A simple solution of the laminar dam break wave

The sudden release of a mass of fluid in a channel generates a highly unsteady flow motion, called dam break wave. While industrial fluids exhibit sometimes non-Newtonian behaviours, the viscous fluid flow assumption remains a useful approximation for simplified analyses. In this study, new solutions of laminar dam break wave are proposed for a semi-infinite reservoir based upon the method of characteristics. The solutions yield simple explicit expressions of the wave front location, wave front celerity and instantaneous free-surface profiles that compare favourably with experimental observations. Both horizontal and sloping channel configurations are treated. The simplicity of the equations may allow future extension to more complicated fluid flows.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

A new wavelet-based method for the solution of the population balance equation

A new wavelet-based method for solving population balance equations with simultaneous nucleation, growth and agglomeration is proposed, which uses wavelets to express the functions. The technique is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that often characterize previous techniques in this area. It is also applicable to an arbitrary grid to control resolution and computational efficiency. The proposed technique has been tested for pure agglomeration, simultaneous nucleation and growth, and simultaneous growth and agglomeration. In all cases, the predicted and analytical particle size distributions are in excellent agreement. The presence of moving sharp fronts can be addressed without the prior investigation of the characteristics of the processes. (C) 2001 Published by Elsevier Science Ltd.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Solution structure of BSTI: A new trypsin inhibitor from skin secretions of Bombina bombina

The three-dimensional solution structure of BSTI, a trypsin inhibitor from the European frog Bombina bombina, has been solved using H-1 NMR spectroscopy. The 60 amino acid protein contains five disulfide bonds, which were unambiguously determined to be Cvs (4-38), Cys (13-34), Cys (17-30), Cys (21-60), and Cys (40-54) by experimental restraints and subsequent structure calculations. The main elements of secondary structure are four beta -strands, arranged as two small antiparallel beta -sheets, The overall fold of BSTI is disk shaped and is characterized by the lack of a hydrophobic core. The presumed active site is located on a loop comprising residues 21-34, which is a relatively disordered region similar to that seen in many other protease inhibitors. However, the overall fold is different to other known protease inhibitors with the exception of a small family of inhibitors isolated from nematodes of the family Ascaris and recently also from the haemolymph of Apis mellifera. BSTI may thus be classified as a new member of this recently discovered family of protease inhibitors.

The solution structure of C1-T1, a two-domain proteinase inhibitor derived from a circular precursor protein from Nicotiana alata

A two-domain portion of the proteinase inhibitor precursor from Nicotiana alata (NaProPI) has been expressed and its structure determined by NMR spectroscopy. NaProPI contains six almost identical 53 amino acid repeats that fold into six highly similar domains; however, the sequence repeats do nut coincide with the structural domains. Five of the structural domains comprise the C-terminal portion of one repeat and the N-terminal portion of the next. The sixth domain contains the C-terminal portion of the sixth repeat and the N-terminal portion of the first repeat. Disulphide bonds link these C and N-terminal fragments to generate the clasped-bracelet fold of NaProPI. The three-dimensional structure of NaProPI is not known, but it is conceivable that adjacent domains in NaProPI interact to generate the circular bracelet with the N and C termini in close enough proximity to facilitate formation of the disulphide bonds that form the clasp The expressed protein, examined in the current study, comprises residues 25-135 of NaProPI and encompasses the first two contiguous structural domains, namely the chymotrypsin inhibitor C1 and the trypsin inhibitor T1, joined by a five-residue linker, and is referred to as C1-T1. The tertiary structure of each domain in C1-T1 is identical to that found in the isolated inhibitors. However, no nuclear Overhauser effect contacts are observed between the two domains and the five-residue linker adopts an extended conformation. The absence of interactions between the domains indicates that adjacent domains do not specifically interact to drive the circularisation of NaProPI. These results are in agreement with recent data which describe similar PI precursors from other members of the Solanaceae having two, three, or four repeats. The lack of strong interdomain association is likely to be important for the function of individual inhibitors by ensuring that there is no masking of reactive sites upon release from the precursor. (C) 2001 Academic Press.

Three-dimensional structure of RTD-1, a cyclic antimicrobial defensin from rhesus macaque leukocytes

Most mammalian defensins are cationic peptides of 29-42 amino acids long, stabilized by three disulfide bonds. However, recently Tang et al. (1999, Science 286, 498-502) reported the isolation of a new defensin type found in the leukocytes of rhesus macaques. In contrast to all the other defensins found so far, rhesus theta defensin-1 (RTD-1) is composed of just 18 amino acids with the backbone cyclized through peptide bonds. Antibacterial activities of both the native cyclic peptide and a linear form were examined, showing that the cyclic form was 3-fold more active than the open chain analogue [Tang et al. (1999) Science 286, 498-502]. To elucidate the three-dimensional structure of RTD-1 and its open chain analogue, both peptides were synthesized using solid-phase peptide synthesis and tert-butyloxycarbonyl chemistry. The structures of both peptides in aqueous solution were determined from two-dimensional H-1 NMR data recorded at 500 and 750 MHz. Structural constraints consisting of interproton distances and dihedral angles were used as input for simulated-annealing calculations and water refinement with the program CNS. RTD-1 and its open chain analogue oRTD-1 adopt very similar structures in water. Both comprise an extended beta -hairpin structure with turns at one or both ends. The turns are well defined within themselves and seem to be flexible with respect to the extended regions of the molecules. Although the two strands of the beta -sheet are connected by three disulfide bonds, this region displays a degree of flexibility. The structural similarity of RTD-1 and its open chain analogue oRTD-1, as well as their comparable degree of flexibility, support the theory that the additional charges at the termini of the open chain analogue rather than overall differences in structure or flexibility are the cause for oRTD-1's lower antimicrobial activity. In contrast to numerous other antimicrobial peptides, RTD-1 does not display any amphiphilic character, even though surface models of RTD-1 exhibit a certain clustering of positive charges. Some amide protons of RTD-1 that should be solvent-exposed in monomeric beta -sheet structures show low-temperature coefficients, suggesting the possible presence of weak intermolecular hydrogen bonds.

