Generalizations of Poisson Structures Related to Rational Gaudin Model

International audience

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Hexagonal mesoporous silica modified with 2-mercaptothiazoline for removing mercury from water solution

A method for the attachment of 2-mercaptothiazoline (MTZ) to modified silica gel has been developed. In the first step, a new silylant agent was synthesized, named SiMTZ, by the reaction between MTZ molecule and chloropropyltrimethoxysilane (SiCl). SiMTZ and tetraethylortosilicate were co-condensed in the presence of n-dodecylamine, a neutral surfactant template, to produce a modified ordered hexagonal mesoporous silica named HMTZ. The modified material contained 0.89 +/- 0.03 mmol of 2-mercaptothiazoline per gram of silica. FT-IR, FT-Raman, Si-29- and C-13-NMR spectra were in agreement with the proposed structure of the modified mesoporous silica in the solid state. HMTZ material has been used for divalent mercury adsorption from aqueous solution at 298 I K. The series of adsorption isotherms were adjusted to a modified Langmuir equation. The maximum number of moles of mercury adsorbed gave 2.34 +/- 0.09 mmol/g of material. The same interaction was followed by calorimetric titration on an isoperibol calorimeter. The HMTZ presented a high capacity for the removal of the contaminant mercury from water. The Delta H and Delta G values for the interaction were determined to be -56.34 +/- 1.07 and -2.14 +/- 0.11 kJ mol(-1). This interaction process was accompanied by a decrease of entropy value (- 182 J mol(-1) K-1). Thus, the interaction between mercury and HMTZ resulted in a spontaneous thermodynamic system with a high favorable exothermic enthalpic effect. (c) 2007 Elsevier B.V. All rights reserved.

4-amine-2-mercaptopyrimidine modified silica gel applied in Cd(II) and Pb(II) extraction from an aqueous medium

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Preconcentration and determination of Cu(II) in a fresh water sample using modified silica gel as a solid-phase extraction adsorbent

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synthesis, characterization, and application of modified silica in the removal and preconcentration of lead ions from natural river water

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Concentration of Cu(II) and Cd(II) from natural river water by Adsorption on a Modified Silica Surface

A high surface area silica gel (737 ± m2 g-1) was synthesized modified through a two-step reaction with a 4-amino-2-mercaptopyrimidine ligand and applied to Cu(II) and Cd(II) adsorption from an aqueous medium. The modified material was characterized by FTIR, which showed that attachment of the molecule occurred via thiol groups at 2547 and 2600 cm-1, and by elemental analysis that indicated the presence of 0.0102 mmol of ligand. The data from adsorption experiments were adjusted to a modified Langmuir equation and the maximum adsorption capacity was 6.6 and 3.8 μmol g-1 for Cu(II) and Cd(II), respectively. After adjusting several parameters, the material was applied in the preconcentration of natural river water using a continuous flow system before and after sample mineralization, and the results showed a 10-fold enrichment factor. The proposed method was validated through preconcentration and analysis of certified standard reference material (1643e), whose results were in agreement with the values provided by the manufacturer.

Microemulsion: prediction of the phase diagram with a modified Helfrich free energy

Microemulsions are thermodynamically stable, macroscopically homogeneous but microscopically heterogeneous, mixtures of water and oil stabilised by surfactant molecules. They have unique properties like ultralow interfacial tension, large interfacial area and the ability to solubilise other immiscible liquids. Depending on the temperature and concentration, non-ionic surfactants self assemble to micelles, flat lamellar, hexagonal and sponge like bicontinuous morphologies. Microemulsions have three different macroscopic phases (a) 1phase- microemulsion (isotropic), (b) 2phase-microemulsion coexisting with either expelled water or oil and (c) 3phase- microemulsion coexisting with expelled water and oil.rnrnOne of the most important fundamental questions in this field is the relation between the properties of the surfactant monolayer at water-oil interface and those of microemulsion. This monolayer forms an extended interface whose local curvature determines the structure of the microemulsion. The main part of my thesis deals with the quantitative measurements of the temperature induced phase transitions of water-oil-nonionic microemulsions and their interpretation using the temperature dependent spontaneous curvature [c0(T)] of the surfactant monolayer. In a 1phase- region, conservation of the components determines the droplet (domain) size (R) whereas in 2phase-region, it is determined by the temperature dependence of c0(T). The Helfrich bending free energy density includes the dependence of the droplet size on c0(T) as

The anisotropic λ -deformed SU(2) model is integrable

The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang–Baxter equation.

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Nurse-determined assessment of cardiac output. Comparing a non-invasive cardiac output device and pulmonary artery catheter: a prospective observational study.

Background The accurate measurement of Cardiac output (CO) is vital in guiding the treatment of critically ill patients. Invasive or minimally invasive measurement of CO is not without inherent risks to the patient. Skilled Intensive Care Unit (ICU) nursing staff are in an ideal position to assess changes in CO following therapeutic measures. The USCOM (Ultrasonic Cardiac Output Monitor) device is a non-invasive CO monitor whose clinical utility and ease of use requires testing. Objectives To compare cardiac output measurement using a non-invasive ultrasonic device (USCOM) operated by a non-echocardiograhically trained ICU Registered Nurse (RN), with the conventional pulmonary artery catheter (PAC) using both thermodilution and Fick methods. Design Prospective observational study. Setting and participants Between April 2006 and March 2007, we evaluated 30 spontaneously breathing patients requiring PAC for assessment of heart failure and/or pulmonary hypertension at a tertiary level cardiothoracic hospital. Methods SCOM CO was compared with thermodilution measurements via PAC and CO estimated using a modified Fick equation. This catheter was inserted by a medical officer, and all USCOM measurements by a senior ICU nurse. Mean values, bias and precision, and mean percentage difference between measures were determined to compare methods. The Intra-Class Correlation statistic was also used to assess agreement. The USCOM time to measure was recorded to assess the learning curve for USCOM use performed by an ICU RN and a line of best fit demonstrated to describe the operator learning curve. Results In 24 of 30 (80%) patients studied, CO measures were obtained. In 6 of 30 (20%) patients, an adequate USCOM signal was not achieved. The mean difference (±standard deviation) between USCOM and PAC, USCOM and Fick, and Fick and PAC CO were small, −0.34 ± 0.52 L/min, −0.33 ± 0.90 L/min and −0.25 ± 0.63 L/min respectively across a range of outputs from 2.6 L/min to 7.2 L/min. The percent limits of agreement (LOA) for all measures were −34.6% to 17.8% for USCOM and PAC, −49.8% to 34.1% for USCOM and Fick and −36.4% to 23.7% for PAC and Fick. Signal acquisition time reduced on average by 0.6 min per measure to less than 10 min at the end of the study. Conclusions In 80% of our cohort, USCOM, PAC and Fick measures of CO all showed clinically acceptable agreement and the learning curve for operation of the non-invasive USCOM device by an ICU RN was found to be satisfactorily short. Further work is required in patients receiving positive pressure ventilation.

Operation and control of a microgrid containing inertial and non-inertial micro sources

In this paper, a new power sharing control method for a microgrid with several distributed generation units is proposed. The presence of both inertial and noninertial sources with different power ratings, maximum power point tracking, and various types of loads pose a great challenge for the power sharing and system stability. The conventional droop control method is modified to achieve the desired power sharing ensuring system stability in a highly resistive network. A transformation matrix is formed to derive equivalent real and reactive power output of the converter and equivalent feedback gain matrix for the modified droop equation. The proposed control strategy, aimed for the prototype microgrid planned at Queensland University of Technology, is validated through extensive simulation results using PSCAD/EMTDC software.