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Second Order (second + order)
Selected AbstractsReactivity Pattern in the Room-Temperature Activation of NH3 by the Main-Group Atomic Ions Ga+, Ge+, As+ and Se+EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 10 2010Gregory K. Koyanagi Abstract The activation of ammonia by the main-group cations Ga+, Ge+, As+ and Se+ has been explored both experimentally and theoretically. ICP/SIFT tandem mass spectrometer measurements of room-temperature kinetics have revealed a substantial variation in rates and product distributions across the Periodic Table of Elements. The main features of the observed primary chemistry include H-atom elimination, ammonia addition and a cation-assisted proton transfer to yield NH4+ that is second order in ammonia. These observations are shown to be completely consistent with computed potential energy surfaces for the reactions of each of the four atomic cations. Dehydrogenation by the elimination of molecular hydrogen, not observed experimentally, is shown by the calculations to be inhibited by the presence of a kinetic barrier. [source] Kinetics and mechanism of the reaction between maleic anhydride and fatty acid esters and the structure of the productsEUROPEAN JOURNAL OF LIPID SCIENCE AND TECHNOLOGY, Issue 5 2008Florina Stefanoiu Abstract Alkenyl succinic anhydrides (ASA) were obtained by reaction between maleic anhydride and high-oleic sunflower oil (HOSO) esters. A kinetics study of the maleinization of alkyl esters indicated that the maleinization reaction was second order overall and first order with respect to the individual reactants, and the activation energy was 77.2,±,3.3,kJ/mol in the investigated temperature range (185,225,°C). These results showed that the cis configuration and the central position of the double bond in HOSO esters facilitate the maleinization of the latter. On the contrary, the length of the linear ester moiety had no influence on the course of the maleinization reaction. Moreover, new evidence demonstrates that there are two different reaction mechanisms: ene-reaction and addition in allylic position with a 2,:,1 ratio, respectively. This ratio was constant throughout the reaction, thus indicating that these mechanisms are independent. [source] Traveltime computation by wavefront-orientated ray tracingGEOPHYSICAL PROSPECTING, Issue 1 2005Radu Coman ABSTRACT For multivalued traveltime computation on dense grids, we propose a wavefront-orientated ray-tracing (WRT) technique. At the source, we start with a few rays which are propagated stepwise through a smooth two-dimensional (2D) velocity model. The ray field is examined at wavefronts and a new ray might be inserted between two adjacent rays if one of the following criteria is satisfied: (1) the distance between the two rays is larger than a predefined threshold; (2) the difference in wavefront curvature between the rays is larger than a predefined threshold; (3) the adjacent rays intersect. The last two criteria may lead to oversampling by rays in caustic regions. To avoid this oversampling, we do not insert a ray if the distance between adjacent rays is smaller than a predefined threshold. We insert the new ray by tracing it from the source. This approach leads to an improved accuracy compared with the insertion of a new ray by interpolation, which is the method usually applied in wavefront construction. The traveltimes computed along the rays are used for the estimation of traveltimes on a rectangular grid. This estimation is carried out within a region bounded by adjacent wavefronts and rays. As for the insertion criterion, we consider the wavefront curvature and extrapolate the traveltimes, up to the second order, from the intersection points between rays and wavefronts to a gridpoint. The extrapolated values are weighted with respect to the distances to wavefronts and rays. Because dynamic ray tracing is not applied, we approximate the wavefront curvature at a given point using the slowness vector at this point and an adjacent point on the same wavefront. The efficiency of the WRT technique is strongly dependent on the input parameters which control the wavefront and ray densities. On the basis of traveltimes computed in a smoothed Marmousi model, we analyse these dependences and suggest some rules for a correct choice of input parameters. With suitable input parameters, the WRT technique allows an accurate traveltime computation using a small number of rays and wavefronts. [source] A General Approach to First Order Phase Transitions and the Anomalous Behavior of Coexisting Phases in the Magnetic CaseADVANCED FUNCTIONAL MATERIALS, Issue 6 2009Sergio Gama Abstract First order phase transitions for materials with exotic properties are usually believed to happen at fixed values of the intensive parameters (such as pressure, temperature, etc.) characterizing their properties. It is also considered that the extensive properties of the phases (such as entropy, volume, etc.) have discontinuities at the transition point, but that for each phase the intensive parameters remain constant during the transition. These features are a hallmark for systems described by two thermodynamic degrees of freedom. In this work it is shown that first order phase transitions must be understood in the broader framework of thermodynamic