There currently exists no reliable, non-destructive method for measuring stress in railroads and other similar structures without the need for a calibration measurement. Major limitations which have hindered previous techniques include sensitivity to boundary conditions, insensitivity to stress, and intolerance for material and geometry uncertainty. In this work, a technique is developed which seeks to solve these challenges by extracting the spectrum relation, or dispersion curve, of a waveguide from dispersive wave propagation meaasurements. The technique is based on spectral analysis of waves in structures modeled as beams, and as such is based on relatively low frequency vibrations, as opposed to other techniques which use nonlinear elastic modeling of structures at ultrasonic frequencies. The major contribution of this work is the development of a frequency-domain based signal processing technique which is capable of compensating for the dispersive, long wavelength reflections which have limited the ability of previous techniques to go low enough in frequency to achieve high stress sensitivity. By compensating for reflections, the present work is able to automate the process of analyzing wave propagation signals such that the entire dispersion curve can be extracted, enabling the identification of various parameters including stress, stiffness, density, and other material and geometry properties. This in turn enables measuring stress, performing model-updating for material and geometry uncertainty, and being indifferent to boundary conditions. The theory and algorithmic implementation is presented, along with simulations and experimental validation on a rectangular beam. / Master of Science / The ability to detect damage or the potential for damage in structures is highly desirable, especially in industries such as civil infrastructure in which failure can be incredibly costly and dangerous. In particular, non-destructive techniques which can predict failure without interfering with the operations of a structure are particularly sought after. In this work, a technique for non-intrusively and non-destructively measuring stress is developed, with the primary application being for measuring stress in railroads. The technique seeks to advance the state-of-the-art in wave-propagation-based techniques by adding the capability to automatically identify reflected waves. With this new capability, the method is able to quickly and efficiently analyze a large set of vibration measurements to extract information about the structure's material, geometry, and loading characteristics which enables solving for stress even when the structures material, geometry, and boundary conditions are not precisely known. The technique is demonstrated on both simulated and experimental data, in which a rectangular beam is tensioned and the stress is then identified.

Yes / A new approach of modelling the electromagnetic wave propagation and the penetration of small objects, are investigated and analysed. The travelling electromagnetic wave from source is simulated by time-dependent Maxwell's solutions. Subgridding technique is imposed at the point of interest for observing the electromagnetic field in high resolution. The computational burden caused by a large number of time steps has been parried by implementing the state of art of quasi-static approach. The induced electromagnetic fields near a buried pipeline runs parallel to a 400 kV power transmission lines are presented, and discussed.

Yes / The Rician K-factor of the vehicle-to-vehicle (V2V) wireless propagation channel is estimated using a moment-based method on the envelope of measured pulse data. The measurements were carried out under vehicle-to-vehicle wireless communication channel condition with car rooftop antenna heights at one end of the link and very low antenna height at the other end. Data captured from typical urban, suburban and rural areas are analyzed and the K-factor probability density function is generated for each scenario to give an insight into the V2V channel behavior. For all three areas, the majority of K values are found to be within the range of -10 to +10 dB. The K-factor distributions are close to normal with mean values of 1.8, 2.6 and 3 dB respectively for urban, suburban and rural area.

