93,436 research outputs found
Entropy Production in Relativistic Binary Mixtures
In this paper we calculate the entropy production of a relativistic binary
mixture of inert dilute gases using kinetic theory. For this purpose we use the
covariant form of Boltzmann's equation which, when suitably transformed, yields
a formal expression for such quantity. Its physical meaning is extracted when
the distribution function is expanded in the gradients using the well-known
Chapman-Enskog method. Retaining the terms to first order, consistently with
Linear Irreversible Thermodynamics we show that indeed, the entropy production
can be expressed as a bilinear form of products between the fluxes and their
corresponding forces. The implications of this result are thoroughly discussed
Bifurcation analysis and phase diagram of a spin-string model with buckled states
We analyze a one-dimensional spin-string model, in which string oscillators
are linearly coupled to their two nearest neighbors and to Ising spins
representing internal degrees of freedom. String-spin coupling induces a
long-range ferromagnetic interaction among spins that competes with a spin-spin
antiferromagnetic coupling. As a consequence, the complex phase diagram of the
system exhibits different flat rippled and buckled states, with first or second
order transition lines between states. The two-dimensional version of the model
has a similar phase diagram, which has been recently used to explain the
rippled to buckled transition observed in scanning tunnelling microscopy
experiments with suspended graphene sheets. Here we describe in detail the
phase diagram of the simpler one-dimensional model and phase stability using
bifurcation theory. This gives additional insight into the physical mechanisms
underlying the different phases and the behavior observed in experiments.Comment: 15 pages, 7 figure
On the role of the chaotic velocity in relativistic kinetic theory
In this paper we revisit the concept of chaotic velocity within the context
of relativistic kinetic theory. Its importance as the key ingredient which
allows to clearly distinguish convective and dissipative effects is discussed
to some detail. Also, by addressing the case of the two component mixture, the
relevance of the barycentric comoving frame is established and thus the
convenience for the introduction of peculiar velocities for each species. The
fact that the decomposition of molecular velocity in systematic and peculiar
components does not alter the covariance of the theory is emphasized. Moreover,
we show that within an equivalent decomposition into space-like and time-like
tensors, based on a generalization of the relative velocity concept, the
Lorentz factor for the chaotic velocity can be expressed explicitly as an
invariant quantity. This idea, based on Ellis' theorem, allows to foresee a
natural generalization to the general relativistic case.Comment: 12 pages, 2 figure
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