Organization: Università degli Studi di Firenze
Department: Dipartimento di Fisica e Astronomia
Mailing address: Via G. Sansone 1 - C.A.P. 50019, Sesto Fiorentino, Italy
I study the dynamical of microscopic entities in mutual
interaction. In this scenario, species are conﬁned in a closed
volume. Occasionally, low concentration can occur as a result
of the complex mutual interaction between
microscopic actors. Under such conditions, the effects of the
intrinsic discreteness need to be properly accounted for. The
continuous kinetic equations are inadequate,
to understand the dynamic of the system and the ﬁnite
size corrections becoming signiﬁcant. We studying
analytically the associated master equation,
via the systematic van Kampen system size expansion.
To leading order, the mean–ﬁeld deterministic equations
were recovered, while higher order corrections enabled us to
describe the intrinsec stochasticity of the system.
The discreteness of individual based stochastic models,
under specific conditions, can act like amplifer and through a
complex resonance mechanism,
leads to organized the system in spatio-temporal patterns.
The concentration which reflects the distribution of the
interacting entities can oscillate regularly in time and
display spatially organized profile.
Our research is aimed at exploring these
effects from a theoretical point of view. We have revisited the
reference mechanism for patterns formation in biology, called
Turing instability,classically refered on a mean-field
By explicitly accounting for the stochastic nature
of the microscopic system, we extended the
concept of Turing instability. In particular we worked with a
modified Brusselator model and we studied the emergence
of "stochastic travelling waves", in a region
of paramiters in wich is not possible to have order for the
classical Turing approach.
In our approach the model is wrote like chemical reactions.
By using the van Kampen system size expansion
of the master equation, we obtain the Fokker Planck equation
that describe the fluctuations distribution. The dynamic of the
system is described from an intrinsic point of view.
The stochasticity, or the noise is not added artificially. It is
emblematic example the case of the diffusion dynamics of a
chemical system. Starting from a microscopic formulation
and accounting for the finite carrying capacity of the
hosting volume, one recovers a modified diffusive behavior.
Cross diffusive terms appear which links multiple diffusing
Publications & Preprints