Matteo Gorgone

University of Messina | UNIME

A complete thermodynamical analysis for a blood model, based on mixture theory, is performed. The model is developed considering the blood as a suspension of red blood cells (solid component) in the plasma (fluid component), and taking into account the temperature effects. Furthermore, two independent scalar internal variables are introduced accoun...

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. Iterating the procedure, an infinite hierarchy of systems made of an o...

We are pleased to announce the first international congress: Mediterranean Conference on Neutrosophic Theory (MeCoNeT 2024) which will be held in Messina, Italy at the Accademia Peloritana dei Pericolanti on 24th and 25th September 2024 in a hybrid format, i.e. ensuring participation both in presence and online on the Teams platform. MeCoNeT 2024 i...

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...

In this paper, non-variational systems of differential equations containing small terms are considered, and a consistent approach for deriving approximate conservation laws through the introduction of approximate Lagrange multipliers is developed. The proposed formulation of the approximate direct method starts by assuming the Lagrange multipliers...

A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy...

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, a single nonlinear elliptic equation is derived such that the equilibrium conditions are identically satisfi...

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 illust...

A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal energies of both constituents, together with their first gradients, on the symmetric part of the gradient of b...

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...

We consider a model of a third-grade viscous Korteweg-type fluid in three space dimensions and apply the extended Liu procedure in order to explicitly solve the constraints imposed by the entropy principle on the nonlocal constitutive relations. We detail the algorithm we use and are able to characterize the material functions involved in the const...

In this paper, we consider a system of balance laws sufficiently general to contain the equations describing the thermomechanics of a one-dimensional continuum; this system involves some constitutive functions depending on the elements of the so called state space assumed to contain the spatial gradients of some of the unknown fields. The compatibi...

We provide a thermodynamic framework for binary mixtures of Korteweg fluids with two velocities and two temperatures. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal energy of both constituents, together with their first gradients, as well as on the mass density of the mixture and the concentrati...

In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, has been introduced. According to the formal mathematical apparatus of quantum mechanics, H denotes the Hamiltonian for S, while ρ is a certain rule applied periodically on S. In this approach the rule acts at...

Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, i.e., classes of differential equations that are in correspondence with their Lie point symmetries. In particular, we determine hierarchies of second order partial differential equations uniquely characterized by affine transformation...

In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non-Newtonian coefficient. According to a recently introduced approach, the first order approximate Lie symmetries of the equations are computed, some classes of appr...

Lie theory of continuous transformations provides a unified and powerful approach for handling differential equations. Unfortunately, any small perturbation of an equation usually destroys some important symmetries, and this reduces the applicability of Lie group methods to differential equations arising in concrete applications. On the other hand,...

Following a recently introduced approach to approximate Lie symmetries of differential equations which is consistent with the principles of perturbative analysis of differential equations containing small terms, we analyze the case of approximate Q–conditional symmetries. An application of the method to a hyperbolic variant of a reaction-diffusion-...

An operatorial theoretical model based on raising and lowering fermionic operators for the description of the dynamics of a political system consisting of macro–groups affected by turncoat–like behaviors is presented. The analysis of the party system dynamics is carried on by combining the action of a suitable quadratic Hamiltonian operator with sp...

The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous systems. Necessary and sufficient conditions for the partial or full decoupling of the systems at hand are provided....

It is proved a theorem providing necessary and sufficient conditions enabling one to map a nonlinear system of first order partial differential equations, polynomial in the derivatives, to an equivalent autonomous first order system polynomially homogeneous in the derivatives. The result is intimately related to the symmetry properties of the sourc...

A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear form is performed by constructing the canonical variables associated to the Lie point symmetries admitted by t...

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...