Roberto Natalini
Main scientific interests : Nonlinear partial differential equations, hyperbolic and parabolic problems, conservation laws, relaxation and fluid dynamical limits, numerical approximation of shock and diffusive waves, filtration problems in porous media, mechanical and chemical damage in natural stones in historical monuments, numerical approximation of problems in financial mathematics, mathematical models in biomathematics (chemotaxis, biofilms and algae, stem cells, signal transduction).
Phone: office: +39 0649270961
Address: Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, via dei Taurini 19, I-00185, Rome (Italy)
Phone: office: +39 0649270961
Address: Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, via dei Taurini 19, I-00185, Rome (Italy)
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Papers by Roberto Natalini
uids in the framework of mixture theory. The considered systems, in their more general form,
contain both the gradient of a hydrostatic pressure, generated by an
incompressibility constraint, and a compressible pressure depending on the volume
fractions of some of the di erent phases. To approach these systems, we de ne an
approximation based on the Leray projection, which involves the use of a symbolic
symmetrizer for quasi-linear hyperbolic systems and related paradi erential
techniques. In two space dimensions, we prove its well-posedness and convergence
to the unique classical solution to the original system. In the last part, we shortly
discuss the three dimensional case.
growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters
in the form of spheres (Cardiospheres ). The approach is hybrid: discrete at cellular
scale and continuous at molecular level. In the present model cells are subject to the
self-organizing collective dynamics mechanism and, additionally, they can proliferate
and differentiate, also depending on stochastic processes. The two latter processes are
triggered and regulated by chemical signals present in the environment. Numerical
simulations show the structure and the development of the clustered progenitors and
are in a good agreement with the results obtained from in vitro experiments.
discrete in continuous mathematical model for the morphogenesis of the posterior lateral
line system in zebrafish. Our hybrid description is discrete on the cellular level and continuous on the molecular level. We prove the existence of steady solutions corresponding to the formation of particular biological structures, the neuromasts. Numerical simulations are performed to show the dynamics of the model and its accuracy to describe the evolution of the cell aggregate by a qualitative and quantitative point of view. Some related models, applied to the collective motion of cells, and to the behaviour of cardiac stem cells, are indicated.
uids in the framework of mixture theory. The considered systems, in their more general form,
contain both the gradient of a hydrostatic pressure, generated by an
incompressibility constraint, and a compressible pressure depending on the volume
fractions of some of the di erent phases. To approach these systems, we de ne an
approximation based on the Leray projection, which involves the use of a symbolic
symmetrizer for quasi-linear hyperbolic systems and related paradi erential
techniques. In two space dimensions, we prove its well-posedness and convergence
to the unique classical solution to the original system. In the last part, we shortly
discuss the three dimensional case.
growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters
in the form of spheres (Cardiospheres ). The approach is hybrid: discrete at cellular
scale and continuous at molecular level. In the present model cells are subject to the
self-organizing collective dynamics mechanism and, additionally, they can proliferate
and differentiate, also depending on stochastic processes. The two latter processes are
triggered and regulated by chemical signals present in the environment. Numerical
simulations show the structure and the development of the clustered progenitors and
are in a good agreement with the results obtained from in vitro experiments.
discrete in continuous mathematical model for the morphogenesis of the posterior lateral
line system in zebrafish. Our hybrid description is discrete on the cellular level and continuous on the molecular level. We prove the existence of steady solutions corresponding to the formation of particular biological structures, the neuromasts. Numerical simulations are performed to show the dynamics of the model and its accuracy to describe the evolution of the cell aggregate by a qualitative and quantitative point of view. Some related models, applied to the collective motion of cells, and to the behaviour of cardiac stem cells, are indicated.