arXiv subjects

Andrea Carati

Publications and source records attributed to Andrea Carati.

23 records · Page 2Linked to original sources

arXiv2014

Theoretical thermodynamic analysis of a closed-cycle process for the conversion of heat into electrical energy by means of a distiller and an electrochemical cell

We analyse a device aimed at the conversion of heat into electrical energy, based on a closed cycle in which a distiller generates two solutions at different concentrations, and an electrochemical cell consumes the concentration difference, converting it into electrical current. We first study an ideal model of such a process. We show that, if the device works at a single fixed pressure (i.e. with a ``single effect''), then the efficiency of the conversion of heat into electrical power can approach the efficiency of a reversible Carnot engine operating between the boiling temperature of the concentrated solution and that of the pure solvent. When two heat reservoirs with a higher temperature difference are available, the overall efficiency can be incremented by employing an arrangement of multiple cells working at different pressures (``multiple effects''). We find that a given efficiency can be achieved with a reduced number of effects by using solutions with a high boiling point elevation.

physics.chem-ph↗

arXiv2013

An averaging theorem for FPU in the thermodynamic limit

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $β^{-1}$. Given a fixed $K 0$) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $β$. The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\to\infty$, $β>0$.

math-ph↗

arXiv2012

Transition to chaos in magnetized, weakly coupled plasmas

We report the results of numerical simulations for a model of a one component plasma (a system of N point electrons with mutual Coulomb interactions) in a uniform stationary magnetic field. We take N up to 512, with periodic boundary conditions, and macroscopic parameters corresponding to the weak coupling regime, with a coupling parameter Γ=1/64. We find that a transition from order to chaos takes place when the density is increased or the field decreased so that the ratio ω_p/ω_c between plasma and cyclotron frequencies becomes of order 1 (or equivalently the ratio r_L/λ_D between Larmor radius and Debye length becomes of order 1). The result is in agreement with the theoretical prediction obtained in [1], on the basis of an old estimate of Iglesias, Lebowitz and MacGowan [2] for the intensity of the electric field acting on one electron and due to all the other ones. A comparison can be made with the threshold obtained from kinetic theory arguments, which corresponds to the condition ν_{ee}/ω_c=1, where ν_{ee} is the electron collision frequency. The latter threshold has a completely different dependence on the physical parameters and, for Γ=1/64, gives a critical value of ω_p about 80 times larger.

cond-mat.stat-mech↗

arXiv2012

A series expansion for the time autocorrelation of dynamical variables

We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical in nature, which enable one to decide whether the decay of the correlations is exponentially fast or not. One of these criteria is implemented numerically for the case of the Fermi-Pasta-Ulam system, and we find indications which might suggest a sub-exponential decay of the time autocorrelation of a relevant dynamical variable.

math-ph↗

arXiv2011

Exponentially long stability times for a nonlinear lattice in the thermodynamic limit

In this paper, we construct an adiabatic invariant for a large 1--$d$ lattice of particles, which is the so called Klein Gordon lattice. The time evolution of such a quantity is bounded by a stretched exponential as the perturbation parameters tend to zero. At variance with the results available in the literature, our result holds uniformly in the thermodynamic limit. The proof consists of two steps: first, one uses techniques of Hamiltonian perturbation theory to construct a formal adiabatic invariant; second, one uses probabilistic methods to show that, with large probability, the adiabatic invariant is approximately constant. As a corollary, we can give a bound from below to the relaxation time for the considered system, through estimates on the autocorrelation of the adiabatic invariant.

math-ph↗