Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

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.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

Response of shock wave deformation in AA5086 aluminum alloy

The AA5086 aluminum alloy sheets with different starting textures were subjected to shock wave deformation with an input impulse of similar to 0.2 Ns. Microstructural examination indicate no significant change in grain size; however, the evolution of substructure manifesting intra-granular misorientation was evident. The improvement in hardness indicates the absence of recovery and strain hardening during shock deformation. Shock deformed samples show characteristic texture evolution with high Brass {110}< 112 > component. The study demonstrates the viability of high velocity forming of AA5086 aluminum alloy sheet using shock wave. (C) 2014 Elsevier B.V. All rights reserved.

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Remotely triggered micro-shock wave responsive drug delivery system for resolving diabetic wound infection and controlling blood sugar levels

A novel, micro-shock wave responsive spermidine and dextran sulfate microparticle was developed. Almost 90% of the drug release was observed when the particles were exposed to micro-shock waves 5 times. Micro-shock waves served two purposes; of releasing the antibiotic from the system and perhaps disrupting the S. aureus biofilm in the skin infection model. A combination of shock waves with ciprofloxacin loaded microparticles could completely cure the S. aureus infection lesion in a diabetic mouse model. As a proof of concept insulin release was triggered using micro-shock waves in diabetic mice to reduce the blood glucose level. Insulin release could be triggered for at least 3 days by exposing subcutaneously injected insulin loaded particles.

Wave propagation of phonon and phason displacement modes in quasicrystals: Determination of wave parameters

The paper presents the study of wave propagation in quasicrystals. Our interest is in the computation of the wavenumber (k(n)) and group speed (c(g)) of the phonon and phason displacement modes of one, two, and three dimensional quasicrystals. These wave parameter expressions are derived and computed using the elasto-hydrodynamic equations for quasicrystals. For the computation of the wavenumber and group speeds, we use Fourier transform approximation of the phonon and the phason displacement modes. The characteristic equations obtained are a polynomial equation of the wavenumber (k(n)), with frequency as a parameter. The corresponding group speeds (c(g)) for different frequencies are then computed from the wavenumber k(n). The variation of wavenumber and group speeds with frequency is plotted for the 1-D quasicrystal, 2-D decagonal Al-Ni-Co quasicrystals, and 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. From the wavenumber and group speeds plots, we obtain the cut-off frequencies for different spatial wavenumber eta(m). The results show that for 1-D, 2-D, and 3-D quasicrystals, the phonon displacement modes are non-dispersive for low values of eta(m) and becomes dispersive for increasing values of eta(m). The cut-off frequencies are not observed for very low values of eta(m), whereas the cut-off frequency starts to appear with increasing eta(m). The group speeds of the phason displacement modes are orders of magnitude lower than that of the phonon displacement modes, showing that the phason modes do not propagate, and they are essentially the diffusive modes. The group speeds of the phason modes are also not influenced by eta(m). The group speeds for the 2-D quasicrystal at 35 kHz is also simulated numerically using Galerkin spectral finite element methods in frequency domain and is compared with the results obtained using wave propagation analysis. The effect of the phonon and phason elastic constants on the group speeds is studied using 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. It is also shown that the phason elastic constants and the coupling coefficient do not affect the group speeds of the phonon displacement modes. (C) 2015 AIP Publishing LLC.

Optimal Pulse Width Modulation of Voltage-Source Inverter fed Motor Drives with Relaxation of Quarter Wave Symmetry Condition

Optimal switching angles for minimization of total harmonic distortion of line current (I-THD) in a voltage source inverter are determined traditionally by imposing half-wave symmetry (HWS) and quarter-wave symmetry (QWS) conditions on the pulse width modulated waveform. This paper investigates optimal switching angles with QWS relaxed. Relaxing QWS expands the solution space and presents the possibility of improved solutions. The optimal solutions without QWS are shown here to outperform the optimal solutions with QWS over a range of modulation index (M) between 0.82 and 0.94 for a switching frequency to fundamental frequency ratio of 5. Theoretical and experimental results are presented on a 2.3kW induction motor drive.

A comparative study of a direct discretization and an operator-splitting solver for population balance systems

A direct discretization approach and an operator-splitting scheme are applied for the numerical simulation of a population balance system which models the synthesis of urea with a uni-variate population. The problem is formulated in axisymmetric form and the setup is chosen such that a steady state is reached. Both solvers are assessed with respect to the accuracy of the results, where experimental data are used for comparison, and the efficiency of the simulations. Depending on the goal of simulations, to track the evolution of the process accurately or to reach the steady state fast, recommendations for the choice of the solver are given. (C) 2015 Elsevier Ltd. All rights reserved.

