| dc.description.abstract | Many books and/or papers have been published on linear generalizations of
Fourier's equation in order to introduce relaxational and nonlocal e ects for the
heat
ux [1{9]. Describing a heat-pulse propagation with a nite speed [10{15],
in agreement with experimental observations, such works are of much conceptual
interest both because they may be applied to small systems (the characteristic size
of which is comparable to the mean-free path of the heat carriers) [16{23] or to
fast processes (as for instance response to short laser pulses) [24{28], and because
they have stimulated generalized formulations of non-equilibrium thermodynamics,
with generalized expressions of the entropy and of the entropy
ux incorporating
heat-
ux contributions [1{4, 7, 22, 29, 30].
The linear generalizations of Fourier's equation should be only employed to analyze
the propagation of small-amplitude waves. When the amplitude of temperature
waves (or of heat-
ux waves) is not negligible, in fact, nonlinear e ects cannot be neglected:
this is the case, for example, when short and intense laser pulses are applied
to heat a given material. Therefore, there is much interest in generalizing the linear
theory of heat waves which has been, up to now, a fruitful stimulus to generalizations
of non-equilibrium thermodynamics [1{4, 7, 9, 11, 12, 14, 29, 31{34] to nonlinear
situations, namely, for waves with su ciently high amplitudes [18, 20, 35{39]; indeed,
there are many possible nonlinear generalizations and, from a thermodynamic
point of view, it is of special interest selecting the forms which t in a most direct
way with the requirements of the second law of thermodynamics.
The present thesis aims at being a contribution to the study of heat waves
when nonlinear and/or nonlocal generalizations of the Maxwell-Cattaneo equation
in the context of extended thermodynamics [1, 4, 7, 35, 40] are introduced. Whereas
nonlocal e ects in heat transport have led to fruitful analogies with hydrodynamics,
especially in the so-called phonon hydrodynamics, in the present thesis we also
show how some particular nonlinear e ects lead to fruitful analogies with nonlinear
optics. We think that these analogies of heat transport with hydrodynamics and
with optics are a nice illustration of the deep unity of physics, where results in
some eld may also be helpful to other elds, provided that the connection between
both elds is found. The present thesis is a contribution in that direction, and the
results contained in it may be of interest to current researches aiming to nd new
ways of control and applications of the heat
ux, which is the main goal of the socalled
phononics [25, 27]. In particular, the interaction of intense laser pulses with
heat-conducting solids has motivated nonlinear phononics [24, 26, 28], requiring a
combination of nonlinear optics and nonlinear heat transport.
The plan of this thesis is the following.
In Chapter 1 we recall the basic mathematical de nitions and concepts which will
be employed in this thesis, and brie
y summarize the theoretical thermodynamic
background. ... [edited by Author] | it_IT |
