Tracking analysis of an LMS decision feedback equalizer for a wireless channel

We consider a time varying wireless fading channel, equalized by an LMS Decision Feedback equalizer (DFE). We study how well this equalizer tracks the optimal MMSEDFE (Wiener) equalizer. We model the channel by an Autoregressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs, we show via some examples that the LMS equalizer moves close to the instantaneous Wiener filter after initial transience. We also compare the LMS equalizer with the instantaneous optimal DFE (the commonly used Wiener filter) designed assuming perfect previous decisions and computed using perfect channel estimate (we will call it as IDFE). We show that the LMS equalizer outperforms the IDFE almost all the time after initial transience.

Simulation of RNA silencing pathway for time-dependent transgene transcription rate

The synthesis of dsRNA is analyzed using a pathway model with amplifications caused by the aberrant RNAs. The transgene influx rate is assumed time-decaying considering the fact that the number of transgenes can not be infinite. The dynamics of the transgene induced RNA silencing is investigated using a system of coupled nonautonomous ordinary nonlinear differential equations which describe the model phenomenologically. The silencing phenomena are detected after a period of transcription. Important contributions of certain parameters are discussed with several numerical examples.

Tracking performance of an LMS-Linear Equalizer for fading channels

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer. We study how well this equalizer tracks the optimal Wiener equalizer. We model the channel by an Auto-regressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs, the error between the LMS equalizer and the instantaneous Wiener filter is shown to decay exponentially/polynomially to zero unless the channel is marginally stable in which case the convergence may not hold.Using the same ODEs, we also show that the corresponding Mean Square Error (MSE) converges towards minimum MSE(MMSE) at the same rate for a stable channel. We further show that the difference between the MSE and the MMSE does not explode with time even when the channel is unstable. Finally we obtain an optimum step size for the linear equalizer in terms of the AR parameters, whenever the error decay is exponential.

Exact controllability of generalized Hammerstein type equation

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Noise reduction with perforated three-duct muffler components

This paper describes the authors’ distributed parameter approach for derivation of closed-form expressions for the four-pole parameters of the perforated three-duct muffler components. In this method, three simultaneous second-order partial differential equations are first reduced to a set of six first-order ordinary differential equations. These equations are then uncoupled by means of a modal matrix. The resulting 6 × 6 matrix is reduced to the 2 × 2 transfer matrix using the relevant boundary conditions. This is combined with transfer matrices of other elements (upstream and downstream of this perforated element) to predict muffler performance like noise reduction, which is also measured. The correlation between experimental and theoretical values of noise reduction is shown to be satisfactory.

Switching Transients in Single-Phase Induction Motors

The subject of transients in polyphase induction motors and synchronous machines has been studied in very great detail by several investigators, but no published literature exists dealing exclusively with the analysis of the problem of transients in single-phase induction motors. This particular problem has been studied in this paper by applying the Laplace transform. The results of actual computation of the currents and developed electrical torque are compared with the data obtained by setting up the integro-differential equations of the machine on an electronic differential analyzer. It is shown that if the motor is switched on to the supply when the potential passes through its zero value, there is a pulsating fundamental frequency torque superimposed on the average steady-state unidirectional torque. If, on the other hand, the switch is closed when the applied potential passes through its maximum value, the developed electrical torque settles down to its final steady-state value during the first cycle of the supply voltage.

The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.

Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure (beta) and the underlying polytropic index (gamma) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of beta and then gamma, which affects solutions described in the standard literature based on constant beta. Certain solutions for a particular set of initial parameters with a constant beta do not exist when the variation of beta is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of beta. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, beta of the flow could vary up to similar to 300%, while gamma up to similar to 20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant gamma and beta should be taken with caution and corrected. (C) 2011 Elsevier B.V. All rights reserved.

Prediction of Breakout Noise from a Rectangular Duct with Compliant Walls

Breakout noise from HVAC ducts is important at low frequencies, and the coupling between the acoustic waves and the structural waves plays a critical role in the prediction of the transverse transmission loss. This paper describes the analytical calculation of breakout noise by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The first step in the breakout noise prediction is to calculate the inside duct pressure field and the normal duct wall vibration by using the solution of the governing differential equations in terms of Green's function. The resultant equations are rearranged in terms of impedance and mobility, which results in a compact matrix formulation. The Green's function selected for the current problem is the cavity Green's function with modification of wave number in the longitudinal direction in order to incorporate the terminal impedance. The second step is to calculate the radiated sound power from the compliant duct walls by means of an ``equivalent unfolded plate'' model. The transverse transmission loss from the duct walls is calculated using the ratio of the incident power due to surface source inside the duct to the acoustic power radiated from the compliant duct walls. Analytical results are validated with the FE-BE numerical models.

