The kinetics and reactivity of several polyatomic free radicals in reactions with NO2, O2, Cl2, and HCl

In this thesis, the kinetics of several alkyl, halogenated alkyl, and alkenyl free radical reactions with NO2, O2, Cl2, and HCl reactants were studied over a wide temperature range in time resolved conditions. Laser photolysis photoionisation mass spectrometer coupled to a flow reactor was the experimental method employed and this thesis present the first measurements performed with the experimental system constructed. During this thesis a great amount of work was devoted to the designing, building, testing, and improving the experimental apparatus. Carbon-centred free radicals were generated by the pulsed 193 or 248 nm photolysis of suitable precursors along the tubular reactor. The kinetics was studied under pseudo-first-order conditions using either He or N2 buffer gas. The temperature and pressure ranges employed were between 190 and 500 K, and 0.5 45 torr, respectively. The possible role of heterogeneous wall reactions was investigated employing reactor tubes with different sizes, i.e. to significantly vary the surface to volume ratio. In this thesis, significant new contributions to the kinetics of carbon-centred free radical reactions with nitrogen dioxide were obtained. Altogether eight substituted alkyl (CH2Cl, CHCl2, CCl3, CH2I, CH2Br, CHBr2, CHBrCl, and CHBrCH3) and two alkenyl (C2H3, C3H3) free radical reactions with NO2 were investigated as a function of temperature. The bimolecular rate coefficients of all these reactions were observed to possess negative temperature dependencies, while pressure dependencies were not noticed for any of these reactions. Halogen substitution was observed to moderately reduce the reactivity of substituted alkyl radicals in the reaction with NO2, while the resonance stabilisation of the alkenyl radical lowers its reactivity with respect to NO2 only slightly. Two reactions relevant to atmospheric chemistry, CH2Br + O2 and CH2I + O2, were also investigated. It was noticed that while CH2Br + O2 reaction shows pronounced pressure dependence, characteristic of peroxy radical formation, no such dependence was observed for the CH2I + O2 reaction. Observed primary products of the CH2I + O2 reaction were the I-atom and the IO radical. Kinetics of CH3 + HCl, CD3 + HCl, CH3 + DCl, and CD3 + DCl reactions were also studied. While all these reactions possess positive activation energies, in contrast to the other systems investigated in this thesis, the CH3 + HCl and CD3 + HCl reactions show a non-linear temperature dependency on the Arrhenius plot. The reactivity of substituted methyl radicals toward NO2 was observed to increase with decreasing electron affinity of the radical. The same trend was observed for the reactions of substituted methyl radicals with Cl2. It is proposed that interactions of frontier orbitals are responsible to these observations and Frontier Orbital Theory could be used to explain the observed reactivity trends of these highly exothermic reactions having reactant-like transition states.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

Let X be a topological space and K the real algebra of the reals, the complex numbers, the quaternions, or the octonions. The functions form X to K form an algebra T(X,K) with pointwise addition and multiplication. We study first-order definability of the constant function set N' corresponding to the set of the naturals in certain subalgebras of T(X,K). In the vocabulary the symbols Constant, +, *, 0', and 1' are used, where Constant denotes the predicate defining the constants, and 0' and 1' denote the constant functions with values 0 and 1 respectively. The most important result is the following. Let X be a topological space, K the real algebra of the reals, the compelex numbers, the quaternions, or the octonions, and R a subalgebra of the algebra of all functions from X to K containing all constants. Then N' is definable in , if at least one of the following conditions is true. (1) The algebra R is a subalgebra of the algebra of all continuous functions containing a piecewise open mapping from X to K. (2) The space X is sigma-compact, and R is a subalgebra of the algebra of all continuous functions containing a function whose range contains a nonempty open set of K. (3) The algebra K is the set of reals or the complex numbers, and R contains a piecewise open mapping from X to K and does not contain an everywhere unbounded function. (4) The algebra R contains a piecewise open mapping from X to the set of the reals and function whose range contains a nonempty open subset of K. Furthermore R does not contain an everywhere unbounded function.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Finite element analysis of curved anisotropic laminated hollow bars

