Riccardo Ricci

R-Actions, derivations, and Fröbenius theorem on graded manifolds

Abstract The relationship between actions of the additive group R and derivations on a graded manifold is discussed. An extension of the classical Frobenius theorem is also established for a particular class of involutive distributions on a graded manifold.

On the stability of some solutions of the Stefan problem

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

Tetrad fields and metric tensor in the gauge theory of gravitation

The most relevant geometrical aspects of the gauge theory of gravitation are considered. A global definition of the tetrad fields is given and emphasis is placed on their role in defining an isomorphism between the tangent bundle of space-time and an appropriate vector bundle B associated to the gauge bundle. It is finally shown how to construct the fundamental geometrical objects on space-time, starting from B.

Mathematical Problems in the Ziegler—Natta Polymerization Process

Some models describing the Ziegler-Natta polymerization are reviewed, and their mathematical aspects are discussed. A model for the heterogeneous polymerization is developed assuming a continuous approximation of the catalyst site distribution. Some mathematical results about these models are presented.

A REACTION INFILTRATION PROBLEM: EXISTENCE, UNIQUENESS, AND REGULARITY OF SOLUTIONS IN TWO SPACE DIMENSIONS

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. We establish global existence, uniqueness and regularity of the solution in a two-dimensional finite strip (−M, M)×(0, 1) and the existence and partial regularity of solutions in an infinite strip (−∞, ∞)×(0, 1).

Existence and uniqueness for a reaction-diffusion problem in infiltration

We consider a system of coupled PDEsmodeling the infiltration of a reacting fluid in a soluble porous medium. The system is made of a parabolic equation for the concentration of the dissolved material, an ODE (hyperbolic equation with characteristic x=Const.)for the porosity, and an elliptic equation for the fluid pressure. We prove the existence and uniqueness of a classical solution. The classical solution is global in time in the one-dimensional case. Global existence of a weak solution is proved for the n- dimensional case.

Convergence to the psuedo-steady-state approximation for the unreacted core model

We prove that the solution of a parabolic free boundary problem, arising from a model for some isothermal equimolal non-cathalytic reactions between a fluid and a solid (e.g. oxidization), converges to the solution of the pseudo-steady-state approximation.

Hamiltonian formulation for the gauge theory of the gravitational coupling

This paper studies the Hamiltonian mechanics of a relativistic particle interacting with a gravitational field considered as a gauge field of the Poincare group. We follow a general method developed by Sternberg for the case of internal symmetries, that describes the interaction by a suitable modification of the symplectic form. This approach is reviewed and the explicit examples of the electromagnetic and Yang–Mills gauge interactions are widely explained in local coordinates. The peculiar features of a gauge theory of the Poincare group are then discussed and the geometrical picture that emerges suggests the way of modifying the symplectic form for a correct description of the gravitational coupling.

A classical particle in a Poincar gauge field as a model for the gravitational interaction

The geometrical and mechanical aspects of a particle interacting with a Poincaré gauge field are considered and the relation with a gravitational interaction is studied.

Solid Core Revisited

We present a hyperbolic model for the growth of a polymer particel in the Zigler-Natta process.