systems described by three or more degrees of freedom. This means that the transitions occur along intervals of the intensive parameters, that the properties of the phases coexisting during the transition may show peculiar behaviors characteristic of each system, and that a generalized Clausius,Clapeyron equation must be obeyed. These features for the magnetic case are confirmed, and it is shown that experimental calorimetric data agree well with the magnetic Clausius,Clapeyron equation for MnAs. An estimate for the point in the temperature-field plane where the first order magnetic transition turns to a second order one is obtained (the critical parameters) for MnAs and Gd5Ge2Si2 compounds. Anomalous behavior of the volumes of the coexisting phases during the magnetic first order transition is measured, and it is shown that the anomalies for the individual phases are hidden in the behavior of the global properties as the volume. [source] A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003K. Djidjeli Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Dan Givoli Abstract A new finite element (FE) scheme is proposed for the solution of time-dependent semi-infinite wave-guide problems, in dispersive or non-dispersive media. The semi-infinite domain is truncated via an artificial boundary ,, and a high-order non-reflecting boundary condition (NRBC), based on the Higdon non-reflecting operators, is developed and applied on ,. The new NRBC does not involve any high derivatives beyond second order, but its order of accuracy is as high as one desires. It involves some parameters which are chosen automatically as a pre-process. A C0 semi-discrete FE formulation incorporating this NRBC is constructed for the problem in the finite domain bounded by ,. Augmented and split versions of this FE formulation are proposed. The semi-discrete system of equations is solved by the Newmark time-integration scheme. Numerical examples concerning dispersive waves in a semi-infinite wave guide are used to demonstrate the performance of the new method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Orthogonal grids around convex bodies using foliationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003B. Herrera Abstract A new technique for the construction of orthogonal grids around convex bodies is presented. The method, which is analytical or numerical depending on how the body boundary is expressed, is based on the development of geometric foliations that follow a prescribed direction (for instance, the prevailing direction of flow) around convex bodies of arbitrary shape. The construction of these foliations is straightforward and does not require the solution of any system of algebraic or differential equations, nor the use of iterative procedures. The method is applicable both to two- and three-dimensional domains since it is based solely on the concept of local curvature. The lines or surfaces given by the foliations of first and second order, together with the complementary orthogonal lines, respectively, define the orthogonal two- or three-dimensional grids. Copyright © 2002 John Wiley & Sons, Ltd. [source] On the spectrum of the electric field integral equation and the convergence of the moment methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Karl F. Warnick Abstract Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low-order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd. [source] A two-step Taylor-characteristic-based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence anglesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010Yan Bao Abstract An alternative characteristic-based scheme, the two-step Taylor-characteristic-based Galerkin method is developed based on the introduction of multi-step temporal Taylor series expansion up to second order along the characteristic of the momentum equation. Contrary to the classical characteristic-based split (CBS) method, the current characteristic-based method does not require splitting the momentum equation, and segregate the calculation of the pressure from that of the velocity by using the momentum,pressure Poisson equation method. Some benchmark problems are used to examine the effectiveness of the proposed algorithm and to compare with the original CBS method, and the results show that the proposed method has preferable accuracy with less numerical dissipation. We further applied the method to the numerical simulation of flow around equilateral triangular cylinder with different incidence angles in free stream. In this numerical investigation, the flow simulations are carried out in the low Reynolds number range. Instantaneous streamlines around the cylinder are used as a means to visualize the wake region behind, and they clearly show the flow pattern around the cylinder in time. The influence of incidence angle on flow characteristic parameters such as Strouhal number, Drag and Lift coefficients are discussed quantitatively. