A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

An Empirical Model of the Process of Synthesis of Multiple State Mechanical Devices

Automated synthesis of mechanical designs is an important step towards the development of an intelligent CAD system. Research into methods for supporting conceptual design using automated synthesis has attracted much attention in the past decades. The research work presented here is based on the processes of synthesizing multiple state mechanical devices carried out individually by ten engineering designers. The designers are asked to think aloud, while carrying out the synthesis. The ten design synthesis processes are video recorded, and the records are transcribed and coded for identifying activities occurring in the synthesis processes, as well as for identifying the inputs to and outputs from the activities. A mathematical representation for specifying multi-state design task is proposed. Further, a descriptive model capturing all the ten synthesis processes is developed and presented in this paper. This will be used to identify the outstanding issues to be resolved before a system for supporting design synthesis of multiple state mechanical devices that is capable of creating a comprehensive variety of solution alternatives could be developed.

Swam Intelligent Based Inverse Model for Laboratory Double Reservoir Diffusion Experiments

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are, in general, estimated by fitting the theoretical models to a field monitoring or laboratory experimental data. Double-reservoir diffusion (Transient Through-Diffusion) experiments are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. These design parameters are estimated by manual parameter adjusting techniques (also called eye-fitting) like Pollute. In this work an automated inverse model is developed to estimate the mass transport parameters from transient through-diffusion experimental data. The proposed inverse model uses particle swarm optimization (PSO) algorithm which is based on the social behaviour of animals for finding their food sources. Finite difference numerical solution of the transient through-diffusion mathematical model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation.The working principle of the new solver is demonstrated by estimating mass transport parameters from the published transient through-diffusion experimental data. The estimated values are compared with the values obtained by existing procedure. The present technique is robust and efficient. The mass transport parameters are obtained with a very good precision in less time

A k-epsilon model for turbulent weld pool convection in gas metal arc welding process

In this paper, we present a modified k - epsilon model capable of addressing turbulent weld-pool convection in a GMAW process, taking into account the morphology of the phase change interface during a Gas Metal Arc Welding (GMAW) process. A three-dimensional turbulence mathematical model has been developed to study the heat transfer and fluid flow within the weld pool by considering the combined effect of three driving forces, viz., buoyancy, Lorentz force and surface tension (Marangoni convection). Mass and energy transports by the droplets are considered through the thermal analysis of the electrode. The falling droplet's heat addition to the molten pool is considered to be a volumetric heat source distributed in an imaginary cylindrical cavity ("cavity model") within the weld pool. This nature of heat source distribution takes into account the momentum and the thermal, energy of the falling droplets. The numerically predicted weld pool dimensions both from turbulence and laminar models are then compared with the experimental post-weld results sectioned across the weld axis. The above comparison enables us to analyze the overall effects of turbulent convection on the nature of heat and fluid flow and hence on the weld pool shape/size during the arc welding processes.

A Study of Early Afterdepolarizations in a Model for Human Ventricular Tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I-Kr blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

An extended finite element model coupled with level set method for stable pitting corrosion

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution), which requires only three inputs, namely the solid metal concentration, saturation concentration of the dissolved metal ions and diffusion coefficient. A combined eXtended Finite Element Model (XFEM) and level set method is developed in this paper. The extended finite element model handles the jump discontinuity in the metal concentrations at the interface, by using discontinuous-derivative enrichment formulation for concentration discontinuity at the interface. This eliminates the requirement of using front conforming mesh and re-meshing after each time step as in conventional finite element method. A numerical technique known as level set method tracks the position of the moving interface and updates it over time. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed method is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions.

An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

Virus-sized colloid transport in a single pore: Model development and sensitivity analysis

A mathematical model is developed to simulate the transport and deposition of virus-sized colloids in a cylindrical pore throat considering various processes such as advection, diffusion, colloid-collector surface interactions and hydrodynamic wall effects. The pore space is divided into three different regions, namely, bulk, diffusion and potential regions, based on the dominant processes acting in each of these regions. In the bulk region, colloid transport is governed by advection and diffusion whereas in the diffusion region, colloid mobility due to diffusion is retarded by hydrodynamic wall effects. Colloid-collector interaction forces dominate the transport in the potential region where colloid deposition occurs. The governing equations are non-dimensionalized and solved numerically. A sensitivity analysis indicates that the virus-sized colloid transport and deposition is significantly affected by various pore-scale parameters such as the surface potentials on colloid and collector, ionic strength of the solution, flow velocity, pore size and colloid size. The adsorbed concentration and hence, the favorability of the surface for adsorption increases with: (i) decreasing magnitude and ratio of surface potentials on colloid and collector, (ii) increasing ionic strength and (iii) increasing pore radius. The adsorbed concentration increases with increasing Pe, reaching a maximum value at Pe = 0.1 and then decreases thereafter. Also, the colloid size significantly affects particle deposition with the adsorbed concentration increasing with increasing particle radius, reaching a maximum value at a particle radius of 100 nm and then decreasing with increasing radius. System hydrodynamics is found to have a greater effect on larger particles than on smaller ones. The secondary minimum contribution to particle deposition has been found to increase as the favorability of the surface for adsorption decreases. The sensitivity of the model to a given parameter will be high if the conditions are favorable for adsorption. The results agree qualitatively with the column-scale experimental observations available in the literature. The current model forms the building block in upscaling colloid transport from pore scale to Darcy scale using Pore-Network Modeling. (C) 2014 Elsevier By. All rights reserved.

A Short-Channel Common Double-Gate MOSFET Model Adapted to Gate Oxide Thickness Asymmetry

Existing compact models for common double-gate (CDG) MOSFETs are based on the fundamental assumption of having symmetric gate oxide thickness. In this paper, we demonstrate that using the unique quasi-linear relationship between the surface potentials, it is possible to develop compact model for CDG-MOSFETs without such approximation while preserving the mathematical complexity at the same level of the existing models. In the proposed model, the surface potential relationship is used to include the drain-induced barrier lowering, channel length modulation, velocity saturation, and quantum mechanical effect in the long-channel model and good agreement is observed with the technology computer aided design simulation results.

Open loop Model for WDM Links

Wavelength Division Multiplexing (WDM) techniques overfibrelinks helps to exploit the high bandwidth capacity of single mode fibres. A typical WDM link consisting of laser source, multiplexer/demultiplexer, amplifier and detectoris considered for obtaining the open loop gain model of the link. The methodology used here is to obtain individual component models using mathematical and different curve fitting techniques. These individual models are then combined to obtain the WDM link model. The objective is to deduce a single variable model for the WDM link in terms of input current to system. Thus it provides a black box solution for a link. The Root Mean Square Error (RMSE) associated with each of the approximated models is given for comparison. This will help the designer to select the suitable WDM link model during a complex link design.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.

A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two-and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.