arXiv subjects

F. Oliveri

Publications and source records attributed to F. Oliveri.

10 recordsLinked to original sources

arXiv2025

Two-dimensional equilibrium configurations in Korteweg fluids

In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two--dimensional setting, it is derived a single nonlinear elliptic equation such that the equilibrium conditions are identically satisfied. Such an equation is discussed both analytically and numerically. Moreover, by considering a particular boundary value problem of Dirichlet type, some preliminary numerical solutions are presented.

math-ph↗

arXiv2025

An operatorial view of competition and cooperation in a network of economic agents

A network of agents interacting both with competitive and/or cooperative mechanisms is modeled by using fermionic ladder operators. The time evolution of the network is assumed to be governed by a Hermitian time-independent Hamiltonian operator, and the mean values of the number operators are interpreted as a measure of the wealth status of the agents. Besides classical Heisenberg, we use the recently introduced $(H,\rho)$-induced dynamics approach to account for some actions able to provide a self-adjustment of the network according to its time evolution. Some numerical simulations are presented and discussed. Remarkably, we show that, in a network where cooperation may emerge, the average wealth of the agents is higher, and there is a very low level of inequality.

physics.soc-ph↗

arXiv2025

Fermionic operatorial model of a system with competitive and cooperative interactions

An operatorial model of a system made by $N$ agents interacting each other with mechanisms that can be thought of as cooperative or competitive is presented. We associate to each agent an annihilation, creation and number fermionic operator, and interpret the mean values of the number operators over an initial condition as measures of the agents' wealth status. The dynamics of the system is assumed to be ruled by a Hermitian Hamiltonian operator $\mathcal{H}$, and the classical Heisenberg view is used. The dynamical outcome is then enriched by using the recently introduced variant of $(\mathcal{H},\rho)$--induced dynamics, where $\rho$ denotes a rule that periodically modifies some of the parameters involved in $\mathcal{H}$. The agents are partitioned in three subgroups, one interacting each other only with a competitive mechanism, one interacting each other only with a cooperative mechanism, and one opportunist subgroup able to compete and cooperate. Some numerical simulations show that the $(\mathcal{H},\rho)$--induced dynamics approach makes, in all the cases, the cooperative subgroup definitely to be more efficient in improving its wealth status than the other subgroups.

physics.soc-ph↗

arXiv2025

Approximate Noether symmetries of perturbed Lagrangians and approximate conservation laws

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we state an approximate Noether theorem leading to the construction of approximate conservation laws. Some illustrative applications are presented.

math-ph↗

arXiv2024

Hierarchy of coupled Burgers-like equations induced by conditional symmetries

It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system of five coupled Burgers-like equations. Using the latter system as a starting point, and iterating the procedure, an infinite hierarchy of systems made of an odd number of coupled Burgers-like equations can be conjectured. Moreover, starting from a pair of Burgers-like equations, a similar hierarchy of systems made of an even number of coupled Burgers-like equations may arise. We prove that these two infinite hierarchies can be unified, and each element of the hierarchy arises from the nonclassical symmetries of the previous one. Writing a generic element of this hierarchy as a matrix Burgers' equation, the existence of the matrix Hopf-Cole transformation allows for its linearization and the determination of its solutions. Finally, it is shown that each element of the hierarchy possesses a five-dimensional Lie algebra of classical point symmetries. Though these Lie algebras are realized in manifolds with different dimensionality, they are all isomorphic.

math-ph↗

arXiv2023

Spreading of information on a network: a quantum view

This paper concerns the modeling of the spread of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the ($H,\rho$)-induced dynamics and one on the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation. For each method, numerical results are presented.

quant-ph↗

arXiv2021

Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation

Within the theoretical framework of a recently introduced approach to approximate Lie symmetries of differential equations containing small terms, which is consistent with the principles of perturbative analysis, we define accordingly approximate Q-conditional symmetries of partial differential equations. The approach is illustrated by considering the hyperbolic version of a reaction-diffusion-convection equation. By looking for its first order approximate Q-conditional symmetries, we are able to explicitly determine a large set of non-trivial approximate solutions.

math-ph↗

arXiv2018

$(H,ρ)$--induced dynamics and large time behaviors

In some recent papers, the so called $(H,ρ)$-induced dynamics of a system $\mathcal{S}$ whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, $H$ is the Hamiltonian for $\mathcal{S}$, while $ρ$ is a certain rule applied periodically (or not) on $\mathcal{S}$. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the $(H,ρ)$-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of $\mathcal{S}$ may converge, for large $t$, to certain asymptotic values. This can not be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics implemented by a suitable hermitian operator $H$ can only give an oscillating behavior. We prove our claims both analytically and numerically for a simple system with two degrees of freedom, and then we apply our general scheme to a model describing a biological system of bacteria living in a two-dimensional lattice, where two different choices of the rule are considered.

physics.soc-ph↗

arXiv2016

$(H,ρ)$-induced dynamics and the quantum game of life

We propose an extended version of quantum dynamics for a certain system S, whose evolution is ruled by a Hamiltonian $H$, its initial conditions, and a suitable set $ρ$ of {\em rules}, acting repeatedly on S. The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of $H$, $ρ$ as well as on the initial conditions. After a general discussion on this $(H,ρ)$-{\em induced dynamics}, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.

quant-ph↗

arXiv2014

Dynamics of closed ecosystems described by operators

We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently adopted in the description of several classical systems, in the analysis of the dynamics of some models of closed ecosystems. In particular, we discuss two linear models, for which the solution can be found analytically, and a nonlinear system, for which we produce numerical results. We also discuss how a damping effect could be {\em effectively} implemented in the model.

physics.bio-ph↗