Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

Study of Pulsed Plasma in a Crossed Flow Dielectric Barrier Discharge Reactor for Improvement of NOx Removal in Raw Diesel Engine Exhaust

Improved performance of plasma in raw engine exhaust treatment is reported. A new type of reactor referred to as of cross-flow dielectric barrier discharge (DBD) was used, in which the gas flow is perpendicular to the corona electrode. In raw exhaust environment, the cross-flow (radial-flow) reactor exhibits a superior performance with regard to NOX removal when compared to that with axial flow of gas. Experiments were conducted at different flow rates ranging from 2 L/min to 25 L/min. The plasma assisted barrier discharge reactor has shown encouraging results in NOx removal at high flow rates.

Partial Discharge Resistant Characteristics of Epoxy Nanocomposites

Epoxy nanocomposite samples with a good dispersion of alumina nanoparticles in epoxy matrix were prepared and experiments were performed to measure their partial discharge resistant characteristics. Epoxy alumina nanocomposites with 0.1, 1, 5, 10 and 15 wt% nanofillers were prepared in the laboratory and partial discharge (PD) experiments were conducted at a voltage of 10 kV for different durations using IEC (b) type electrodes. The degradation of the sample surfaces were analyzed using SEM techniques, surface profile studies, FTIR spectroscopy as well as PD studies. An attempt was made to understand the interaction dynamics between the nanoparticle and the epoxy chain by measuring the glass transition temperature of the nanocomposites. The partial discharge resistance obtained for the nanocomposites are compared with those of unfilled epoxy and epoxy microcomposites. It was observed that even with 0.1 wt% of nanofiller added to the epoxy matrix, the partial discharge resistance to degradation gets improved considerably. It was also observed that the inter particle distance has a significant effect on the discharge resistance to degradation. The improvement in the degradation resistance is attributed to the interactions between the nanoparticle and the epoxy chain. A possible mechanism for the surface degradation of nanocomposites has been proposed.

Studies on Compact Discharge Plasma Source for NOX Treatment in Engine Exhaust

This paper proposes a compact electric discharge plasma source for controlling NOX emission in diesel engine exhaust. An automobile ignition coil was used to generate the high voltage pulse using flyback topology. This design is aimed at retrofitting the existing catalytic converters with pulse assisted cleaning technique. In this paper we bring out a relative comparison of discharge plasma and plasma-adsorbent process at different gas flow rates. Activated alumina was used as adsorbent. The main emphasis is laid on the development of a compact pulse source from a DC supply for the removal of NOX from the filtered diesel engine exhaust.

Influence of Bi 3+ ions in enhancing the magnitude of positive temperature coefficients of resistance in n-BaTiO3 ceramics

Bi3+ ions substituting at Ba-sites in a limited concentration range with another donor dopant occupying the Ti-sites in polycrystalline BaTiO3 enhanced the positive temperature coefficient of resistance (PTCR) by over seven orders of magnitude. These ceramics did not require normal post sinter annealing or a change to an oxygen atmosphere during annealing. These ceramics had low porosities coupled with better stabilities to large applied electric fields and chemically reducing atmospheres. Bi3+ ions limited the grain growth to less than 8 mum in size, they enhanced the concentration of acceptor-type trap centres at the grain-boundary-layer regions and maintained complete tetragonality at low grain sizes in BaTiO3 ceramics.

A study of partial discharge characteristics in oil impregnated pressboard insulation

An attempt has been made to study the effect of time and test procedure on the behaviour of partial discharge (PD) pulses causing failure of oil-pressboard system under power frequency voltages using circular disc shaped samples and uniform field electrodes. Weibull statistics have been used to handle the large amount of PD data. The PD phenomena has been found to be stress and time dependent. On the basis of stress level, three different regions are identified and in one of the regions, the rate of deterioration of the sample is at a maximum. The work presents some interesting features of Weibull parameters as related to the condition of insulation studied in addition to its usual PD characteristics

