusion-limited reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three persistence parameters (survival probabilities in reaction) of the hopping particle. We consider isotropic and anisotropic diffusion (hopping with a drift) in 1d. We find that the particle density decays as a power-law for certain choices of the persistence parameter values. In the anisotropic case, on one symmetric line in the parameter space, the decay exponent is monotonically varying between the values close to 1/3 and 1/2. On another, less symmetric line, the exponent is constant. For most parameter values, the density does not follow a power-law. We also calculated various characteristic exponents for the distance of nearest particles and domain structure. Our results support the recently proposed possibility that 1d diffusion-limited reactions with a drift do not fall within a limited number of distinct universality classes.Comment: 12 pages in plain LaTeX and four Postscript files with figure

On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals

The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical processes, which as a consequence of the time evolution develop a characteristic length of the form $\xi \propto t^{1/z}$, where z is the dynamic exponent. So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables, with a fundamental time scaling ratio given by $\tau = b_1 ^z$. The conjecture is tested numerically for random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.Comment: 6 pages, 3 figures. Submitted to EP

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function