Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations. (C) 2010 Elsevier Ltd. All rights reserved.

Experimental validation of analytical performance models for IEEE 802.11 networks

We consider the simplest IEEE 802.11 WLAN networks for which analytical models are available and seek to provide an experimental validation of these models. Our experiments include the following cases: (i) two nodes with saturated queues, sending fixed-length UDP packets to each other, and (ii) a TCP-controlled transfer between two nodes. Our experiments are based entirely on Aruba AP-70 access points operating under Linux. We report our observations on certain non-standard behavior of the devices. In cases where the devices adhere to the standards, we find that the results from the analytical models estimate the experimental data with a mean error of 3-5%.

Analytical models for energy consumption in infrastructure WLAN STAs carrying TCP traffic

We develop analytical models for estimating the energy spent by stations (STAs) in infrastructure WLANs when performing TCP controlled file downloads. We focus on the energy spent in radio communication when the STAs are in the Continuously Active Mode (CAM), or in the static Power Save Mode (PSM). Our approach is to develop accurate models for obtaining the fraction of times the STA radios spend in idling, receiving and transmitting. We discuss two traffic models for each mode of operation: (i) each STA performs one large file download, and (ii) the STAs perform short file transfers. We evaluate the rate of STA energy expenditure with long file downloads, and show that static PSM is worse than just using CAM. For short file downloads we compute the number of file downloads that can be completed with given battery capacity, and show that PSM performs better than CAM for this case. We provide a validation of our analytical models using the NS-2 simulator.

Analytical solutions for heat transfer during cyclic melting and freezing of a phase change material used in electronic or electrical packaging

In this paper we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each subdomain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.

Analytical Study of Low-Field Diffusive Transport in Highly Asymmetric Bilayer Graphene Nanoribbon

We present a simplified theory of carrier backscattering coefficient in a twofold degenerate asymmetric bilayer graphene nanoribbon (BGN) under the application of a low static electric field. We show that for a highly asymmetric BGN(Delta = gamma), the density of states in the lower subband increases more that of the upper, in which Delta and gamma are the gap and the interlayer coupling constant, respectively. We also demonstrate that under the acoustic phonon scattering regime, the formation of two distinct sets of energy subbands signatures a quantized transmission coefficient as a function of ribbon width and provides an extremely low carrier reflection coefficient for a better Landauer conductance even at room temperature. The well-known result for the ballistic condition has been obtained as a special case of the present analysis under certain limiting conditions which forms an indirect validation of our theoretical formalism.

Analytical Evaluation of Squeeze Film Forces in a CMUT With Sealed Air-Filled Cavity

The presence of vacuum inside the cavity of a capacitive micromachined ultrasonic transducer (CMUT) causes the membrane of the device (which is the main vibrating structural component) to deflect towards the substrate, thereby causing a reduction in the effective gap height. This reduction causes a drastic decrease in the pull-in voltage of the device limiting the DC bias at which the device can be operated for maximum efficiency. In addition, this initial deflection of the membrane due to atmospheric pressure, causes significant stress stiffening of the the membrane, changing the natural frequency of the device significantly from the design value. To circumvent the deleterious effects of vacuum in the sealed cavity, we investigate the possibility of using sealed CMUT cavities with air inside at ambient pressure. In order to estimate the transducer loss due to the presence of air in the sealed cavity, we evaluate the resulting damping and determine the forces acting on the vibrating membrane resulting from the compression of the trapped air film. We take into account the flexure of the top vibrating membrane instead of assuming the motion to be parallel-plate like. Towards this end, we solve the linearized Reynolds equation using the appropriate boundary conditions and show that, for a sealed CMUT cavity, the presence of air does not cause any squeeze film damping.

Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

An analytical model for an IEEE~802.11 WLAN using DCF with two types of VoIP calls

In this paper we develop and numerically explore the modeling heuristic of using saturation attempt probabilities as state dependent attempt probabilities in an IEEE 802.11e infrastructure network carrying packet telephone calls and TCP controlled file downloads, using enhanced distributed channel access (EDCA). We build upon the fixed point analysis and performance insights. When there are a certain number of nodes of each class contending for the channel (i.e., have nonempty queues), then their attempt probabilities are taken to be those obtained from saturation analysis for that number of nodes. Then we model the system queue dynamics at the network nodes. With the proposed heuristic, the system evolution at channel slot boundaries becomes a Markov renewal process, and regenerative analysis yields the desired performance measures. The results obtained from this approach match well with ns2 simulations. We find that, with the default IEEE 802.11e EDCA parameters for AC 1 and AC 3, the voice call capacity decreases if even one file download is initiated by some station. Subsequently, reducing the voice calls increases the file download capacity almost linearly (by 1/3 Mbps per voice call for the 11 Mbps PHY)

Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects

In this paper, we address a closed-form analytical solution of the Joule-heating equation for metallic single-walled carbon nanotubes (SWCNTs). Temperature-dependent thermal conductivity kappa has been considered on the basis of second-order three-phonon Umklapp, mass difference, and boundary scattering phenomena. It is found that kappa, in case of pure SWCNT, leads to a low rising in the temperature profile along the via length. However, in an impure SWCNT, kappa reduces due to the presence of mass difference scattering, which significantly elevates the temperature. With an increase in impurity, there is a significant shift of the hot spot location toward the higher temperature end point contact. Our analytical model, as presented in this study, agrees well with the numerical solution and can be treated as a method for obtaining an accurate analysis of the temperature profile along the CNT-based interconnects.

Construction of equivalent circuit of a transformer winding from driving-point impedance function - analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.

Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs have been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (similar to 10(14) G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the average energy density of matter) the number of Landau levels is restricted to one or two. We analyze the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zeroth Landau level to first Landau level occurs. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.