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Taylor series-based finite volume method for the Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008G. X. Wu Abstract A Taylor series-based finite volume formulation has been developed to solve the Navier,Stokes equations. Within each cell, velocity and pressure are obtained from the Taylor expansion at its centre. The derivatives in the expansion are found by applying the Gauss theorem over the cell. The resultant integration over the faces of the cell is calculated from the value at the middle point of the face and its derivatives, which are further obtained from a higher order interpolation based on the values at the centres of two cells sharing this face. The terms up to second order in the velocity and the terms up to first order in pressure in the Taylor expansion are retained throughout the derivation. The test cases for channel flow, flow past a circular cylinder and flow in a collapsible channel have shown that the method is quite accurate and flexible. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stability and accuracy of a semi-implicit Godunov scheme for mass transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Scott F. Bradford Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source] A projection scheme for incompressible multiphase flow using adaptive Eulerian gridINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004T. Chen Abstract This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second-order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least-squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure-stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure-computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free-surface problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Simulation of shockwave propagation with a thermal lattice Boltzmann modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003ShiDe Feng Abstract A two-dimensional 19-velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u4) rather than the usual O(u3) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher-order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13-velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 John Wiley & Sons, Ltd. [source] Relaxation schemes for the shallow water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003A. I. Delis Abstract We present a class of first and second order in space and time relaxation schemes for the shallow water (SW) equations. A new approach of incorporating the geometrical source term in the relaxation model is also presented. The schemes are based on classical relaxation models combined with Runge,Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems with or without the source term present. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solvent and substituent effects on the reaction of 2- and 4-chloro-3,5-dinitrobenzotrifluorides with substituted anilinesINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 12 2009Basim H. M. Asghar The solvent effect on a nucleophilic substitution reaction of 2- and 4-chloro-3,5-dinitrobenzotrifluoride with substituted anilines was studied in methanol, acetonitrile, and toluene at 25°C. This reaction is of second order, except 2-chloro-3,5-dinitrobenzotrifluoride in toluene shows third order. The kA values are found to be dependent on the substituent in aniline and give good Hammett correlations. The obtained , values are ,4.07 and ,4.62, for the reaction of anilines with 2-chloro-3,5-dinitrobenzotrifluoride in methanol and acetonitrile, respectively. The , values for the reaction of the anilines with 4-chloro-3,5-dinitrobenzotrifluoride are ,3.38, ,4.11, and ,4.34 in methanol, acetonitrile, and toluene, respectively. The reaction of the former compound with anilines in toluene shows a second order in aniline. The dependence of the reaction on the external base such as DABCO suggests a proton transfer controlling step. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 777,786, 2009 [source] Studies on the oxygen atom transfer reactions of peroxomonosulfate: Catalytic effect of hemiacetalINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 10 2009S. Shailaja The reaction of peroxomonosulfate (PMS) with glycolic acid (GLYCA), an alpha hydroxy acid, in the presence of Ni(II) ions and formaldehyde was studied in the pH range 4.05,5.89 and at 31°C and 38°C. When formaldehyde and Ni(II) ions concentrations are ,5.0 × 10,4 M to 10.0 × 10,4 M, the reaction is second order in PMS concentration. The rate is catalyzed by formaldehyde, and the observed rate equation is (,d[PMS])/dt = (k,2[HCHO][Ni(II)][PMS]2)/{[H+](1+K2[GLYCA])}. The number of PMS decomposed for each mole of formaldehyde (turnover number) is 5,10, and the major reaction product is oxygen gas. The first step of the reaction mechanism is the formation of hemiacetal by the interaction of HCHO with the hydroxyl group of nickel glycolate. The peroxomonosulfate intermediate of the Ni-hemiacetal reacts with another molecule of PMS in the rate-limiting step to give the product. This reaction is similar to the thermal decomposition of PMS catalyzed by Ni(II) ions. