arXiv subjects

Francesco Oliveri

Publications and source records attributed to Francesco Oliveri.

24 records · Page 2Linked to original sources

arXiv2021

Reduction of balance laws in (3+1)--dimensions to autonomous conservation laws by means of equivalence transformations

A class of partial differential equations (a conservation law and four balance laws), with four independent variables and involving sixteen arbitrary continuously differentiable functions, is considered in the framework of equivalence transformations. These are point transformations of differential equations involving arbitrary elements and live in an augmented space of independent, dependent and additional variables representing values taken by the arbitrary elements. Projecting the admitted symmetries into the space of independent and dependent variables, we determine some finite transformations mapping the system of balance laws to an equivalent one with the same differential structure but involving different arbitrary elements; in particular, the target system we want to recover is an autonomous system of conservation laws. An application to a physical problem is considered.

math-ph↗

arXiv2021

ReLie: a Reduce program for Lie group analysis of differential equations

Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many computer algebra packages have been developed along the years to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, which since 2008 is an open source program (http://www.reduce-algebra.com) and is available for all platforms. \relie is able to perform almost automatically the needed computations for Lie symmetry analysis of differential equations. Its source code is freely available at the url http://mat521.unime.it/oliveri. The use of the program is illustrated by means of some simple examples; nevertheless, it is to be underlined that it provides effective also for more complex computations where one has to deal with very large expressions.

cs.MS↗

arXiv2014

A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies

We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two--dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non--trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out.

physics.soc-ph↗

arXiv2014

Ordinary differential equations described by their Lie symmetry algebra

The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras.

math-ph↗

arXiv2012

A phenomenological operator description of interactions between populations with applications to migration

We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss diffusion processes modeled by a quadratic hamiltonian. This general procedure will be adopted, in particular, in the description of migration phenomena. With respect to our previous analogous results, we use here fermionic operators since they automatically implement an upper bound for the population densities.

physics.bio-ph↗

arXiv2010

An Operator--like Description of Love Affairs

We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations. We start with a simple model, involving two actors (Alice and Bob): in the linear case we obtain periodic dynamics, whereas in the nonlinear regime either periodic or quasiperiodic solutions are found. Then we extend the model to a love triangle involving Alice, Bob and a third actress, Carla. Interesting features appear, and in particular we find analytical conditions for the linear model of love triangle to have periodic or quasiperiodic solutions. Numerical solutions are exhibited in the nonlinear case.

physics.soc-ph↗