866 research outputs found
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 different pairs of sites selected randomly where and
denote the chain length and the shortcut density, respectively. Particles flow
into a chain at one boundary at rate and out of a chain at the other
boundary at rate , 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 , a jammed phase with , and a shock phase
with where 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 -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 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 and LiTiOPO, 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 of semi-stable
coherent sheaves of a fixed slope 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 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
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