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 642,649, 2009 [source] Kinetic investigation on the reactions of p -toluenesulfonyl chloride with p -substituted benzoic acid(s) in the presence of triethylamine in aprotic solventsINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 5 2009Subbiah Ananthalakshmi Second-order rate constants of the reactions of p -toluenesulfonyl chloride with p -substituted benzoic acids in the presence of triethylamine in acetonitrile/acetone under equimolar and pseudo-first-order conditions have been determined by the conductometric method using the Guggenheim principle at 25, 30, 35, and 40°C. The reactions follow second order with respect to the whole and first order with respect to each of the reactants. The order of reactivity of the substituents in benzoic acid is rationalized. Activation parameters are obtained by applying the usual methods. The Hammett plot has been found nonlinear, whereas the Bronsted plot shows good correlation. This may be explained on the basis of electronic effects of substituents on the reaction center. Kinetic data and the product analyses indicate that the reaction proceeds through direct nucleophilic attack on the sulfur center. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 303,308, 2009 [source] Kinetics and mechanism of myristic acid and isopropyl alcohol esterification reaction with homogeneous and heterogeneous catalystsINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 3 2008Tuncer Yalçinyuva The reaction of myristic acid (MA) and isopropyl alcohol (IPA) was carried out by using both homogeneous and heterogeneous catalysts. For a homogeneously catalyzed system, the experimental data have been interpreted with a second order, using the power-law kinetic model, and a good agreement between the experimental data and the model has been obtained. In this approach, it was assumed that a protonated carboxylic acid is a possible reaction intermediate. After a mathematical model was proposed, reaction rate constants were computed by the Polymath* program. For a heterogeneously catalyzed system, interestingly, no pore diffusion limitation was detected. The influences of initial molar ratios, catalyst loading and type, temperature, and water amount in the feed have been examined, as well as the effects of catalyst size for heterogeneous catalyst systems. Among used catalysts, p -toluene sulfonic acid (p -TSA) gave highest reaction rates. Kinetic parameters such as activation energy and frequency factor were determined from model fitting. Experimental K values were found to be 0.54 and 1.49 at 60°C and 80°C, respectively. Furthermore, activation energy and frequency factor at forward were calculated as 54.2 kJ mol,1 and 1828 L mol,1 s,1, respectively. © 2008 Wiley Periodicals, Inc. 40: 136,144, 2008 [source] Effects of NO2, CO, O2, and SO2 on oxidation kinetics of NO over Pt-WO3/TiO2 catalyst for fast selective catalytic reduction processINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 10 2006Muhammad Faisal Irfan The selective catalytic reduction rate of NO with N-containing reducing agents can be enhanced considerably by converting a part of NO into NO2. The enhanced reaction rate is more pronounced at lower temperatures by using an equimolar mixture of NO and NO2. The kinetics of NO oxidation over Pt-WO3/TiO2 catalyst has been determined in a fixed-bed reactor with different concentrations of oxygen, nitric oxide, and nitrogen dioxide in the presence of 8% water. It has been found that the reaction is second order with respect to nitric oxide, first order for oxygen with a third-order rate constant. Also, it is found that there is no effect on the reaction order with an addition of NO2, CO, or SO2. It follows the same second order but the reaction rate is found to be changed. It is observed that in the case of NO2 and SO2, the reaction rate tends to decrease, but it increases with the addition of CO into the feed. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 613,620, 2006 [source] Kinetic evidence for the copper peroxide intermediate with two copper ions in proximityINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 7 2006S. Selvarani The decomposition of caroate (peroxomonosulfate, PMS) is catalyzed by Cu(II) ions even at 5 × 10,5 M in aqueous alkaline solution. The rate is second order in copper(II) ions concentrations and first order in [PMS]. The rate constant values are found to decrease with increase in hydroxide ion concentrations. The turnover number for the reaction is estimated as >1000. The experimental results suggest that the formation of peroxide type intermediate with two copper(II) ions is the rate-determining step. This peroxide intermediate reacts with another molecule of PMS to give the products oxygen, SO and copper ions. The overall entropy of activation is positive with a value of ,20 cals/mol/K. The very high turnover number suggests that Cu(II) ion is one of the best catalysts for the decomposition of caroate ions in alkaline medium. The reaction also represents a system in which metal ion catalyzed decomposition of caroate does not involve radical intermediates. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 439,443, 2006 [source] Kinetic study of triphenylphosphine addition to para -benzoquinoneINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 9 2004Davood Nori-Shargh Kinetics of the addition reaction of triphenylphosphine to para -benzoquinone in 1,2-dichloroethane as solvent was studied. Initial rate method was used to determine the order of the reaction with respect to the reactants. Pseudo-first-order method was also used to calculate the rate constant. This reaction was monitored by UV-vis spectrophotometry at 520 nm by variable time method. On the basis of the obtained results, the Arrhenius equation of this reaction was obtained: The activation parameters, Ea, ,H#, ,G#, and ,S# at 300 K were 5.701, 6.294, 19.958 kcal mol,1 and ,45.853 cal mol,1 K,1, respectively. This reaction is first and second order with respect to triphenylphosphine and para -benzoquinone, respectively. