Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

Unsteady boundary layer flow on a cylinder in a channel

The unsteady laminar incompressible nonsimilar boundary layer flow over a circular cylinder placed symmetrically inside a channel has been studied when the unsteadiness and nonsimilarity are due to the free stream velocity. The nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference in combination with the quasilinearization technique. It is found that the channel blockage parameter controls the transfer of heat from the cylinder and delays separation. The skin friction and heat transfer are significantly affected by the free stream velocity distributions.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

The unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter lambda, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number. Untersucht wurde die instationäre laminare Mischkonvektion längs eines vertikalen, in einem porösen Medium eingebetteten Zylinders unter kombinierten Auftriebseffekten von thermischer und spezieller Diffusion. Der Einfluß der Permeabilität des Mediums sowie des magnetischen Feldes wurden in die Betrachtung einbezogen. Die partiellen Differentialgleichungen mit drei unabhängigen Variablen, welche die Strömung beschreiben, wurde numerisch anhand des Schemas der endlichen Differenzen in Verbindung mit der Technik der Quasilinearisation gelöst. Berechnungen für die beschleunigte, verzögerte und oszillierende Geschwindigkeitsverteilung der freien Strömung sind durchgeführt worden. Untersucht wurden ebenfalls die Effekte der Permeabilität des Mediums, der Auftriebskräfte, der transversalen Krümmung, des magnetischen Feldes auf die Oberflächenreibung sowie die Wärmeund Stoffübertragung. Es wurde festgestellt, daß die Geschwindigkeit mehr Einfluß auf die Oberflächenreibung als auf die Wärmeund Stoffübertragung hat. Die Oberflächenreibung sowie die Wärme- und Stoffübertragung werden durch die Auftriebskräfte und die Krümmungsparameter verbessert. Die Wärmeübertragung ist stark abhängig von den Parametern der viskosen Dissipation und der Prandtl-Zahl; die Stoffübertragung von der Schmidt-Zahl.

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Robust Relay Precoder Design for MIMO-Relay Networks

In this paper, we consider a robust design of MIMO-relay precoder and receive filter for the destination nodes in a non-regenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a single MIMO-relay node. The source and destination nodes are single antenna nodes, whereas the MIMO-relay node has multiple transmit and multiple receive antennas. The channel state information (CSI) available at the MIMO-relay node for precoding purpose is assumed to be imperfect. We assume that the norms of errors in CSI are upper-bounded, and the MIMO-relay node knows these bounds. We consider the robust design of the MIMO-relay precoder and receive filter based on the minimization of the total MIMO-relay transmit power with constraints on the mean square error (MSE) at the destination nodes. We show that this design problem can be solved by solving an alternating sequence of minimization and worst-case analysis problems. The minimization problem is formulated as a convex optimization problem that can be solved efficiently using interior-point methods. The worst-case analysis problem can be solved analytically using an approximation for the MSEs at the destination nodes. We demonstrate the robust performance of the proposed design through simulations.

Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis

Scattering of coherent light from scattering particles causes phase shift to the scattered light. The interference of unscattered and scattered light causes the formation of speckles. When the scattering particles, under the influence of an ultrasound (US) pressure wave, vibrate, the phase shift fluctuates, thereby causing fluctuation in speckle intensity. We use the laser speckle contrast analysis (LSCA) to reconstruct a map of the elastic property (Young's modulus) of soft tissue-mimicking phantom. The displacement of the scatters is inversely related to the Young's modulus of the medium. The elastic properties of soft biological tissues vary, many fold with malignancy. The experimental results show that laser speckle contrast (LSC) is very sensitive to the pathological changes in a soft tissue medium. The experiments are carried out on a phantom with two cylindrical inclusions of sizes 6 mm in diameter, separated by 8 mm between them. Three samples are made. One inclusion has Young's modulus E of 40 kPa. The second inclusion has either a Young's modulus E of 20 kPa, or scattering coefficient of mu'(s), = 3.00 mm(-1) or absorption coefficient of mu(a) = 0.03 mm(-1). The optical absorption (mu(a)), reduced scattering (mu'(s)) coefficient, and the Young's modulus of the background are mu(a) = 0.01 mm(-1), mu'(s) = 1.00 mm(-1) and 12kPa, respectively. The experiments are carried out on all three phantoms. On a phantom with two inclusions of Young's modulus of 20 and 40 kPa, the measured relative speckle image contrasts are 36.55% and 63.72%, respectively. Experiments are repeated on phantoms with inclusions of mu(a) = 0.03 mm-1, E = 40 kPa and mu'(s) = 3.00 mm(-1). The results show that it is possible to detect inclusions with contrasts in optical absorption, optical scattering, and Young's modulus. Studies of the variation of laser speckle contrast with ultrasound driving force for various values of mu(a), mu'(s), and Young's modulus of the tissue mimicking medium are also carried out. (C) 2011 American Institute of Physics. doi:10.1063/1.3592352]

Holistic Schema Mappings for XML-on-RDBMS

When hosting XML information on relational backends, a mapping has to be established between the schemas of the information source and the target storage repositories. A rich body of recent literature exists for mapping isolated components of XML Schema to their relational counterparts, especially with regard to table configurations. In this paper, we present the Elixir system for designing industrial-strength mappings for real-world applications. Specifically, it produces an information-preserving holistic mapping that transforms the complete XML world-view (XML schema with constraints, XML documents XQuery queries including triggers and views) into a full-scale relational mapping (table definitions, integrity constraints, indices, triggers and views) that is tuned to the application workload. A key design feature of Elixir is that it performs all its mapping-related optimizations in the XML source space, rather than in the relational target space. Further, unlike the XML mapping tools of commercial database systems, which rely heavily on user inputs, Elixir takes a principled cost-based approach to automatically find an efficient relational mapping. A prototype of Elixir is operational and we quantitatively demonstrate its functionality and efficacy on a variety of real-life XML schemas.

The pursuit-evasion problem of two aircraft in a horizontal plane

The pursuit-evasion problem of two aircraft in a horizontal plane is modelled as a zerosum differential game with capture time as payoff. The aircraft are modelled as point masses with thrust and bank angle controls. The games of kind and degree for this differential game are solved.

A Finite Element Method Based Approach for Evaluating the Sensitivity of Faraday-Type Electromagnetic Flow Meter for Liquid Sodium Flow

Faraday-type electromagnetic flow meters are employed for measuring the flow rate of liquid sodium in fast breeder reactors. The calibration of such flow meters, owing to the required elaborative arrangements is rather difficult. On the other hand, theoretical approach requires solution of two coupled electromagnetic partial differential equation with profile of the flow and applied magnetic field as the inputs. This is also quite involved due to the 3D nature of the problem. Alternatively, Galerkin finite element method based numerical solution is suggested in the literature as an attractive option for the required calibration. Based on the same, a computer code in Matlab platform has been developed in this work with both 20 and 27 node brick elements. The boundary conditions are correctly defined and several intermediate validation exercises are carried out. Finally it is shown that the sensitivities predicted by the code for flow meters of four different dimensions agrees well with the results given by analytical expression, thereby providing strong validation. Sensitivity for higher flow rates, for which analytical approach does not exist, is shown to decrease with increase in flow velocity.

Auditory-motivated Gammatone wavelet transform

The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals. (C) 2013 Elsevier B.V. All rights reserved.

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

GRMHD formulation of highly super-Chandrasekhar rotating magnetized white dwarfs: stable configurations of non-spherical white dwarfs

Here we extend the exploration of significantly super-Chandrasekhar magnetized white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetized polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetized axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2-3 solar mass, with central (deep interior) magnetic fields of the order of 10(14) G and differential rotation with surface time periods of about 1-10 s. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous Type Ia supernovae, to which observational evidence ascribes mass in the range 2.1-2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.