Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations

Abstract

We analyze the two-species reaction-diffusion system including trapping reaction $A+B\to A$ as well as coagulation/annihilation reactions $A+A\to (A,0)$ where particles of both species are performing Lévy flights with control parameter $0<\sigma <2$, known to lead to superdiffusive behaviour. The density, as well as the correlation function for target particles $B$ in such systems, are known to scale with nontrivial universal exponents at space dimension $d\le d_c$. Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension $d_c=\sigma$. The numerical simulations in one-dimensional case are performed as well. The quantitative estimates for the decay exponent of the density of survived particles $B$ are in good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in a superdiffusive regime is higher than that in a system with ordinary diffusion.

arXiv comment24 pages, 11 figures

References in corpus (33)

• Intermittent search strategies
• Lévy walks
• Optimal search strategies for hidden targets
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Random lasers, Lévy statistics and spin glasses: Synergy between photonics and complex systems
• Statistical regimes of random laser fluctuations
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• First-passage and first-hitting times of Levy flights and Levy walks
• A model for anomalous directed percolation
• Lévy flights versus Lévy walks in bounded domains
• Kinetics of Heterogeneous Single-Species Annihilation
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Criticality of Spin Systems with Weak Long-Range Interactions
• Fluctuation Kinetics in a Multispecies Reaction-Diffusion System
• Computer Simulation Study of the Levy Flight Process
• Branching and annihilating Levy flights
• Weak localization of light in superdiffusive random systems
• Persistence properties of a system of coagulating and annihilating random walkers
• Long-range multi-scalar models at three loops
• Field theory of directed percolation with long-range spreading
• Two-time scale subordination in physical processes with long-term memory
• Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
• Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
• A Fractional Diffusion Equation for an n-Dimensional Correlated Levy Walk
• Kang-Redner Anomaly in Cluster-Cluster Aggregation
• Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability
• Anomalous Dimension in a Two-Species Reaction-Diffusion System
• Application of the Bogolyubov's theory of weakly non-ideal Bose gas on the A+A, A+B, B+B reaction-diffusion system
• Vicious Lévy flights
• Field-theoretic technique for irreversible reaction processes
• Numerical Simulation of the Trapping Reaction with Mobile and Reacting Traps

Cited by in corpus (2)

• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Two-species reaction-diffusion system in the presence of random velocity fluctuations