Alberto Rosso - Academia.edu (original) (raw)
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Papers by Alberto Rosso
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction... more We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.
Physical Review E, 2007
The fractional Laplacian operator, −(−△) α 2 , appears in a wide class of physical systems, inclu... more The fractional Laplacian operator, −(−△) α 2 , appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction... more We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behaviour can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.
Physical Review E, 2007
The fractional Laplacian operator, −(−△) α 2 , appears in a wide class of physical systems, inclu... more The fractional Laplacian operator, −(−△) α 2 , appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.