The IWA Anaerobic Digestion Model No 1 (ADM1)

The IWA Anaerobic Digestion Modelling Task Group was established in 1997 at the 8th World Congress on,Anaerobic Digestion (Sendai, Japan) with the goal of developing a generalised anaerobic digestion model. The structured model includes multiple steps describing biochemical as well as physicochemical processes. The biochemical steps include disintegration from homogeneous particulates to carbohydrates, proteins and lipids; extracellular hydrolysis of these particulate substrates to sugars, amino acids, and long chain fatty acids (LCFA), respectively; acidogenesis from sugars and amino acids to volatile fatty acids (VFAs) and hydrogen; acetogenesis of LCFA and VFAs to acetate; and separate methanogenesis steps from acetate and hydrogen/CO2. The physico-chemical equations describe ion association and dissociation, and gas-liquid transfer. Implemented as a differential and algebraic equation (DAE) set, there are 26 dynamic state concentration variables, and 8 implicit algebraic variables per reactor vessel or element. Implemented as differential equations (DE) only, there are 32 dynamic concentration state variables.

A(2)((2)) parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A(2)((2))/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)((2)) parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two. (C) 2002 Published by Elsevier Science B.V.

Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model within the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Integrable variant of the one-dimensional Hubbard model

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the eta-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. (C) 2002 American Institute of Physics.

Effects of slurry rheology on industrial grinding performance

To determine the effect of slurry rheology on industrial grinding performance, 45 surveys were conducted on 16 full-scale grinding mills in five sites. Four operating variables - mill throughput, slurry density, slurry viscosity and feed fines content-were investigated. The rheology of the mill discharge slurries was measured either on-line or off-line, and the data were processed using a standard procedure to obtain a full range of flow curves. Multi-linear regression was employed as a statistical analysis tool to determine whether or not rheological effects exert an influence on industrial grinding, and to assess the influence of the four mill operating conditions on mill performance in terms of the Grinding Index, a criterion describing the overall breakage of particles across the mill. The results show that slurry rheology does influence industrial grinding. The trends of these effects on Grinding Index depend upon the rheological nature of the slurry-whether the slurries are dilatant or pseudoplastic, and whether they exhibit a high or low yield stress. The interpretation of the regression results is discussed, the observed effects are summarised, and the potential for incorporating rheological principles into process control is considered, Guidelines are established to improve industrial grinding operations based on knowledge of the rheological effects. This study confirms some trends in the effect of slurry rheology on grinding reported in the literature, and extends these to a broader understanding of the relationship between slurry properties and rheology, and their effects on industrial milling performance. (C) 2002 Elsevier Science B.V. All rights reserved.

Growth of a Bose-Einstein condensate: a detailed comparison of theory and experiment

We extend the earlier model of condensate growth of Davis et at (Davis M J, Gardiner C W and Ballagh R J 2000 Phys. Rev. A 62 063608) to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by Kohl et al (Kohl M, Davis M J, Gardiner C W, Hansch T and Esslinger T 2001 Preprint cond-mat/0106642) who study the formation of a rubidium Bose-Einstein condensate for a range of evaporative cooling parameters. We find that, in the regime where our model is valid, the theoretical curves agree with all the experimental data with no fitting parameters. However, for the slowest cooling of the gas the theoretical curve deviates significantly from the experimental curves. It is possible that this discrepancy may be related to the formation of a quasicondensate.

An in situ study of photosynthetic oxygen exchange and electron transport rate in the marine macroalga Ulva lactuca (Chlorophyta)

Direct comparisons between photosynthetic O-2 evolution rate and electron transport rate (ETR) were made in situ over 24 h using the benthic macroalga Ulva lactuca (Chlorophyta), growing and measured at a depth of 1.8 m, where the midday irradiance rose to 400-600 mumol photons m(-2) s(-1). O-2 exchange was measured with a 5-chamber data-logging apparatus and ETR with a submersible pulse amplitude modulated (PAM) fluorometer (Diving-PAM). Steady-state quantum yield ((Fm'-Ft)/Fm') decreased from 0.7 during the morning to 0.45 at midday, followed by some recovery in the late afternoon. At low to medium irradiances (0-300 mumol photons m(-2) s(-1)), there was a significant correlation between O-2 evolution and ETR, but at higher irradiances, ETR continued to increase steadily, while O-2 evolution tended towards an asymptote. However at high irradiance levels (600-1200 mumol photons m-(2) s(-1)) ETR was significantly lowered. Two methods of measuring ETR, based on either diel ambient light levels and fluorescence yields or rapid light curves, gave similar results at low to moderate irradiance levels. Nutrient enrichment (increases in [NO3-], [NH4+] and [HPO42-] of 5- to 15-fold over ambient concentrations) resulted in an increase, within hours, in photosynthetic rates measured by both ETR and O-2 evolution techniques. At low irradiances, approximately 6.5 to 8.2 electrons passed through PS II during the evolution of one molecule of O-2, i.e., up to twice the theoretical minimum number of four. However, in nutrient-enriched treatments this ratio dropped to 5.1. The results indicate that PAM fluorescence can be used as a good indication of the photosynthetic rate only at low to medium irradiances.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D-obs, for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D-obs, in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2) s(-1). For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.

Supersymmetric t-J Gaudin models and KZ equations

Supersymmetric t-J Gaudin models with open boundary conditions are investigated by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the boundary Gaudin systems are derived, and used to construct and solve the KZ equations associated with sl (2\1)((1)) superalgebra.

Effects of vitamin E deficiency on fatigue and muscle contractile properties

Radical-mediated oxidative damage of skeletal muscle membranes has been implicated in the fatigue process. Vitamin E (VE) is a major chain breaking antioxidant that has been shown to reduce contraction-mediated oxidative damage. We hypothesized that VE deficiency would adversely affect Muscle contractile function, resulting in a more rapid development of muscular fatigue during exercise. To test this postulate, rats were fed either a VE-deficient (EDEF) diet or a control (CON) diet containing VE. Following a 12-week feeding period, animals were anesthetized and mechanically ventilated. Muscle endurance (fatigue) and contractile properties were evaluated using an in situ preparation of the tibialis anterior (TA) muscle. Contractile properties of the TA muscle were determined before and after a fatigue protocol. The muscle fatigue protocol consisted of 60 min of repetitive contractions (250 ms trains at 15 Hz; duty cycle = I I %) of the TA muscle. Prior to the fatigue protocol, no significant differences existed in the force-frequency curves between EDEF and CON animals. At the completion of the fatigue protocol, muscular force production was significantly (P

An age hardening model for Al-7Si-Mg casting alloys

Yield strength (YS) ageing curves have been modelled for A356 and A357 aluminium casting alloys below the solvus temperature of the main hardening precipitate. Predictions are based on the Shercliff and Ashby methodology (Acta MetaH. Mater. 38 (1990) 1789) for wrought alloys. Differences between strengthening in wrought and cast Al-Si-Mg alloys are considered. A Brinell hardness to YS conversion incorporating strain hardening has been established to enable YS ageing curves to be predicted with reduced experimental effort. (C) 2002 Elsevier Science B.V. All rights reserved.

A four-stage index 2 Diagonally Implicit Runge-Kutta method

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.