Asymmetric simple exclusion process in one-dimensional chains with long-range links

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $\alpha$ and out of a chain at the other boundary at rate $\beta$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $\rho = 0$, a jammed phase with $\rho = 1$, and a shock phase with $0<\rho<1$ where $\rho$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.Comment: revised version (16 pages and 6 eps figures

Eigenfunctions of GL(N,\RR) Toda chain: The Mellin-Barnes representation

The recurrent relations between the eigenfunctions for GL(N,\RR) and GL(N-1,\RR) quantum Toda chains is derived. As a corollary, the Mellin-Barnes integral representation for the eigenfunctions of a quantum open Toda chain is constructed for the $N$-particle case.Comment: Latex+amssymb.sty, 7 pages; corrected some typos published in Pis'ma v ZhETF (2000), vol. 71, 338-34

Phase diagram of two-lane driven diffusive systems

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail

Upscaling of LATP synthesis: Stoichiometric screening of phase purity and microstructure to ionic conductivity maps

Lithium aluminum titanium phosphate (LATP) is known to have a high Li-ion conductivity and is therefore a potential candidate as a solid electrolyte. Via sol-gel route, it is already possible to prepare the material at laboratory scale in high purity and with a maximum Li-ion conductivity in the order of 1·10$^{-3}$ s/cm at room temperature. However, for potential use in a commercial, battery-cell upscaling of the synthesis is required. As a first step towards this goal, we investigated whether the sol-gel route is tolerant against possible deviations in the concentration of the precursors. In order to establish a possible process window for sintering, the temperature interval from 800 °C to 1100 °C and holding times of 10 to 480 min were evaluated. The resulting phase compositions and crystal structures were examined by X-ray diffraction. Impedance spectroscopy was performed to determine the electrical properties. The microstructure of sintered pellets was analyzed by scanning electron microscopy and correlated to both density and ionic conductivity. It is shown that the initial concentration of the precursors strongly influences the formation of secondary phases like AlPO$_{4}$ and LiTiOPO$_{4}$, which in turn have an influence on ionic conductivity, densification behavior, and microstructure evolution

The double Ringel-Hall algebra on a hereditary abelian finitary length category

In this paper, we study the category $\mathscr{H}^{(\rho)}$ of semi-stable coherent sheaves of a fixed slope $\rho$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of $\mathscr{H}^{(\rho)}$ and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.Comment: 29 page