Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Photocatalytic degradation of methyl methacrylate copolymers

The photolytic and photocatalytic degradation of the copolymers poly(methyl methacrylate-co-butyl methacrylate) (MMA–BMA), poly(methyl methacrylate-co-ethyl acrylate) (MMA–EA) and poly(methyl methacrylate-co-methacrylic acid) (MMA–MAA) have been carried out in solution in the presence of solution combustion synthesized TiO2 (CS TiO2) and commercial Degussa P-25 TiO2 (DP 25). The degradation rates of the copolymers were compared with the respective homopolymers. The copolymers and the homopolymers degraded randomly along the chain. The degradation rate was determined using continuous distribution kinetics. For all the polymers, CS TiO2 exhibited superior photo-activity compared to the uncatalysed and DP 25 systems, owing to its high surface hydroxyl content and high specific surface area. The time evolution of the hydroxyl and hydroperoxide stretching vibration in the Fourier transform-infrared (FT-IR) spectra of the copolymers indicated that the degradation rate follows the order MMA–MAA > MMA–EA > MMA–BMA. The same order is observed for the rate coefficients of photocatalytic degradation. The photodegradation rate coefficients were compared with the activation energy of pyrolytic degradation. In degradation by pyrolysis, it was observed that MMA–BMA was the least stable followed by MMA–EA and MMA–MAA. The observed contrast in the order of thermal stability compared to the photo-stability of these copolymers was attributed to the two different mechanisms governing the scission of the polymer and the evolution of the products.

Quadratic Nonlinearity of One- and Two-Electron Oxidized Metalloporphyrins and Their Switching in Solution

We report the quadratic nonlinearity of one- and two-electron oxidation products of the first series of transition metal complexes of meso-tetraphenylporphyrin (TPP). Among many MTPP complexes, only CuTPP and ZnTPP show reversible oxidation/reduction cycles as seen from cyclic voltammetry experiments. While centrosymmetric neutral metalloporphyrins have zero first hyperpolarizability, β, as expected, the cation radicals and dications of CuTPP and ZnTPP have very high β values. The one- and two-electron oxidation of the MTPPs leads to symmetry-breaking of the metal−porphyrin core, resulting in a large β value that is perhaps aided in part by contributions from the two-photon resonance enhancement. The calculated static first hyperpolarizabilities, β0, which are evaluated in the framework of density functional theory by a coupled perturbed Hartree−Fock method, support the experimental trend. The switching of optical nonlinearity has been achieved between the neutral and the one-electron oxidation products but not between the one- and the two-electron oxidation products since dications that are electrochemically reversible are unstable due to the formation of stable isoporphyrins in the presence of nucleophiles such as halides.

Rheology of dense sheared granular flows

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin 'boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the 'friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Reliability assessment of internal stability of reinforced soil structures: A pseudo-dynamic approach

A methodology for reliability based optimum design of reinforced soil structures subjected to horizontal and vertical sinusoidal excitation based on pseudo-dynamic approach is presented. The tensile strength of reinforcement required to maintain the stability is computed using logarithmic spiral failure mechanism. The backfill soil properties, geometric and strength properties of reinforcement are treated as random variables. Effects of parameters like soil friction angle, horizontal and vertical seismic accelerations, shear and primary wave velocities, amplification factors for seismic acceleration on the component and system probability of failures in relation to tension and pullout capacities of reinforcement have been discussed. In order to evaluate the validity of the present formulation, static and seismic reinforcement force coefficients computed by the present method are compared with those given by other authors. The importance of the shear wave velocity in the estimation of the reliability of the structure is highlighted. The Ditlevsen's bounds of system probability of failure are also computed by taking into account the correlations between three failure modes, which is evaluated using the direction cosines of the tangent planes at the most probable points of failure. (c) 2009 Elsevier Ltd. All rights reserved.

