Carmela Currò

A reduction procedure for generalized Riemann problems with application to nonlinear transmission lines

Generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of PDEs are obtained through the differential constraint method. These solutions prove to be flexible enough to solve generalized Riemann problems where discontinuous initial data are involved. Within such a theoretical framework, the governing model of nonlinear transmission lines is investigated throughout.

Reduction of nonhomogeneous quasilinear 2×2 systems to homogeneous and autonomous form

By using the invariance with respect to suitable Lie groups of point transformations, necessary and sufficient conditions are determined allowing one to map through an invertible point transformation nonhomogeneous and nonautonomous quasilinear 2×2 systems to homogeneous and autonomous form. The procedure is constructive and the new independent and dependent variables are obtained by determining the canonical variables associated with the Lie groups of point symmetries admitted by the source system. Various examples of physical interest arising from different contexts are considered.

Reduction to linear canonical forms and generation of conservation laws for a class of quasilinear hyperbolic systems

Abstract We consider a quasilinear hyperbolic homogeneous system of two first order equations involving two dependent and two independent variables. For the associated hodograph equations we investigate the reducibility to canonical forms allowing for an explicit integration. Such a kind of requirement, in problems of physical interest, provides a suitable method for characterizing possible material model laws. The theoretical approach shown herein can be relevant for studying the existence of conservation laws to non-homogeneous first order systems and also for describing the evolution of weak shock waves.

Hodograph transformation and differential constraints for wave solutions to 2 ? 2 quasilinear hyperbolic nonhomogeneous systems

The differential constraint method is used to work out a reduction approach to determine solutions in a closed form to the highly nonlinear hodograph system arising from 2 × 2 hyperbolic nonhomogeneous models. These solutions inherit all of the features of the standard wave solutions obtainable via the classical hodograph transformation and in the meantime incorporate the dissipative effects induced on wave processes by the source-like term involved in the governing equations. Within such a theoretical framework the problem of integrating the standard linear hodograph system associated with 2 × 2 homogeneous models is also revisited and a number of results obtained elsewhere of relevant interest in wave problems are recovered as a particular case. Along the lines of the proposed reduction approach, different examples of 2 × 2 governing models are analysed thoroughly in order to highlight the flexibility of the provided solutions to describe hyperbolic dissipative wave processes.

Riemann problems and exact solutions to a traffic flow model

Within the theoretical framework of differential constraints method a nonhomogeneous model describing traffic flows is considered. Classes of exact solutions to the governing equations under interest are determined. Furthermore, Riemann problems and generalized Riemann problems which model situations of interest for traffic flows are solved.

Exact description of simple wave interactions in multicomponent chromatography

Nonlinear wave interaction processes for a quasilinear hyperbolic homogeneous system of first-order partial differential equations multicomponent chromatography are investigated. The wave analysis is worked out by extending to the present multicomponent case the leading ideas of a well-established method of approach that was developed for solving initial value-wave problems in terms of exact solutions to 2 × 2 hyperbolic homogeneous systems. These interaction processes may model different situations concerning the separation of a mixture into its chemical components. Several numerical plots are also given in order to illustrate the behavior of the exact wave solutions arising from the analysis that is accomplished.

A linearization procedure for quasi-linear non-homogeneous and non-autonomous 2 × 2 first-order systems

Abstract We propose a method for reducing to linear form 2 × 2 non-homogeneous and non-autonomous first-order quasi-linear systems. The method reduces the governing system, through the use of a variable transformation, to an homogeneous and an autonomous form which can be linearized by means of hodograph transformation. Within the present theoretical framework, we investigate several models arising from different physical contexts.

Quantitative estimation of the spin-wave features supported by a spin-torque-driven magnetic waveguide

The main features of the spin-waves excited at the threshold via spin-polarized currents in a one-dimensional normally-to-plane magnetized waveguide are quantitatively determined both analytically and numerically. In particular, the dependence of the threshold current, frequency, wavenumber, and decay length is investigated as a function of the size of the nanocontact area through which the electric current is injected. From the analytical viewpoint, such a goal has required to solve the linearized Landau-Lifshitz-Gilbert-Slonczewski equation together with boundary and matching conditions associated with the waveguide geometry. Owing to the complexity of the resulting transcendent system, particular solutions have been obtained in the cases of elongated and contracted nanocontacts. These results have been successfully compared with those arising from numerical integration of the abovementioned transcendent system and with micromagnetic simulations. This quantitative agreement has been achieved thanks to t...

Statistical-Thermodynamic Study of Nonequilibrium Phenomena in Three-Dimensional Anharmonic Crystal Lattices: III. Linear Waves

As typical nonequilibrium phenomena, linear waves propagating in isotropic solids at finite temperatures are studied on the basis of both microscopic and macroscopic systems of basic equations, which were proposed in the previous papers of the present series. The temperature dependences of the propagation speeds of the longitudinal and transverse harmonic waves are derived explicitly for several metals. Their amplitude ratios are also obtained as the functions of the temperature. Singularities of the physical quantities at the melting point are found out and discussed. The validity of the so-called local equilibrium assumption, which has usually been taken for granted in nonequilibrium thermodynamics, is reexamined by comparing the macroscopic results with the microscopic ones in detail. And a possibility of going beyond the local equilibrium assumption in the analyses is discussed in connection with extended thermodynamics.

Nonlinear wave interaction problems in the three-dimensional case

Three-dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three-dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous semi-Hamiltonian hydrodynamic type systems (i.e. possess diagonal form and infinitely many conservation laws). The interaction of N waves was studied. In particular we prove that they behave like simple waves and they distort after the collision region. The amount of the distortion can be analytically computed.