A spectral element for wave propagation in honeycomb sandwich construction considering core flexibility

Spectral elements are found to be extremely resourceful to study the wave propagation characteristics of structures at high frequencies. Most of the aerospace structures use honeycomb sandwich constructions. The existing spectral elements use single layer theories for a sandwich construction wherein the two face sheets vibrate together and this model is sufficient for low frequency excitations. At high frequencies, the two face sheets vibrate independently. The Extended Higher order SAndwich Plate theory (EHSaPT) is suitable for representing the independent motion of the face sheets. A 1D spectral element based on EHSaPT is developed in this work. The wave number and the wave speed characteristics are obtained using the developed spectral element. It is shown that the developed spectral element is capable of representing independent wave motions of the face sheets. The propagation speeds of a high frequency modulated pulse in the face sheets and the core of a honeycomb sandwich are demonstrated. Responses of a typical honeycomb sandwich beam to high frequency shock loads are obtained using the developed spectral element and the response match very well with the finite element results. It is shown that the developed spectral element is able to represent the flexibility of the core resulting into independent wave motions in the face sheets, for which a finite element method needs huge degrees of freedom. (C) 2015 Elsevier Ltd. All rights reserved.

Detection of a quantum particle on a lattice under repeated projective measurements

We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect its arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals tau, and we consider the evolution of the wave function until the time a detection occurs. We study the probabilities of its first detection at some time and, conversely, the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, which consists of unitary transformations followed by projections, to one described by a non-Hermitian Hamiltonian. For some examples of a particle moving on one-and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean-field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one-and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and nontrivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

Modeling Ultrasonic NDE and Guided Wave based Structural Health Monitoring

Structural Health Monitoring (SHM) systems require integration of non-destructive technologies into structural design and operational processes. Modeling and simulation of complex NDE inspection processes are important aspects in the development and deployment of SHM technologies. Ray tracing techniques are vital simulation tools to visualize the wave path inside a material. These techniques also help in optimizing the location of transducers and their orientation with respect to the zone of interrogation. It helps in increasing the chances of detection and identification of a flaw in that zone. While current state-of-the-art techniques such as ray tracing based on geometric principle help in such visualization, other information such as signal losses due to spherical or cylindrical shape of wave front are rarely taken into consideration. The problem becomes a little more complicated in the case of dispersive guided wave propagation and near-field defect scattering. We review the existing models and tools to perform ultrasonic NDE simulation in structural components. As an initial step, we develop a ray-tracing approach, where phase and spectral information are preserved. This enables one to study wave scattering beyond simple time of flight calculation of rays. Challenges in terms of theory and modelling of defects of various kinds are discussed. Various additional considerations such as signal decay and physics of scattering are reviewed and challenges involved in realistic computational implementation are discussed. Potential application of this approach to SHM system design is highlighted and by applying this to complex structural components such as airframe structures, SHM is demonstrated to provide additional value in terms of lighter weight and/or longevity enhancement resulting from an extension of the damage tolerance design principle not compromising safety and reliability.

Study of Degradation in Composite Lap Shear joints using a Guided Wave Technique

Experimental and numerical investigations were carried out using lamb waves to study the degradation in adhesive joints made of carbon fiber reinforced plastic (CFRP) adherends and epoxy adhesive. Degradation was inducted into the epoxy adhesive by adding different amounts of polyvinyl alcohol. Fundamental lamb wave modes were excited in the CFRP adherends using piezoelectric transducer disks and made to propagate through the adhesive layer. The received waveforms across adhesive joints with varied degradation were studied. A 2D finite element model was utilized to verify the experimental results. Good correlation was observed between numerical and experimental results. Details of the investigation and results obtained are presented in the paper.

A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin-Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener-Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

Effects of site stiffness and source to receiver distance on surface wave tests' results

By using six 4.5 Hz geophones, surface wave tests were performed on four different sites by dropping freely a 65 kg mass from a height of 5 m. The receivers were kept far away from the source to eliminate the arrival of body waves. Three different sources to nearest receiver distances (S), namely, 46 m, 56 m and 66 m, were chosen. Dispersion curves were drawn for all the sites. The maximum wavelength (lambda(max)), the maximum depth (d(max)) up to which exploration can be made and the frequency content of the signals depends on the site stiffness and the value of S. A stiffer site yields greater values of lambda(max) and d(max). For stiffer sites, an increase in S leads to an increase in lambda(max). The predominant time durations of the signals increase from stiffer to softer sites. An inverse analysis was also performed based on the stiffness matrix approach in conjunction with the maximum vertical flexibility coefficient of ground surface to establish the governing mode of excitation. For the Site 2, the results from the surface wave tests were found to compare reasonably well with that determined on the basis of cross boreholes seismic tests. (C) 2015 Elsevier Ltd. All rights reserved.