A voltage-sensorless control method to balance the input currents of a three-wire boost rectifier under unbalanced input voltages condition

This paper proposes a control method that can balance the input currents of the three-phase three-wire boost rectifier under unbalanced input voltage condition. The control objective is to operate the rectifier in the high-power-factor mode under balanced input voltage condition but to give overriding priority to the current balance function in case of unbalance in the input voltage. The control structure has been divided into two major functional blocks. The inner loop current-mode controller implements resistor emulation to achieve high-power-factor operation on each of the two orthogonal axes of the stationary reference frame. The outer control loop performs magnitude scaling and phase-shifting operations on current of one of the axes to make it balanced with the current on the other axis. The coefficients of scaling and shifting functions are determined by two closed-loop prportional-integral (PI) controllers that impose the conditions of input current balance as PI references. The control algorithm is simple and high performing. It does not require input voltage sensing and transformation of the control variables into a rotating reference frame. The simulation results on a MATLAB-SIMULINK platform validate the proposed control strategy. In implementation Texas Instrument's digital signal processor TMS320F24OF is used as the digital controller. The control algorithm for high-power-factor operation is tested on a prototype boost rectifier under nominal and unbalanced input voltage conditions.

Seismic passive earth pressures in soils

Seismic passive earth pressure coefficients were computed by the method of limit equilibrium using a pseudostatic approach for seismic forces. Composite curved rupture surfaces were considered in the analysis. While earlier studies using this type of analysis were mainly for sands, seismic passive earth pressure coefficients were obtained in the present study considering the effects of cohesion, surcharge, and own weight. The minimum seismic passive force was obtained by adding the individual minimum values of these components and the validity of the principle of superposition was examined. Other parameters considered in the analysis were wall batter angle, ground surface slope, soil friction angle, wall friction angle, wall adhesion to soil cohesion ratio, and horizontal and vertical seismic accelerations. The seismic earth pressure coefficients were found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and vertical directions. Results of the study are presented in the form of figures and tables. Comparisons of the proposed method with available theories in the seismic case are also presented.

Enzymatic Degradation of Poly(soybean oil-g-methyl methacrylate)

This study discusses grafting of methyl methacrylate units from thepolymeric soybean oil peroxide to produce poly(soybean oil-graft-methyl methacrylate) (PSO-g-PMMA). The degradation of this copolymer in solution was evaluated in the presence of different lipases, viz Candida rugosa (CR), Lipolase 100T (LP), Novozym 435 (N435) and Porcine pancreas (PP), at different temperatures The copolymer degraded by specific chain end scission and the mass fraction of the specific product evolved was determined The degradation was modeled using continuous distribution kinetics to determine the rate coefficients ofmenzymatic chain end scission and deactivation of the enzyme The enzymes, CR. LP and N435 exhibited maximum activity for the degradation of PSO-g-PMMA at 60 degrees C, while PP was most active at 50 degrees C. The thermal degradability of the copolymer, assessed by thermo-gravimetry, indicated that the activation energy of degradation of the copolymer was 154 kJ mol(-1), which was lesser than that of the PMMA homopolymer.

Adsorption of anionic dyes on chitosan grafted poly(alkyl methacrylate)s

Chitosan grafted poly(alkyl methacrylate)s (namely chitosan grafted poly(methyl methacrylate) (ChgPMMA), chitosan grafted poly(ethyl methacrylate)(ChgPEMA), chitosan grafted poly(butyl methacrylate) (ChgPBMA) and chitosan grafted poly(hexyl methacrylate) (ChgPHMA)) were synthesized and characterized by using FT-IR and C-13 NMR techniques. The adsorption batch experiments on these grafted copolymers were conducted by using an anionic sulfonated dye. Orange-G. A pseudo-second-order kinetic model was used to determine the kinetics of adsorption. The effect of grafting, effect of process variables and the effect of different sulfonated anionic dyes (Orange-C, Congo Red, Remazol Brill Blue R and Methyl Blue) on the adsorption kinetics was determined. The Langmuir and Freundlich models were used to fit the adsorption isotherms and from the values of correlation coefficients (R-2), it was observed that the experimental data fits very well to the Langmuir model. The values of the maximum adsorption capacity of the adsorbents follow the order: ChgPMMA > ChgPEMA > ChgPBMA > ChgPHMA > chitosan. (C) 2010 Elsevier B.V. All rights reserved.