On the dual head-discharge characteristics of a modified chimney weir

This paper is concerned with the dual head-discharge characteristics of a modified chimney weir. It is shown by an optimization procedure that the modified chimney weir having an inward trapezoidal weir over an inverted V-notch can produce discharges proportional to both the logarithm of the head as well as the linear power of the head reckoned independently over two different reference planes, within a prefixed maximum allowable percentage error from the theoretical discharge. A new technique is adopted to optimize the weir parameters, in order to obtain the maximum ranges of measurement under logarithmic, linear as well as combined characteristics. In the case of linear weir it is shown that it is possible to enhance the linearity range of the chimney weir by more than 540% and for a weir with constant indication accuracy by more than 350%. In addition, about 86% of the overall depth of the designed linear weir and over 90% of the logarithmic weir is converted as the corresponding measurable ranges. Experiments with four typical weirs give consistent constant average coefficient of discharge for each weir confirming the theory. The practical application of the weir in minor irrigation, hydraulic and other engineering fields is highlighted.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Passive pressure coefficients, critical failure surface and its kinematic admissibility

Using a combination of a logarithmic spiral and a straight line as a failure surface, comprehensive charts have been developed to determine the passive earth pressure coefficients and the positions of the critical failure surface for positive as well as negative wall friction angles. Translational movement of the wall has been examined in detail, considering the soil as either an associated flow dilatant material or a non-dilatant material, to determine the kinematic admissibility of the limit equilibrium solutions.

Surface modification of PDMS using atmospheric glow discharge polymerization of tetrafluoroethane for immobilization of biomolecules

In this study an atmospheric glow discharge with a fluorocarbon gas as precursor was used to modify the surface of polydimethyl siloxane (PDMS -(CH3)(2)SiO](n)-). The variation in protein immobilizing capability of PDMS was studied for different times of exposure. It was observed that the concentration of proteins adsorbed on the surface varied in an irregular manner with treatment time. The fluorination results in the formation of a thin film of fluorocarbon on the PDMS surface. The AFM and XPS data suggest that the film cracks due to stress and regains its uniformity thereafter. This Stranski-Krastanov growth model of the film was due to the high growth rate offered by atmospheric glow discharge. (C) 2011 Elsevier B. V. All rights reserved.

Dielectric barrier discharge plasma interaction with the airflow over an airfoil

The effect of various parameters on the velocity of the induced jet produced by a dielectric barrier discharge (DBD) plasma was studied experimentally. The glow discharge was created at atmospheric conditions by using a high voltage RF power supply. Flow visualization and photographic studies of the plasma were performed. The parametric investigation of the characteristics of the plasma show that the width of the plasma in the uniform glow discharge regime was an indication of the velocity induced under stagnant conditions. It was observed that the spanwise overlap of the two electrodes, dielectric thickness, voltage and frequency of the applied voltage are the major parameters that govern the velocity and the extent of plasma in the streamwise direction.

Seismic passive earth pressure coefficients using the method of characteristics

The method of characteristics was used to generate passive earth pressure coefficients for an inclined wall retaining cohesionless backfill material in the presence of pseudostatic horizontal earthquake body forces. The variation of the passive earth pressure coefficients K-pq and K-pgamma with changes in horizontal earthquake acceleration coefficient due to the components of soil unit weight and surcharge pressure, respectively, has been obtained; a closed-form solution for K-pq is also provided. The passive earth resistance has been found to decrease sharply with an increase in the magnitude of horizontal earthquake acceleration. The computed passive earth pressure coefficients were found to be the lowest when compared to all of the previous solutions available in the literature.

A cascaded discharge plasma-adsorbent technique for engine exhaust treatment

A cascaded system of electrical discharges (non-thermal plasma) and adsorption process was investigated for the removal of oxides of Nitrogen (NOx) and total hydrocarbons (THC) from an actual diesel engine exhaust. The non-thermal plasma and adsorption processes were separately studied first and then the cascaded process was studied. In this study, different types of adsorbents were used. The NOx removal efficiency was higher with plasma-associated adsorption (cascaded) process compared to the individual processes and the removal efficiency was found almost invariant in time. When associated by plasma, among the adsorbents studied, activated charcoal and MS-13X were more effective for NOx and THC removal respectively. The experiments were conducted at no load and at 50% load conditions. The plasma reactor was kept at room temperature throughout the experiment, while the temperature of the adsorbent reactor was varied. A relative comparison of adsorbents was discussed at the end.