An Overview of Homogenization

Homogenization of partial differential equations is relatively a new area and has tremendous applications in various branches of engineering sciences like: material science,porous media, study of vibrations of thin structures, composite materials to name a few. Though the material scientists and others had reasonable idea about the homogenization process, it was lacking a good mathematical theory till early seventies. The first proper mathematical procedure was developed in the seventies and later in the last 30 years or so it has flourished in various ways both application wise and mathematically. This is not a full survey article and on the other hand we will not be concentrating on a specialized problem. Indeed, we do indicate certain specialized problems of our interest without much details and that is not the main theme of the article. I plan to give an introductory presentation with the aim of catering to a wider audience. We go through few examples to understand homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and if possible some details about some of the techniques. A possible definition of homogenization would be that it is a process of understanding a heterogeneous (in-homogeneous) media, where the heterogeneties are at the microscopic level, like in composite materials, by a homogeneous media. In other words, one would like to obtain a homogeneous description of a highly oscillating in-homogeneous media. We also present other generalizations to non linear problems, porous media and so on. Finally, we will like to see a closely related issue of optimal bounds which itself is an independent area of research.

Longitudinal Magnetic Field Effect on Nonlocal Ultrasonic Vibration Analysis of Single-Walled Carbon Nanotubes Based on Wave Propagation Approach

This paper studies the effect of longitudinal magnetic field on ultrasonic vibration in single walled carbon nanotubes (CNTs) based on nonlocal continuum medium theory. Governing partial differential equations of CNTs are derived by considering the Lorentz magnetic forces applied on CNTs induced by a longitudinal magnetic field through Maxwell equations. The vibration characteristics of CNTs under a longitudinal magnetic field are obtained by solving the governing equations via wave propagation approach. The effects of longitudinal magnetic field on vibration of CNTs are discussed through numerical experiments. The present analysis show that vibration frequencies of CNTs drops dramatically in the presence of the magnetic field for various circumferential wavenumbers. Such effect is also observed for various boundary conditions of the CNT. New features for the effect of longitudinal magnetic field on ultrasonic vibration of CNTs, presented in this paper are useful in the design of nano-drive device, nano-oscillator and actuators and nano-electron technology, where carbon nanotubes act as basic elements.

Determination of alpha(s)(M-tau(2)) from improved fixed order perturbation theory

We revisit the extraction of alpha(s)(M-tau(2)) from the QCD perturbative corrections to the hadronic tau branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions D-n, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the (MS) over bar scheme alpha(s)(M-tau(2)) = 0.338 +/- 0.010, using as input a precise value for the perturbative contribution to the hadronic width of the tau lepton reported recently in the literature.

Co-evolution of content popularity and delivery in mobile P2P networks

Mobile P2P technology provides a scalable approach for content delivery to a large number of users on their mobile devices. In this work, we study the dissemination of a single item of content (e. g., an item of news, a song or a video clip) among a population of mobile nodes. Each node in the population is either a destination (interested in the content) or a potential relay (not yet interested in the content). There is an interest evolution process by which nodes not yet interested in the content (i.e., relays) can become interested (i.e., become destinations) on learning about the popularity of the content (i.e., the number of already interested nodes). In our work, the interest in the content evolves under the linear threshold model. The content is copied between nodes when they make random contact. For this we employ a controlled epidemic spread model. We model the joint evolution of the copying process and the interest evolution process, and derive joint fluid limit ordinary differential equations. We then study the selection of parameters under the content provider's control, for the optimization of various objective functions that aim at maximizing content popularity and efficient content delivery.

Nonlocal continuum mechanics based ultrasonic flexural wave dispersion characteristics of a monolayer graphene embedded in polymer matrix

Wave propagation in graphene sheet embedded in elastic medium (polymer matrix) has been a topic of great interest in nanomechanics of graphene sheets, where the equivalent continuum models are widely used. In this manuscript, we examined this issue by incorporating the nonlocal theory into the classical plate model. The influence of the nonlocal scale effects has been investigated in detail. The results are qualitatively different from those obtained based on the local/classical plate theory and thus, are important for the development of monolayer graphene-based nanodevices. In the present work, the graphene sheet is modeled as an isotropic plate of one-atom thick. The chemical bonds are assumed to be formed between the graphene sheet and the elastic medium. The polymer matrix is described by a Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation of the surrounding elastic medium. When the shear effects are neglected, the model reduces to Winkler foundation model. The normal pressure or Winkler elastic foundation parameter is approximated as a series of closely spaced, mutually independent, vertical linear elastic springs where the foundation modulus is assumed equivalent to stiffness of the springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of flexural wave propagation model is also derived and the results of the wave dispersion analysis are shown for both local and nonlocal elasticity calculations. From this analysis we show that the elastic matrix highly affects the flexural wave mode and it rapidly increases the frequency band gap of flexural mode. The flexural wavenumbers obtained from nonlocal elasticity calculations are higher than the local elasticity calculations. The corresponding wave group speeds are smaller in nonlocal calculation as compared to local elasticity calculation. The effect of y-directional wavenumber (eta(q)) on the spectrum and dispersion relations of the graphene embedded in polymer matrix is also observed. We also show that the cut-off frequencies of flexural wave mode depends not only on the y-direction wavenumber but also on nonlocal scaling parameter (e(0)a). The effect of eta(q) and e(0)a on the cut-off frequency variation is also captured for the cases of with and without elastic matrix effect. For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(0)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this article. (c) 2012 Elsevier Ltd. All rights reserved.