Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalize classes of integrable models relevant to the description of Bose-Einstein condensation in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra. (C) 2003 American Institute of Physics.

Numerical investigation of turbulent flow around a rotating stepped cylinder for corrosion study

Direct numerical simulation has been carried out for turbulent flow set up by a rotating cylinder with two backward-facing steps axisymmetrically mounted in the circumferential direction. This flow geometry creates a qualitatively similar flow pattern as observed near, a sudden, pipe expansion or a plane backward-facing step, characterized by flow separation and reattachment. A region of intense turbulence intensity and high wall-shear-stress fluctuations is formed in,the recirculating I region downstream of the step, where high mass-transfer capacity was also experimentally observed. Since, corrosion is frequently mass-transfer., controlled, our findings, put forward this apparatus as useful tool for future corrosion research.

Heat transfer and flow behind a step in high enthalpy superorbital flow

Heat transfer levels have been investigated behind a rearward-facing step in a superorbital expansion tube. The heat transfer was measured along a flat plate and behind 2 and 3mm steps with the same length to step height ratio. Results were obtained with air as the test gas at speeds of 6.76kms(-1) and 9-60kms(-1) corresponding to stagnation enthalpies of 26MJ/kg and 48MJ/kg respectively. A laminar boundary layer was established on the flat plate and measured heat transfer levels were consistent with classical empirical correlations. In the case of flow behind a step, the measurements showed a gradual rise in heat transfer from the rear of the step to a plateau several step heights downstream for both flow conditions. Reattachment distance was estimated to be approximately 1.6 step heights downstream of the 2mm step at the low enthalpy condition through the use of flow visualisation.

Linking physiological and architectural models of cotton

Despite the strong influence of plant architecture on crop yield, most crop models either ignore it or deal with it in a very rudimentary way. This paper demonstrates the feasibility of linking a model that simulates the morphogenesis and resultant architecture of individual cotton plants with a crop model that simulates the effects of environmental factors on critical physiological processes and resulting yield in cotton. First the varietal parameters of the models were made concordant. Then routines were developed to allocate the flower buds produced each day by the crop model amongst the potential positions generated by the architectural model. This allocation is done according to a set of heuristic rules. The final weight of individual bolls and the shedding of buds and fruit caused by water, N, and C stresses are processed in a similar manner. Observations of the positions of harvestable fruits, both within and between plants, made under a variety of agronomic conditions that had resulted in a broad range of plant architectures were compared to those predicted by the model with the same environmental inputs. As illustrated by comparisons of plant maps, the linked models performed reasonably well, though performance of the fruiting point allocation and shedding algorithms could probably be improved by further analysis of the spatial relationships of retained fruit. (C) 2002 Elsevier Science Ltd. All rights reserved.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Gene flow in great bustard populations across the Strait of Gibraltar as elucidated from excremental PCR and mtDNA sequencing

Recent advances in molecular biology have made it possible to use the trace amounts of DNA in faeces to non-invasively sample endangered species for genetic studies. Here we use faeces as a source of DNA and mtDNA sequence data to elucidate the relationship among Spanish and Moroccan populations of great bustards. 834 bp of combined control region and cytochrome-b mtDNA fragments revealed four variable sites that defined seven closely related haplotypes in 54 individuals. Morocco was fixed for a single mtDNA haplotype that occurs at moderate frequency (28%) in Spain. We could not differentiate among the sampled Spanish populations of Caceres and Andalucia but these combined populations were differentiated from the Moroccan population. Estimates of gene flow (Nm = 0.82) are consistent with extensive observations on the southern Iberian peninsular indicating that few individuals fly across the Strait of Gibraltar. We demonstrate that both this sea barrier and mountain barriers in Spain limit dispersal among adjacent great bustard populations to a similar extent. The Moroccan population is of high ornithological significance as it holds the only population of great bustards in Africa. This population is critically small and genetic and observational data indicate that it is unlikely to be recolonised via immigration from Spain should it be extirpated. In light of the evidence presented here it deserves the maximum level of protection.

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B-k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B(mum)s) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B(mum)s for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the surface diffusion mechanism in activated carbon. (C) 2003 Elsevier Ltd. All rights reserved.