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Mathematical Treatment (mathematical + treatment)
Selected AbstractsIn situ X-ray diffraction analysis of (CFx)n batteries: signal extraction by multivariate analysisJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2007Mark A. Rodriguez (CFx)n cathode reaction during discharge has been investigated using in situ X-ray diffraction (XRD). Mathematical treatment of the in situ XRD data set was performed using multivariate curve resolution with alternating least squares (MCR,ALS), a technique of multivariate analysis. MCR,ALS analysis successfully separated the relatively weak XRD signal intensity due to the chemical reaction from the other inert cell component signals. The resulting dynamic reaction component revealed the loss of (CFx)n cathode signal together with the simultaneous appearance of LiF by-product intensity. Careful examination of the XRD data set revealed an additional dynamic component which may be associated with the formation of an intermediate compound during the discharge process. [source] A study of ground-structure interaction in dynamic plate load testingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2002Bojan B. Guzina Abstract A mathematical treatment is presented for the forced vertical vibration of a padded annular footing on a layered viscoelastic half-space. On assuming a depth-independent stress distribution for the interfacial buffer, the set of triple integral equations stemming from the problem is reduced to a Fredholm integral equation of the second kind. The solution method, which is tailored to capture the stress concentrations beneath footing edges, is highlighted. To cater to small-scale geophysical applications, the model is used to investigate the near-field effects of ground-loading system interaction in dynamic geotechnical and pavement testing. Numerical results indicate that the uniform-pressure assumption for the contact load between the composite disc and the ground which is customary in dynamic plate load testing may lead to significant errors in the diagnosis of subsurface soil and pavement conditions. Beyond its direct application to non-intrusive site characterization, the proposed solution can be used in the seismic analysis of a variety of structures involving annular foundation geometries. Copyright © 2002 John Wiley & Sons, Ltd. [source] Kinetic studies of hydrazine and 2-hydroxyethylhydrazine alkylation by 2-chloroethanol: Influence of a strong base in the mediumINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 6 2009V. Goutelle To optimize yields, the study of reaction kinetics related to the synthesis of 2-hydroxyethylhydrazine (HEH) obtained from the alkylation of N2H4 by 2-chloroethanol (CletOH) was carried out with and without sodium hydroxide. In both cases, the main reaction of HEH formation was followed by a consecutive, parallel reaction of HEH alkylation (or dialkylation of N2H4), leading to the formation of two isomers: 1,1-di(hydroxyethyl)hydrazine and 1,2-di(hydroxyethyl)hydrazine. In this study, hydrazine and hydroxyalkylhydrazine alkylations followed SN2 reactions triggered directly by CletOH or indirectly in the presence of a strong base by ethylene oxide, an intermediate compound. The kinetics was studied in diluted mediums by quantifying HEH and CletOH by gas chromatography and gas chromatography coupled with mass spectrometry (GC-MS). The activation parameters of each reaction and the influence of a strong base present in the medium on the reaction mechanisms were established. A global mathematical treatment was applied for each alternative. It allowed modeling the reactions as a function of reagent concentrations and temperature. In the case of direct alkylation by CletOH, simulation was established for semi-batch and batch syntheses and was confirmed in experiments for concentrated mediums (1.0 M , [CletOH]0 , 3.2 M and 15.7 M , [N2H4]0 , 18.8 M). Simulation therefore permits the prediction of the instantaneous concentration of reagents and products, in particular ethylene oxide concentration in the case of indirect alkylation, which must be as weak as possible. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 382,393, 2009 [source] Kinetic characterization of a transient reaction by degeneration of the precursor mechanism: Application to the synthesis of 3,4-diazabicyclo[4.3.0]- non-2-eneINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 5 2006H. Delalu The rate of the oxidation of N -amino-3-azabicyclo[3.3.0]octane by chloramine has been studied by GC and HPLC between pH 10.5 and 13.5. The second-order reaction exhibits specific acid catalysis. The formation of N,N,-azo-3-azabicyclo[3.3.0]octane or 3,4-diazabicyclo[4.3.0]non-2-ene is pH, concentration, and temperature dependent. In alkaline media, the exclusive formation of 3,4-diazabicyclo[4.3.0]non-2-ene is observed. Kinetic studies show that the oxidation of N -amino-3-azabicyclo[3.3.0]octane by chloramine is a multistep process with the initial formation of a diazene-type intermediate, which is converted by hydroxide ions into 3,4-diazabicyclo[4.3.0]non-2-ene. Because it was not possible to follow the rate of change of the intermediate concentration, to determine the kinetics of 3,4-diazabicyclo[4.3.0]non-2-ene formation, a procedure based on the degeneration of the precursor process was adopted. An appropriate mathematical treatment allowed a quantitative interpretation of all the phenomena observed over the given pH interval. The activation parameters were determined. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 327,338, 2006 [source] Thermal decomposition of tert -butyl peroxide in a gas chromatographic reactor: A comparison of kinetic approachesINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 7 2004Peter J. Skrdla The thermal decomposition of tert -butyl peroxide is investigated utilizing both the column and the injection port of a commercial gas chromatograph (GC) as chemical reactors. Using the injector liner as the reactor, the chromatographic peak areas of the reactant, measured at various injector temperatures, are used in the determination of the activation energy of the decomposition (Ea). With the column serving as the reactor, both the reactant peak areas and the product peak shapes are similarly utilized for this purpose. Values of Ea obtained using different mathematical treatments for each of the three approaches are found to range from 115 to 164 kJ/mol. Of these methods, the column reactor approach utilizing peak area measurements (referred to as PACR, for "peak area, column reactor") is found to be far superior in terms of its speed, robustness, and its accuracy in determining Ea. The PACR method's effectiveness can be largely attributed to the mathematical treatment that is described in the approach. