Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].

Solution of adsorption problems involving steep moving profiles

The moving finite element collocation method proposed by Kill et al. (1995) Chem. Engng Sci. 51 (4), 2793-2799 for solution of problems with steep gradients is further developed to solve transient problems arising in the field of adsorption. The technique is applied to a model of adsorption in solids with bidisperse pore structures. Numerical solutions were found to match the analytical solution when it exists (i.e. when the adsorption isotherm is linear). The method is simple yet sufficiently accurate for use in adsorption problems, where global collocation methods fail. (C) 1998 Elsevier Science Ltd. All rights reserved.

New integrable boundary conditions for the q-deformed supersymmetric U model and Bethe ansatz equations

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Nine classes of integrable boundary conditions for the eight-state supersymmetric fermion model

Nine classes of integrable boundary conditions for the eight-state supersymmetric model of strongly correlated fermions are presented. The boundary systems are solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations for all nine cases are given.

Measurement of grain boundary composition for X52 pipeline steel

Analytical electron microscopy was used to measure the composition of grain boundaries (GBs) and interconstituent boundaries (IBs) of X52 pipeline steel using specimens about 40-60 nm in thickness. All elements of interest were examined with the exception of carbon. With this caveat; there was no segregation at proeutectoid ferrite GBs. This indicated that the commonly expected species S and P are not responsible for preferential corrosion of GBs during intergranular stress corrosion cracking of pipeline steels. Manganese was the only species measured to segregate at the IBs. Manganese segregated to the IBs between proeutectoid ferrite and pearlitic cementite, and desegregated from IBs between proeutectoid ferrite and pearlitic ferrite. The pearlitic cementite was Mn rich. There was no Mn segregation at the IBs between pearlitic ferrite and pearlitic cementite. The pattern of Mn segregation could be explained in terms of diffusion in the process zone ahead of the pearlite during the austenite to pearlite transformation and diffusion in the IBs between the proeutectoid ferrite and pearlite. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Implications of specimen preparation and of surface contamination for the measurement of the grain boundary carbon concentration of steels using x-ray microanalysis in an UHVFESTEM

The purpose of the present investigation was to gain an understanding of the nature of the carbon contamination on the surface of standard steel transmission electron spectroscopy (TEM) specimens, the effect of exposure of a clean specimen to normal laboratory air, and the efficacy of plasma-cleaning treatments. This knowledge is a necessary prerequisite to the development of appropriate specimen preparation and/or specimen cleaning methods. X-ray photoelectron spectroscopy in combination with argon ion beam profiling was used to characterize the specimen surfaces of X65 steel and 316 stainless steel. The only clean carbon-free surface obtained was that during argon etching of the sample in the surface analysis chamber. Any exposure of a previously cleaned sample to laboratory air resulted in a rapid carbon (hydrocarbon) contamination of the sample surface and the development of surface oxidation, Plasma cleaning with subsequent exposure of the specimen to the laboratory air also resulted in a carbon-contaminated surface. This suggests that procedures of preparation of TEM specimens of steels outside an ultrahigh vacuum chamber are unlikely to result in the lowering of contamination rates on specimens to levels where measurements for carbon in the grain boundaries are possible. What is needed is a cleaning system as an integral part of the specimen insertion system into the field-emission scanning transmission electron microscope. This cleaning could be carried out by argon ion etching. Copyright (C) 2000 John Wiley & Sons, Ltd.

The q-deformed supersymmetric t-J model with a boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U-q[sl(2\1)]. We. give the bosonization of the boundary states. We give an integral expression for the correlation functions of the boundary model, and derive the difference equations which they satisfy.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Turbulent spots in boundary layers in a free-piston shock-tunnel flow

In this paper, experiments to detect turbulent spots in the transitional boundary layers, formed on a flat plate in a free-piston shock tunnel how, are reported. Experiments indicate that thin-film heat-transfer gauges are suitable for identifying turbulent-spot activity and can be used to identify parameters such as the convection rate of spots and the intermittency of turbulence.