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:472,479, 2004 [source] A new approach to response surface development for detailed gas-phase and surface reaction kinetic model optimizationINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2004Scott G. Davis We propose a new method for constructing kinetic response surfaces used in the development and optimization of gas-phase and surface reaction kinetic models. The method, termed as the sensitivity analysis based (SAB) method, is based on a multivariate Taylor expansion of model response with respect to model parameters, neglecting terms higher than the second order. The expansion coefficients are obtained by a first-order local sensitivity analysis. Tests are made for gas-phase combustion reaction models. The results show that the response surface obtained with the SAB method is as accurate as the factorial design method traditionally used in reaction model optimization. The SAB method, however, presents significant computational savings compared to factorial design. The effect of including the partial and full third order terms was also examined and discussed. The SAB method is applied to optimization of a relatively complex surface reaction mechanism where large uncertainty in rate parameters exists. The example chosen is laser-induced fluorescence signal of OH desorption from a platinum foil in the water/oxygen reaction at low pressures. We introduce an iterative solution mapping and optimization approach for improved accuracy. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 94,106, 2004 [source] An application of dynamic positioning control using wave feed forwardINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2001A. B. Aalbers Abstract The paper presents the results of model tests for a large tanker in which wave drift force feed forward was applied in the dynamic positioning control system. The estimation method of the nonlinear (second order) wave drift forces from the measurement of relative water motions at the side of a ship hull is presented. The estimated wave drift forces are used in the DP control system, to enhance the filter process of the extended Kalman filter, and in the required thruster set-points. The EKF uses the nonlinear equations of low-frequency ship motions on the horizontal plane, which are also presented. The results of the model tests show that the use of wave drift force feed forward significantly improves the positioning accuracy in sea states with 3.5 m significant wave height or higher. Copyright © 2001 John Wiley & Sons, Ltd. [source] Decomposition of monochlorobiphenyl isomers in supercritical water in the presence of methanolAICHE JOURNAL, Issue 7 2004Gheorghe Anitescu Abstract Comprehensive studies of monochlorobiphenyl (MCB) decomposition in supercritical water in the presence of methanol and other cosolvents, both with and without oxygen, are being conducted to understand the reaction kinetics and pathways of individual PCB isomers and to determine the structure,reactivity relationships. In the present study the disappearance rate of MCBs, delivered in an isothermal plug-flow tubular reactor as methanolic solutions, is investigated at 25 MPa and temperatures of 673, 723, and 773 K. Experiments are conducted at nominal MCB feed concentrations of 1,100 ,mol/L (reaction conditions) using MCB/MeOH and H2O2/H2O solutions (1,3 g/L and 0,10 wt. %, respectively). Molar conversions of these isomers vary from 3% (2-CB, 773 K, 2 s) to 30% (4-CB, 773 K, 46 s) without oxygen (SCWT) and from 1% (2-CB, 673 K, 3.8 s) to 97% (4-CB, 773 K, 24.5 s) with oxygen (SCWO). For SCWT the overall conversion follows apparent first order, whereas for SCWO the conversion is second order. The regressed data lead to Arrhenius parameters of frequency factor and activation energy with values of 1020.5,1021.3 s,1 and 320,331 kJ/mol for SCWT and 1024.1,1024.8 s,1 (mol/L),1 and 281,292 kJ/mol for SCWO, respectively. The reactivity of the MCB isomers increases in the order 2-MCB < 3-MCB < 4-MCB. The positively identified reaction products by GC-MSD and GC-FID/ECD/TCD analyses are mainly biphenyl, open-ring biphenyl compounds such as acetophenone and benzaldehydes, and mineral products (CO, CO2, and HCl). More studies are in progress regarding the role of the second solvent on reaction rates and reaction mechanisms and pathways. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1536,1544, 2004 [source] Amide and lactam hydrolysis of N -(2-hydroxyacetyl)-2-pyrrolidone: effective catalysis,JOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 11 2006Lisaedy García Borboa Abstract When N -(2-hydroxyacetyl)-2-pyrrolidone (open form) is dissolved in water at pH,>,8, irreversible cleavage of the exocyclic and endocyclic amide CN bond occurs. The latter rupture corresponds to the lactam opening yielding N -(4-hydroxyacetyl)butanoic acid (NBA). NBA is produced from the ester hydrolysis of the ester-amide macrocycle that is in equilibrium with the cyclol form of the open form. We have previously reported this latter equilibrium for N -(2-aminoacetyl)-2-lactams. 