Statistical properties of inelastic Lorentz gas

The inelastic Lorentz gas in cooling states is studied. It is found that the inelastic Lorentz gas is localized and that the mean square displacement of the inelastic Lorentz gas obeys a power of a logarithmic function of time. It is also found that the scaled position distribution of the inelastic Lorentz gas has an exponential tail, while the distribution is close to the Gaussian near the peak. Using a random walk model, we derive an analytical expression of the mean square displacement as a function of time and the restitution coefficient, which well agrees with the data of our simulation. The exponential tail of the scaled position distribution function is also obtained by the method of steepest descent.Comment: 31pages,9figures, to appear Journal of Physical Society of Japan Vol.70 No.7 (2001

Statistical properties of inelastic Lorentz gas

The inelastic Lorentz gas in cooling states is studied. It is found that the inelastic Lorentz gas is localized and that the mean square displacement of the inelastic Lorentz gas obeys a power of a logarithmic function of time. It is also found that the scaled position distribution of the inelastic Lorentz gas has an exponential tail, while the distribution is close to the Gaussian near the peak. Using a random walk model, we derive an analytical expression of the mean square displacement as a function of time and the restitution coefficient, which well agrees with the data of our simulation. The exponential tail of the scaled position distribution function is also obtained by the method of steepest descent.Comment: 31pages,9figures, to appear Journal of Physical Society of Japan Vol.70 No.7 (2001

Efficient electrochemical model for lithium-ion cells

Lithium-ion batteries are used to store energy in electric vehicles. Physical models based on electro-chemistry accurately predict the cell dynamics, in particular the state of charge. However, these models are nonlinear partial differential equations coupled to algebraic equations, and they are computationally intensive. Furthermore, a variable solid-state diffusivity model is recommended for cells with a lithium ion phosphate positive electrode to provide more accuracy. This variable structure adds more complexities to the model. However, a low-order model is required to represent the lithium-ion cells' dynamics for real-time applications. In this paper, a simplification of the electrochemical equations with variable solid-state diffusivity that preserves the key cells' dynamics is derived. The simplified model is transformed into a numerically efficient fully dynamical form. It is proved that the simplified model is well-posed and can be approximated by a low-order finite-dimensional model. Simulations are very quick and show good agreement with experimental data

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a-priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.Comment: 25 pages, 11 figure

Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations

We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find agree with direct simulation of the model and seem to have some stability