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Register a new userReaction-diffusion processes and metapopulation models in heterogeneous networks
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Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the physical laws. Here, we study the behavior of two basic reaction-diffusion processes ($B to A$ and $A+B to 2B$) defined on networks with heterogeneous topology and no limit on the nodes occupation number. We investigate the effect of network topology on the basic properties of the systems phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density driven phase transitions, whereas phase transition and critical points, independent of the particle density, are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic meta-populations models and agent-based models that include the complex features of real world networks.
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We give an exact analytical results for diffusion with a power-law position dependent diffusion coefficient along the main channel (backbone) on a comb and grid comb structures. For the mean square displacement along the backbone of the comb we obtain behavior $langle x^2(t)ranglesim t^{1/(2-alpha)}$, where $alpha$ is the power-law exponent of the position dependent diffusion coefficient $D(x)sim |x|^{alpha}$. Depending on the value of $alpha$ we observe different regimes, from anomalous subdiffusion, superdiffusion, and hyperdiffusion. For the case of the fractal grid we observe the mean square displacement, which depends on the fractal dimension of the structure of the backbones, i.e., $langle x^2(t)ranglesim t^{(1+ u)/(2-alpha)}$, where $0< u<1$ is the fractal dimension of the backbones structure. The reduced probability distribution functions for both cases are obtained by help of the Fox $H$-functions.
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