On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger`s column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger`s column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

New Analytic Solution of Boltzmann Transform for Horizontal Water Infiltration into Sand

The use of the Boltzmann transform function, lambda(theta), to solve the Richards equation when the diffusivity, D, is a function of only soil water content,., is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform lambda(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(theta). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform lambda(theta). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

Nickel adsorption in two Oxisols and an Alfisol as affected by pH, nature of the electrolyte, and ionic strength of soil solution

Background, aim, and scope The retention of potentially toxic metals in highly weathered soils can follow different pathways that variably affect their mobility and availability in the soil-water-plant system. This study aimed to evaluate the effects of pH, nature of electrolyte, and ionic strength of the solution on nickel (Ni) adsorption by two acric Oxisols and a less weathered Alfisol. Materials and methods The effect of pH on Ni adsorption was evaluated in surface and subsurface samples from a clayey textured Anionic `Rhodic` Acrudox ( RA), a sandy-clayey textured Anionic `Xantic` Acrudox (XA), and a heavy clayey textured Rhodic Kandiudalf (RK). All soil samples were equilibrated with the same concentration of Ni solution (5.0 mg L(-1)) and two electrolyte solutions (CaCl(2) or NaCl) with different ionic strengths (IS) (1.0, 0.1 and 0.01 mol L(-1)). The pH of each sample set varied from 3 to 10 in order to obtain sorption envelopes. Results and discussion Ni adsorption increased as the pH increased, reaching its maximum of nearly pH 6. The adsorption was highest in Alfisol, followed by RA and XA. Competition between Ni(2+) and Ca(2+) was higher than that between Ni(2+) and Na(+) in all soil samples, as shown by the higher percentage of Ni adsorption at pH 5. At pH values below the intersection point of the three ionic strength curves (zero point of salt effect), Ni adsorption was generally higher in the more concentrated solution (highest IS), probably due to the neutralization of positive charges of soil colloids by Cl(-) ions and consequent adsorption of Ni(2+). Above this point, Ni adsorption was higher in the more diluted solution (lowest ionic strength), due to the higher negative potential at the colloid surfaces and the lower ionic competition for exchange sites in soil colloids. Conclusions The effect of ionic strength was lower in the Oxisols than in the Alfisol. The main mechanism that controlled Ni adsorption in the soils was the ionic exchange, since the adsorption of ionic species varied according to the variation of pH values. The ionic competition revealed the importance of electrolyte composition and ionic strength on Ni adsorption in soils from the humid tropics. Recommendations and perspectives The presence of NaCl or CaCl(2) in different ionic strengths affects the availability of heavy metals in contaminated soils. Therefore, the study of heavy metal dynamics in highly weathered soils must consider this behavior, especially in soils with large amounts of acric components.

Novel and facile solution-phase synthesis of 2,5-diketopiperazines and O-glycosylated analogs

This work describes the synthesis in Solution of a series of related diketopiperazines with potential biological activities: cyclo(L-Pro-L-Ser), cyclo(L-Phe-L-Ser), cyclo(D-Phe-L-Ser) and the corresponding glycosylated analogs of the latter, cyclo[D-Phe-L-Ser(alpha GlcNAc)] and cyclo[D-Phe-L-Ser(beta GlcNAc)]. The synthetic approach involved coupling reactions of -OH or O-glycosylated serine benzyl esters with NFmoc-protected amino acids (Pro or Phe), followed by one-pot deprotection-cyclization reaction in the presence of 20% piperidine in DMF. (C) 2009 Elsevier Ltd. All rights reserved.

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.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

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.