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Claudia Cianci

Position: PHd
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

Research Interests

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

  • Cianci C, at all. Impact of the climatic change on animal diseases spread: example of blue tongue in SpainRCCV, 5 (1), 120-131 (2011).

  • Claudia Cianci , Francesca Di Patti, Duccio Fanelli. Non-Gaussian fluctuations in stochastic models with absorbing barriers. Eur. Phys. Lett., 96 (5), 50011. (2011).

  • Claudia Cianci , Francesca Di Patti , Duccio Fanelli, Luigi Barletti. Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions. Eur. Phys. J. Special Topics, 212, 5-22 (2012).

  • Duccio Fanelli, Claudia Cianci, Francesca di Patti, Turing instabilities in reaction-diffusion systems with cross diffusion. Eur. Phys. J. B(2013) 86: 142.

  • Cianci Claudia,Duccio Fanelli, Stochastic patterns and the role of crowding(Accepted) Discontinuity, Nonlinearity, and Complexity.

  • Laura Cantini, Claudia Cianci, Duccio Fanelli, Emma Massi, Luigi Barletti, Stochastic Turing Patterns for systems with one diffusing speciesSubmitted to Journal of Mathematical Biology.