Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

Solution structure of robustoxin, the lethal neurotoxin from the funnel-web spider Atrax robustus

The solution structure of robustoxin, the lethal neurotoxin from the Sydney funnel-web spider Atrax robustus, has been determined from 2D H-1 NMR data, Robustoxin is a polypeptide of 42 residues cross-linked by four disulphide bonds, the connectivities of which were determined from NMR data and trial structure calculations to be 1-15, 8-20, 14-31 and 16-42 (a 1-4/2-6/3-7/5-8 pattern), The structure consists of a small three-stranded, anti-parallel beta-sheet and a series of interlocking gamma-turns at the C-terminus. It also contains a cystine knot, thus placing it in the inhibitor cystine knot motif family of structures, which includes the omega-conotoxins and a number of plant and animal toxins and protease inhibitors. Robustoxin contains three distinct charged patches on its surface, and an extended loop that includes several aromatic and non-polar residues, Both of these structural features may play a role in its binding to the voltage-gated sodium channel. (C) 1997 Federation of European Biochemical Societies.

Solution structure and proposed binding mechanism of a novel potassium channel toxin kappa-conotoxin PVIIA

Background: kappa-PVIIA is a 27-residue polypeptide isolated from the venom of Conus purpurascens and is the first member of a new class of conotoxins that block potassium channels. By comparison to other ion channels of eukaryotic cell membranes, voltage-sensitive potassium channels are relatively simple and methodology has been developed for mapping their interactions with small-peptide toxins, PVIIA, therefore, is a valuable new probe of potassium channel structure. This study of the solution structure and mode of channel binding of PVIIA forms the basis for mapping the interacting residues at the conotoxin-ion channel interface. Results: The three-dimensional structure of PVIIA resembles the triple-stranded beta sheet/cystine-knot motif formed by a number of toxic and inhibitory peptides. Subtle structural differences, predominantly in loops 2 and 4, are observed between PVIIA and other conotoxins with similar structural frameworks, however. Electrophysiological binding data suggest that PVIIA blocks channel currents by binding in a voltage-sensitive manner to the external vestibule and occluding the pore, Comparison of the electrostatic surface of PVIIA with that of the well-characterised potassium channel blocker charybdotoxin suggests a likely binding orientation for PVIIA, Conclusions: Although the structure of PVIIA is considerably different to that of the alpha K scorpion toxins, it has a similar mechanism of channel blockade. On the basis of a comparison of the structures of PVIIA and charybdotoxin, we suggest that Lys19 of PVIIA is the residue which is responsible for physically occluding the pore of the potassium channel.

Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution

A class of integrable boundary terms for the eight-state supersymmetric U model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1998 Elsevier Science B.V.

Analytical solution for the Mollow and Autler-Townes probe absorption spectra of a three-level atom in a squeezed vacuum

The Mellow and Autler-Townes probe absorption spectra of a three-level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed-vacuum field are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mellow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.

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.

Solution structure of amyloid beta-peptide(1-40) in a water-micelle environment. Is the membrane-spanning domain where we think it is?

The three-dimensional solution structure of the 40 residue amyloid beta-peptide, A beta(1-40), has been determined using NMR spectroscopy at pH 5.1, in aqueous sodium dodecyl sulfate (SDS) micelles, In this environment, which simulates to some extent a water-membrane medium, the peptide is unstructured between residues 1 and 14 which are mainly polar and likely solvated by water. However, the rest of the protein adopts an alpha-helical conformation between residues 15 and 36 with a kink or hinge at 25-27. This largely hydrophobic region is likely solvated by SDS. Based on the derived structures, evidence is provided in support of a possible new location for the transmembrane domain of A beta within the amyloid precursor protein (APP). Studies between pH 4.2 and 7.9 reveal a pH-dependent helix-coil conformational switch. At the lower pH values, where the carboxylate residues are protonated, the helix is uncharged, intact, and lipid-soluble. As the pH increases above 6.0, part of the helical region (15-24) becomes less structured, particularly near residues E22 and D23 where deprotonation appears to facilitate unwinding of the helix. This pH-dependent unfolding to a random coil conformation precedes any tendency of this peptide to aggregate to a beta-sheet as the pH increases. The structural biology described herein for A beta(1-40) suggests that (i) the C-terminal two-thirds of the peptide is an alpha-helix in membrane-like environments, (ii) deprotonation of two acidic amino acids in the helix promotes a helix-coil conformational transition that precedes aggregation, (iii) a mobile hinge exists in the helical region of A beta(1-40) and this may be relevant to its membrane-inserting properties and conformational rearrangements, and (iv) the location of the transmembrane domain of amyloid precursor proteins may be different from that accepted in the Literature. These results may provide new insight to the structural properties of amyloid beta-peptides of relevance to Alzheimer's disease.

Solution structure of methionine-oxidized amyloid beta-peptide (1-40). Does oxidation affect conformational switching?

The solution structure of A beta(1-40)Met(O), the methionine-oxidized form of amyloid beta-peptide A beta(1-40), has been investigated by CD and NMR spectroscopy. Oxidation of Met35 may have implications in the aetiology of Alzheimer's disease. Circular dichroism experiments showed that whereas A beta(1-40) and A beta(1-40)Met(O) both adopt essentially random coil structures in water (pH 4) at micromolar concentrations, the former aggregates within several days while the latter is stable for at least 7 days under these conditions. This remarkable difference led us to determine the solution structure of A beta(1-40)Met(O) using H-1 NMR spectroscopy. In a water-SDS micelle medium needed to solubilize both peptides at the millimolar concentrations required to measure NMR spectra, chemical shift and NOE data for A beta(1-40)Met(O) strongly suggest the presence of a helical region between residues 16 and 24. This is supported by slow H-D exchange of amide protons in this region and by structure calculations using simulated annealing with the program XPLOR. The remainder of the structure is relatively disordered. Our previously reported NMR data for A beta(1-40) in the same solvent shows that helices are present over residues 15-24 (helix 1) and 28-36 (helix 2), Oxidation of Met35 thus causes a local and selective disruption of helix 2. In addition to this helix-coil rearrangement in aqueous micelles, the CD data show that oxidation inhibits a coil-to-beta-sheet transition in water. These significant structural rearrangements in the C-terminal region of A beta may be important clues to the chemistry and biology of A beta(1-40) and A beta(1-42).