692 research outputs found
An exactly solvable model of a highly efficient thermoelectric engine
We propose a simple classical dynamical model of a thermoelectric (or
thermochemical) heat engine based on a pair of ideal gas containers connected
by two unequal scattering channels. The model is solved analytically and it is
shown that a suitable combination of parameters can be chosen such that the
engine operates at Carnot's efficiency.Comment: 4 pages, 3 figure
An Autonomous Reference Frame for Relativistic GNSS
Current GNSS systems rely on global reference frames which are fixed to the
Earth (via the ground stations) so their precision and stability in time are
limited by our knowledge of the Earth dynamics. These drawbacks could be
avoided by giving to the constellation of satellites the possibility of
constituting by itself a primary and autonomous positioning system, without any
a priori realization of a terrestrial reference frame. Our work shows that it
is possible to construct such a system, an Autonomous Basis of Coordinates, via
emission coordinates. Here we present the idea of the Autonomous Basis of
Coordinates and its implementation in the perturbed space-time of Earth, where
the motion of satellites, light propagation, and gravitational perturbations
are treated in the formalism of general relativity.Comment: 5 pages, 3 figures, in proceedings of the 4th International
Colloquium: Scientific and Fundamental Aspects of the Galileo Programme, 4-6
December 2013, Prague, Czech Republic; removed unnecessary indices from eqs.
3,6,7 and corrected minus signs in eqs. 6 and
Nanocoolers
We present a simple kinematic model of a non-equilibrium steady state device,
which can operate either as a heat engine or as a refrigerator. The model is
composed of two or more scattering channels where the motion is fully described
by deterministic classical dynamics, which connect a pair of stochastic
(infinite) heat and particle baths at unequal temperatures. We discuss precise
kinematic conditions under which our model may approach Carnot's optimal
efficiency in different situations.Comment: 21 pages, 9 figure
Dynamical and statistical properties of estimated high-dimensional ODE models: The case of the Lorenz'05 type II model
The performance of estimated models is often evaluated in terms of their
predictive capability. In this study, we investigate another important aspect
of estimated model evaluation: the disparity between the statistical and
dynamical properties of estimated models and their source system. Specifically,
we focus on estimated models obtained via the regression method, sparse
identification of nonlinear dynamics (SINDy), one of the promising algorithms
for determining equations of motion from time series of dynamical systems. We
chose our data source dynamical system to be a higher-dimensional instance of
the Lorenz 2005 type II model, an important meteorological toy model. We
examine how the dynamical and statistical properties of the estimated models
are affected by the standard deviation of white Gaussian noise added to the
numerical data on which the estimated models were fitted. Our results show that
the dynamical properties of the estimated models match those of the source
system reasonably well within a range of data-added noise levels, where the
estimated models do not generate divergent (unbounded) trajectories.
Additionally, we find that the dynamics of the estimated models become
increasingly less chaotic as the data-added noise level increases. We also
perform a variance analysis of the (SINDy) estimated model's free parameters,
revealing strong correlations between parameters belonging to the same
component of the estimated model's ordinary differential equation.Comment: 13 pages + refs, 10 figure
Egorov property in perturbed cat map
We study the time evolution of the quantum-classical correspondence (QCC) for
the well known model of quantised perturbed cat maps on the torus in the very
specific regime of semi-classically small perturbations. The quality of the QCC
is measured by the overlap of classical phase-space density and corresponding
Wigner function of the quantum system called quantum-classical fidelity (QCF).
In the analysed regime the QCF strongly deviates from the known general
behaviour in particular it decays faster then exponential. Here we study and
explain the observed behavior of the QCF and the apparent violation of the QCC
principle.Comment: 12 pages, 7 figure
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