2-pyrrolidone (lactam) and glycolic acid are produced from direct hydrolysis of the open form by means of the amide exocyclic cleavage. The [NBA]/[lactam] ratio increases at higher pH since the NBA production is second order with respect to [OH,] while the corresponding lactam formation is only first order. The obtained kobs is hence the sum of the rate constants that yield lactam and NBA, respectively. This kobs is uncatalyzed and specific base catalyzed with unusually high rate constants of 2.1,×,10,6,s,1 and 0.025,M,1,s,1, respectively. The stability of the corresponding tetrahedral intermediate formed and the intramolecular alkoxy nucleophilic attack on the lactam carbonyl group combined with an effective protonation of the lactam nitrogen that promotes the CN cleavage, contribute to increase the reaction rates and lactam opening. Rate constants for the two parallel reactions are obtained from kobs and [NBA]/[lactam] versus pH plots. Copyright © 2006 John Wiley & Sons, Ltd. [source] Fractionation of Methyl Cellulose According to Polarity , a Tool to Differentiate First and Second Order Heterogeneity of the Substituent DistributionMACROMOLECULAR CHEMISTRY AND PHYSICS, Issue 11 2006Roland Adden Abstract Summary: A set of four MCs (DS 1.80,1.95) has been analyzed with regard to their substituent pattern in the glucosyl units and along the polymer chain. The average heterogeneity of methylation observed for the entire material was analyzed in more detail after fractionation according to polarity. All fractions obtained were analyzed with respect to their DS, monomer composition and deviation from a random distribution of these monomers in the polymer chains. By this approach, heterogeneity of first and second order could be differentiated. While for three of the MCs only a minor DS-gradient over the material was observed, a more pronounced heterogeneity of first order was obtained for MC 4. ESI mass spectrum of the undissolved residue of MC 2 after deuteromethylation and partial hydrolysis; DP 2 and 3 are shown in detail. Signals are assigned according to the number of CH3 -groups. [source] Distinct Diffusion in Macromolecule-Solvent MixturesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2005Alessandro Vergara Abstract Summary: The specificity of interactions between pairs of molecules cannot be explicitly given by experimental transport coefficients such as intra- or mutual diffusion coefficients. But a microscopic interpretation of the transport properties exists, where distinct diffusion coefficients (DDCs) are related to preferential, correlated motion among distinct molecules. Since in general the DDCs do not play the role of an indicator for molecular self-association phenomena if not compared with some appropriate standard, here we propose DDCs of hard spheres at the second order of volume fraction as new standard coefficients. The analysis based on these novel DDCs is designed to study intermolecular interaction between macromolecule and solvent. Comparisons of the novel non-ideal with previous ideal reference states were done, and their combined use is shown to reinforce information conveyed by the usual velocity correlation analysis. The comparison of novel hard sphere standards with real DDCs, corresponding to an homologous chemical series of poly(ethylene glycol)-water mixtures, provides a look at this polymer-solvent mixture in a dilute and semi-dilute regime. Comparison between real (calculated by using Equation (5),(7) and experimental data) and hard-sphere based distinct diffusion coefficients for PEG 200 (1: D; 2: D and 3: D). [source] Finite energy solutions of self-adjoint elliptic mixed boundary value problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2010Giles Auchmuty Abstract This paper describes existence, uniqueness and special eigenfunction representations of H1 -solutions of second order, self-adjoint, elliptic equations with both interior and boundary source terms. The equations are posed on bounded regions with Dirichlet conditions on part of the boundary and Neumann conditions on the complement. The system is decomposed into separate problems defined on orthogonal subspaces of H1(,). One problem involves the equation with the interior source term and the Neumann data. The other problem just involves the homogeneous equation with Dirichlet data. Spectral representations of the solution operators for each of these problems are found. The solutions are described using bases that are, respectively, eigenfunctions of the differential operator with mixed null boundary conditions, and certain mixed Steklov eigenfunctions. These series converge strongly in H1(,). Necessary and sufficient conditions for the Dirichlet part of the boundary data to have a finite energy extension are described. The solutions for a problem that models a cylindrical capacitor is found explicitly. Copyright © 2009 John Wiley & Sons, Ltd. [source] Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical typeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004A. Nazarov, Sergue Abstract The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd. [source] Determining the temperature from incomplete boundary dataMATHEMATISCHE NACHRICHTEN, Issue 16 2007B. Tomas Johansson Abstract An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2 -space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||||||||||||||