Giovanna Valenti

Combined Frequency-Amplitude Nonlinear Modulation: Theory and Applications

In this paper, we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal. The derived analytical solution may give a satisfactory explanation of recent laboratory observations on magnetic spin-transfer oscillators and fully agrees with results of micromagnetic calculations. Since the theory has been developed independently of the mechanism causing the nonlinearities, it may encompass the description of modulation processes of any physical nature, a promising feature for potential applications in the field of communication systems.

Some non-linear effects of stationary heat conduction in 3D domains through extended thermodynamics

We describe stationary heat conduction in an ideal gas at rest between three-dimensional manifolds. To this aim, we refer to the field equations of extended thermodynamics. The solution is determined through a 3rd-order asymptotic expansion with respect to the Knudsen number. As illustrative examples, we show the results for a gas enclosed between two non-coaxial circular cylinders or two confocal elliptical cylinders. With respect to the classical thermodynamics, we obtain corrections on the temperature, stress tensor and heat flux, that give rise to more complex behaviors of these variables. The dependence on the parameters is also analyzed.

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.

A two or three compartments hyperbolic reaction-diffusion model for the aquatic food chain.

Two hyperbolic reaction-diffusion models are built up in the framework of Extended Thermodynamics in order to describe the spatio-temporal interactions occurring in a two or three compartments aquatic food chain. The first model focuses on the dynamics between phytoplankton and zooplankton, whereas the second one accounts also for the nutrient. In these models, infections and influence of illumination on photosynthesis are neglected. It is assumed that the zooplankton predation follows a Holling type-III functional response, while the zooplankton mortality is linear. Owing to the hyperbolic structure of our equations, the wave processes occur at finite velocity, so that the paradox of instantaneous diffusion of biological quantities, typical of parabolic systems, is consequently removed. The character of steady states and travelling waves, together with the occurrence of Hopf bifurcations, is then discussed through linear stability analysis. The governing equations are also integrated numerically to validate the analytical results herein obtained and to extract additional information on the population dynamics.

Analytical solution of the strain-controlled magnetic domain wall motion in bilayer piezoelectric/magnetostrictive nanostructures

The one-dimensional propagation of magnetic domain walls in an isotropic, linearly elastic, magnetostrictive material is investigated in the framework of the extended Landau-Lifshitz-Gilbert equation where the effects of a spin-polarized current and a rate-independent dry-friction dissipation are taken into account. In our analysis, it is assumed that the ferromagnet is subject to a spatially uniform biaxial in-plain stress generated by a piezoelectric substrate combined with the former in a multiferroic heterostructure. Moreover, a possible connection between the dry-friction mechanism and the piezo-induced strains is conjectured. By adopting the traveling waves ansatz, the effect of such a stress on the domain wall dynamics is explored in both steady and precessional regimes. In particular, it is proved that the magnetoelastic contribution, while it does not formally modify the classical solution, affects both the propagation threshold and the Walker Breakdown conditions involved in the steady regime, i...

Wave interaction in magnetogasdynamics

Abstract The interactions of weak non-linear waves in viscous and thermally conducting magnetogasdynamics are investigated. It is shown that the weak non-linear waves in the case under interest are composed of seven groups of quasi-simple waves so that the propagation is ruled separately by either the Burgers equation or the heat equation. The interactions between them arise only through the phase functions whose expressions are given explicitly.

WEAKLY NONLINEAR INTERACTION OF TWO WAVES IN RADIATIVE GASDYNAMICS

The interaction of two weakly nonlinear waves in radiative gasdynamics is investigated following the perturbation analysis developed by He and Moodie. Explicit solutions are given and the two waves interactions are graphically shown.

Asymptotic Wave Propagation in a non-Newtonian Compressible Fluid with Small Dissipation

The spherical motion of a non-Newtonian compressible fluid is considered and a reductive perturbation method is used to study the point-explosion problem. The material response functions involved in the model under consideration are assumed to be of polynomial form and the resulting Burgers-like equation which governs the far-field approximation is investigated. A qualitative analysis of this equation is made via a numerical integration.