Measurement of air leakage in air-handling units and air conditioning ducts

The purpose of this article is to report the experience of design and testing of orifice plate-based flow measuring systems for evaluation of air leakages in components of air conditioning systems. Two of the flow measuring stations were designed with a beta value of 0.405 and 0.418. The third was a dual path unit with orifice plates of beta value 0.613 and 0.525. The flow rates covered with all the four were from 4-94 l/s and the range of Reynolds numbers is from 5600 to 76,000. The coefficients of discharge were evaluated and compared with the Stolz equation. Measured C-d values are generally higher than those obtained from the equation, the deviations being larger in the low Reynolds number region. Further, it is observed that a second-degree polynomial is inadequate to relate the pressure drop and flow rate. The lower Reynolds number limits set by standards appear to be somewhat conservative.

Studies of the polarographic and coulometric behaviour of aromatic nitro-compounds: I. Nitrobenzene in ethanol

A detailed polarographic (a.c. and d.c.) and coulometric investigation of nitrobenzene has been made at various pH values in the presence of different concentrations of ethanol. Below pH 4.7, two waves are apparent but above this pH, the second wave does not appear. Coulometric evidence indicates that the first and second waves correspond to the four-and two-electron processes, respectively. The coulometric method was not applicable in sodium hydroxide and sodium acetate solutions. When the diffusion coefficients (from the diaphragm cell) are used in the Ilkovic equation, no reliable conclusions can be reached for the number of electrons involved in the reduction process in alkaline solutions. The a.c. polarographic method gives evidence for the formation of species such as: C6H5NO2H22+, C6H5NO2− and C6H5NO22−. Analysis of d.c. polarographic data by Delahay's treatment of irreversible waves, indicates that the number of electrons involved in the rate-determining step is 2. In sodium hydroxide solutions, however, the first main wave is split indicating more than one rate-determining step. The results presented in this paper indicate that the first wave in the reduction of nitrobenzene is a four-electron process at all pH values. The second wave, which appears below pH 4.7, corresponds to a two-electron process irrespective of wave heights. The difference in the a.c. polarographic behaviour in acid and alkaline solutions has given evidence for the formation of species like C6H5NO2H2, C6H5NO2−, and C6H5NO22.

Molecular model for U centres in caesium iodide

A molecular model has been developed to study the vibrations of U centres in caesium iodide. Employing the rigid ion model with nearest-neighbour short-range forces, the dynamical matrix of order 27 × 27 was solved to obtain the frequencies of the localized modes and the perturbed lattice modes. The results are compared with those obtained from the Green function method.

A hybrid computer for X-ray crystallography

A hybrid computer for structure factor calculations in X-ray crystallography is described. The computer can calculate three-dimensional structure factors of up to 24 atoms in a single run and can generate the scatter functions of well over 100 atoms using Vand et al., or Forsyth and Wells approximations. The computer is essentially a digital computer with analog function generators, thus combining to advantage the economic data storage of digital systems and simple computing circuitry of analog systems. The digital part serially selects the data, computes and feeds the arguments into specially developed high precision digital-analog function generators, the outputs of which being d.c. voltages, are further processed by analog circuits and finally the sequential adder, which employs a novel digital voltmeter circuit, converts them back into digital form and accumulates them in a dekatron counter which displays the final result. The computer is also capable of carrying out 1-, 2-, or 3-dimensional Fourier summation, although in this case, the lack of sufficient storage space for the large number of coefficients involved, is a serious limitation at present.