Curved hollow bars of laminated anisotropic construction are used as structural members in many industries. They are used in order to save weight without loss of stiffness in comparison with solid sections. In this paper are presented the details of the development of the stiffness matrices of laminated anisotropic curved hollow bars under line member assumptions for two typical sections, circular and square. They are 16dof elements which make use of one-dimensional first-order Hermite interpolation polynomials for the description of assumed displacement state. Problems for which analytical or other solutions are available are first solved using these elements. Good agreement was found between the results. In order to show the capability of the element, application is made to carbon fibre reinforced plastic layered anisotropic curved hollow bars.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Sorption and desorption of sulfuryl fluoride by wheat, flour and semolina

Sulfuryl fluoride (SF) has been developed as a fumigant for control of insect pests in stored grain. However, there is very limited information on the sorption behaviour of this fumigant, which can be critical to its bioactivity, application and potential for residues. We undertook a comprehensive laboratory study of the sorption and desorption of SF by wheat (bread and durum), flour and semolina at 15, 25 and 35 °C, moisture contents 12% and 15%, and concentration × time combinations at CT = 1500 mgh/L (4.167 mg/L × 360 h, 8.928 mg/L × 168 h and 31.25 mg/L × 48 h). At each dosage, sorption rate increased as commodity temperature and moisture content increased. The highest rates of sorption occurred at 35 °C and 15% m.c., and lowest rates at 15 °C and 12% m.c., and the rate was independent of initial concentration. Sorption followed first order reaction kinetics described by the exponential decay equation, Ct = C0·e−k*t, where k is the sorption rate constant. The most important factors determining the rate of sorption were commodity particle size (exposed surfaces) and temperature. Little sorption of fumigant occurred within the first 24 h whereas longer fumigation times resulted in significant sorption. Unbound SF was rapidly lost from the commodity upon aeration with no further desorption detected under any of the test conditions.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

Intrinsic two-phonon-exchange mechanism of superconductivity and enhancement of Tc

It is shown that the intrinsic two-phonon terms occurring in first order in the electron-phonon interaction Hamiltonian can give rise to (i) an essential doubling of the interaction phase space (BCS cutoff) and (ii) an attractive pairing interaction proportional to the phonon occupation numbers. This suggests a possible enhancement of the superconductive transition temperature in the presence of high-frequency acoustic field.

Thermal decomposition of titanyl oxalates II : Kinetics of decomposition of barium titanyl oxalate

Kinetics of the thermal decomposition of barium titanyl oxalate have been studied. Decomposition of the anhydrous oxalate is complex and deceleratory throughout. Kinetics of decomposition of the intermediate carbonate Ba2Ti2O5CO3 is greatly influenced by the thermal effects during its formation. The sigmoidal (α, t) curves obey a power law equation followed by first order decay. Presence of carbon in the vacuum prepared carbonate has a strong deactivating effect. Decomposition of the carbonate is accompanied by growth in particle size of the product, barium titanate.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

Dynamics of a class of social interaction systems

A mathematical model of social interaction in the form of two coupler! first-order non-linear differential equations, forms the topic of this study. This non-conservative model io representative of such varied social interaction problems as coexisting sub-populations of two different species, arms race between two rival countries and the like. Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.

Liquid phase hydrogenation of aniline in a trickle bed reactor

A rate equation is developed for the liquid phase hydrogenation of aniline over cylindrical catalyst pellets of 30% nickel deposited on clay in a trickle bed reactor. The equation takes into account external and internal diffusional limitations, and describes the experimental data adequately. The hydrogenation reaction is first order with respect to hydrogen and zero order with respect to aniline. Effectiveness factors are in the range 0.003-0.03. Apparent activation energy of the reaction is 12.7 kcal/mol and true activation energy is 39.6 kcal/mol.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.