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Reinforcement Learning for Hybrid and Plug-In Hybrid Electric Vehicle Energy Management: Recent Advances and Prospects
Condensation of Eigen Microstate in Statistical Ensemble and Phase Transition
In a statistical ensemble with microstates, we introduce an
correlation matrix with the correlations between microstates as its elements.
Using eigenvectors of the correlation matrix, we can define eigen microstates
of the ensemble. The normalized eigenvalue by represents the weight factor
in the ensemble of the corresponding eigen microstate. In the limit , weight factors go to zero in the ensemble without localization of
microstate. The finite limit of weight factor when indicates a
condensation of the corresponding eigen microstate. This indicates a phase
transition with new phase characterized by the condensed eigen microstate. We
propose a finite-size scaling relation of weight factors near critical point,
which can be used to identify the phase transition and its universality class
of general complex systems. The condensation of eigen microstate and the
finite-size scaling relation of weight factors have been confirmed by the Monte
Carlo data of one-dimensional and two-dimensional Ising models.Comment: 9 pages, 16 figures, accepted for publication in Sci. China-Phys.
Mech. Astro
A Two-stage Polynomial Method for Spectrum Emissivity Modeling
Spectral emissivity is a key in the temperature measurement by radiation methods, but not easy to determine in a combustion environment, due to the interrelated influence of temperature and wave length of the radiation. In multi-wavelength radiation thermometry, knowing the spectral emissivity of the material is a prerequisite. However in many circumstances such a property is a complex function of temperature and wavelength and reliable models are yet to be sought. In this study, a two stages partition low order polynomial fitting is proposed for multi-wavelength radiation thermometry. In the first stage a spectral emissivity model is established as a function of temperature; in the second stage a mathematical model is established to describe the dependence of the coefficients corresponding to the wavelength of the radiation. The new model is tested against the spectral emissivity data of tungsten, and good agreement was found with a maximum error of 0.64
Orbital stability of smooth solitary waves for the -family of Camassa-Holm equations
In this paper, we study the stability of smooth solitary waves for the
-family of Camassa-Holm equations. We verify the stability criterion
analytically for the general case by the idea of the monotonicity of the
period function for planar Hamiltonian systems and show that the smooth
solitary waves are orbitally stable, which gives a positive answer to the open
problem proposed by Lafortune and Pelinovsky [S. Lafortune, D. E. Pelinovsky,
Stability of smooth solitary waves in the -Camassa-Holm equation]
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