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.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Solution Structures of the cis- and trans-Pro30 Isomers of a Novel 38-Residue Toxin from the Venom of Hadronyche Infensa sp. that Contains a Cystine-Knot Motif within Its Four Disulfide Bonds

The primary sequence and three-dimensional structure of a novel peptide toxin isolated from the Australian funnel-web spider Hadronyche infensa sp. is reported. ACTX-HI:OB4219 contains 38 amino acids, including eight-cysteine residues that form four disulfide bonds. The connectivities of these disulfide bonds were previously unknown but have been unambiguously determined in this study. Three of these disulfide bonds are arranged in an inhibitor cystine-knot (ICK) motif, which is observed in a range of other disulfide-rich peptide toxins. The motif incorporates an embedded ring in the structure formed by two of the disulfides and their connecting backbone segments penetrated by a third disulfide bond. Using NMR spectroscopy, we determined that despite the isolation of a single native homologous product by RP-HPLC, ACTX-HI:OB4219 possesses two equally populated conformers in solution. These two conformers were determined to arise from cis/trans isomerization of the bond preceding Pro30. Full assignment of the NMR spectra for both conformers allowed for the calculation of their structures, revealing, the presence of a triple-stranded antiparallel sheet consistent with the inhibitor cystine-knot (ICK) motif.

Solution structure of CnErg1 (Ergtoxin), a HERG specific scorpion toxin

The three-dimensional structure of chemically synthesized CnErg1 (Ergtoxin), which specifically blocks HERG (human ether-a-go-go-related gene) K+ channels, was determined by nuclear magnetic resonance spectroscopy. CnErg1 consists of a triple-stranded beta-sheet and an a-helix, as is typical of K+ channel scorpion toxins. The peptide structure differs from the canonical structures in that the first beta-strand is shorter and is nearer to the second beta-strand rather than to the third beta-strand on the C-terminus. There is also a large hydrophobic patch on the surface of the toxin, surrounding a central lysine residue, Lys13. We postulate that this hydrophobic patch is likely to form part of the binding surface of the toxin. (C) 2003 Published by Elsevier Science B.V. on behalf of the Federation of European Biochemical Societies.

Solution structure of the cyclotide palicourein: Implications for the development of a pharmaceutical framework

The cyclotides are a family of disulfide-rich proteins from plants. They have the characteristic structural features of a circular protein backbone and a knotted arrangement of disulfide bonds. Structural and biochemical studies of the cyclotides suggest that their unique physiological stability can be loaned to bioactive peptide fragments for pharmaceutical and agricultural development. In particular, the cyclotides incorporate a number of solvent-exposed loops that are potentially suitable for epitope grafting applications. Here, we determine the structure of the largest known cyclotide, palicourein, which has an atypical size and composition within one of the surface-exposed loops. The structural data show that an increase in size of a palicourein loop does not perturb the core fold, to which the thermodynamic and chemical stability has been attributed. The cyclotide core fold, thus, can in principle be used as a framework for the development of useful pharmaceutical and agricultural bioactivities.

Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Isolation and characterization of novel cyclotides from Viola hederaceae - Solution structure and anti-HIV activity of vhl-1, a leaf-specific expressed cyclotide

Based on a newly established sequencing strategy featured by its efficiency, simplicity, and easy manipulation, the sequences of four novel cyclotides (macrocyclic knotted proteins) isolated from an Australian plant Viola hederaceae were determined. The three-dimensional solution structure of V. hederaceae leaf cyclotide-1 ( vhl-1), a leaf-specific expressed 31-residue cyclotide, has been determined using two-dimensional H-1 NMR spectroscopy. vhl-1 adopts a compact and well defined structure including a distorted triple-stranded β- sheet, a short 310 helical segment and several turns. It is stabilized by three disulfide bonds, which, together with backbone segments, form a cyclic cystine knot motif. The three-disulfide bonds are almost completely buried into the protein core, and the six cysteines contribute only 3.8% to the molecular surface. A pH titration experiment revealed that the folding of vhl-1 shows little pH dependence and allowed the pK(a) of 3.0 for Glu(3) and ∼ 5.0 for Glu(14) to be determined. Met(7) was found to be oxidized in the native form, consistent with the fact that its side chain protrudes into the solvent, occupying 7.5% of the molecular surface. vhl-1 shows anti-HIV activity with an EC50 value of 0.87 μ m.