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 386,393, 2004 [source] A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2006I. Borsi Abstract We present a rigorous mathematical treatment of a model describing rain water infiltration through the vadose zone in case of runoff of the excess water. The main feature of the mathematical problem emerging from the model lies on the boundary condition on the ground surface which is in the form of a unilateral constraint. Existence and uniqueness of a weak solution is proved under general assumptions. We present also the results of a numerical study comparing the proposed model with other models which approach in a different way the rain water infiltration problem. Copyright © 2006 John Wiley & Sons, Ltd. [source] Shock waves,Phenomenology, experimental, and numerical simulationMETEORITICS & PLANETARY SCIENCE, Issue 9-10 2005Klaus Thoma First, the principal phenomena of shock wave generation and propagation, predominantly in solid media, are presented, and then analytical and numerical mathematical treatment of shock wave processes on the basis of mass, momentum, and energy conservation laws will be described and discussed. Experimental methods of shock wave investigations by means of impact and explosive techniques are summarized, including hypervelocity acceleration facilities and high-pressure explosive devices. Shock pressure barometry by means of mineralogical evidence of distinct material phase transitions and characteristic shock structures is also discussed. [source] Determination of tocopherols and phytosterols in sunflower seeds by NIR spectrometryEUROPEAN JOURNAL OF LIPID SCIENCE AND TECHNOLOGY, Issue 5 2007Alicia Ayerdi Gotor Abstract The objective of this work was to develop a near-infrared reflectance spectrometry (NIRS) calibration estimating the tocopherol and phytosterol contents in sunflower seeds. Approximately 1000 samples of grinded sunflower kernels were scanned by NIRS at 2-nm intervals from 400 to 2500,nm. For each sample, standard measurements of tocopherol and phytosterol contents were performed. The total tocopherol content was obtained by high-performance liquid chromatography coupled with a fluorescence detector, while the total phytosterol content was assessed by gas chromatography. For tocopherol, the calibration data set ranged from 175 to 1005,mg/kg oil (mean value around 510,±,140,mg/kg oil), whereas for the phytosterol content, the calibration data set ranged from 180 to 470,mg/100,g oil (mean value of 320,±,50,mg/100,g oil). The NIRS calibration showed a relatively good correlation (R2,=,0.64) between predicted by NIRS and real values for the total tocopherol content but a poor correlation for the total phytosterol content (R2,=,0.27). These results indicate that NIRS could be useful to classify samples with high and low tocopherol content. In contrast, the estimation of phytosterol contents by NIRS needs further investigation. Moreover, in this study, calibration was obtained by a modified partial least-squares method; the use of other mathematical treatments can be suitable, particularly for total phytosterol content estimation. [source] The radial integration method applied to dynamic problems of anisotropic platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2007E. L. Albuquerque Abstract In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Thermal decomposition of tert -butyl peroxide in a gas chromatographic reactor: A comparison of kinetic approachesINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 7 2004Peter J. Skrdla The thermal decomposition of tert -butyl peroxide is investigated utilizing both the column and the injection port of a commercial gas chromatograph (GC) as chemical reactors. Using the injector liner as the reactor, the chromatographic peak areas of the reactant, measured at various injector temperatures, are used in the determination of the activation energy of the decomposition (Ea). With the column serving as the reactor, both the reactant peak areas and the product peak shapes are similarly utilized for this purpose. Values of Ea obtained using different mathematical treatments for each of the three approaches are found to range from 115 to 164 kJ/mol. Of these methods, the column reactor approach utilizing peak area measurements (referred to as PACR, for "peak area, column reactor") is found to be far superior in terms of its speed, robustness, and its accuracy in determining Ea. The PACR method's effectiveness can be largely attributed to the mathematical treatment that is described in the approach. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 386,393, 2004 [source] Use of mid-infrared spectroscopy in the diffuse-reflectance mode for the prediction of the composition of organic matter in soil and litterJOURNAL OF PLANT NUTRITION AND SOIL SCIENCE, Issue 3 2008Bernard Ludwig Abstract Mid-infrared spectroscopy (MIRS) is assumed to be superior to near-infrared spectroscopy (NIRS) for the prediction of soil constituents, but its usefulness is still not sufficiently explored. The objective of this study was to evaluate the ability of MIRS to predict the chemical and biological properties of organic matter in soils and litter. Reflectance spectra of the mid-infrared region including part of the near-infrared region (7000,400,cm,1) were recorded for 56 soil and litter samples from agricultural and forest sites. Spectra were used to predict general and biological characteristics of the samples as well as the C composition which was measured by 13C CPMAS-NMR spectroscopy. A partial least-square method and cross-validation were used to develop equations for the different constituents over selected spectra ranges after several mathematical treatments of the spectra. Mid-infrared spectroscopy predicted well the C : N ratio: the modeling efficiency EF was 0.95, the regression coefficient (a) of a linear regression (measured against predicted values) was 1.0, and the correlation coefficient (r) was 0.98. Satisfactorily (EF , 0.70, 0.8 , a , 1.2, r , 0.80) assessed were the contents of C, N, and lignin, the production of dissolved organic carbon, and the contents of carbonyl C, aromatic C, O-alkyl C, and alkyl C. However, the N mineralization rate, the microbial biomass and the alkyl,to,aromatic C ratio were predicted less satisfactorily (EF < 0.70). Limiting the sample set to mineral soils did generally not result in improved predictions. The good and satisfactory predictions reported above indicate a marked usefulness of MIRS in the assessment of chemical characteristics of soils and litter, but the accuracies of the MIRS predictions in the diffuse-reflectance mode were generally not superior to those of NIRS. [source] | |||||||||||||