<p dir="ltr">This thesis focuses on the study of wave propagation in architected material systems. Specifically of interest is wave propagation in topologically interlocking material (TIM) systems made of tetrahedra and bio-inspired blocks. TIM systems are assemblies of composed of blocks in which the block geometry constrains blocks in place. Individual blocks can only be removed by disassembling the system. This interlocking of block geometry allows these systems to bear loads without the need for adhesives. Overall, load bearing is affected by block geometry, contact interaction, and assembly architecture. Wavefronts and wave velocities are computed using an explicit finite element code. Wave propagation is investigated first in a row of interlocking tetrahedra, then in 3D planar TIM systems of tetrahedra and bio-inspired scutoid blocks.</p><p dir="ltr">The propagation of linear traveling waves through a row of interlocking tetrahedra is demonstrated by the use of finite element simulations. The wave velocity was found to be independent of wave amplitude for ideal contact conditions but dependent on impact velocity for an exponential pressure-overclosure relationship between surfaces. For a frictionless, constant contact stiffness model, the effective wave velocity is about 50% of the 1D material wave speed. In the presence of friction, the wave velocity increases to about 80% of the 1D material wave speed. The wave velocity is attributed to wave-guiding set by the geometry of the tetrahedra. The wave velocity is further modulated by the rocking motion of the tetrahedra about an axis perpendicular to the wave propagation direction. The rocking motion is affected by friction and is reduced as friction is increased. Experimental results on wave propagation in a row of 3D-printed triangular prisms demonstrate pulse-like voltage versus time wave responses. With rough and tacky surfaces, the velocity of the linear traveling waves is measured as approximately 20% the 1D material wave speed. For smooth and low friction surface conditions, significantly higher wave velocities are measured. Similarly, reducing the number of contact surfaces by fusing pairs of building blocks also results in higher measured wave velocities. Experiments on rectangular prisms lack the wave-guiding geometry and provide a reference configuration. Finite element models are used to gain detailed insight into the wave propagation process. Wave-guide models are defined to predict wave speeds based on the effective path of wave propagation. The proposed models closely predict measured and computed wave speeds for the tetrahedra and triangular prisms.</p><p dir="ltr">Scutoids are prism-like shapes containing lateral vertices between two parallel polygonal surfaces. With the lateral vertices at the midplane, scutoid blocks can be periodically and densely packed. Scutoid-based planar arrays are demonstrated to behave mechanically as TIM systems. Under quasi-static transverse loads, assembly properties (stiffness, strength, toughness) match or exceed those of the corresponding tetrahedra-based TIM systems. The scutoid-based TIM systems have unique chiral characteristics. Chirality is attributed to the combination of building block and assembly symmetry. Chirality leads to asymmetric internal load transfer patterns resulting in unbalanced in-plane reaction forces and reaction moments. Experiments confirm the computational findings. Under transverse indentation, these systems have nonlinear force-displacement responses and measurable torque responses.</p><p dir="ltr">Wave propagation following transverse impact on planar arrays of interlocking tetrahedra and scutoids is investigated. Unique wave speed and wavefront development are demonstrated to occur in these systems. The 1D material wave speed emerges as the limiting wave speed of the TIM systems, rather than the dilatational wave speed. In tetrahedra assemblies, waves propagate with a velocity of approximately 25% of the 1D material wave speed. The wave velocity is attributed to wave-guiding from the interlocking tetrahedra geometry. Tetrahedra are not perfectly space-filling and block-to-block interactions are not limited to one direction. In the scutoid assemblies, waves propagate at velocities between 80% and 90% of the 1D material wave speed. These velocities are along directions associated with dominant load paths. The wave velocities in the scutoid-based TIM systems approach the 1D material wave speed as the contact surfaces are substantially orthogonal to the assembly surface. In comparison to monolithic plates, wavefronts develop with significant spatial non-uniformity. Wave patterns exhibit the symmetry or asymmetry also observed in the quasi-static response. Overall, contact surface orientation, block geometry, and assembly architecture affect wave velocity and wavefront development.</p>

No description available.

Cardiovascular diseases, including heart attacks and strokes, are leading causes of mortality worldwide. A significant contributor to these conditions is the formation of blood clots obstructing blood flow to critical organs. This study looks specifically at the blood flow in the left ventricle (LV) using simulations with Finite Element Method (FEM). Computational simulations of blood flow offer valuable insights into potential risks, aiding in pre-surgical assessments. However, interpreting simulation results, often presented as ambiguous velocity fields, can be difficult. This study examines two different post-processing measurements, triple decomposition of the velocity gradient tensor and E-wave propagation index (EPI), that can turn these complexities into simpler scalar fields and values. This study confirms that both measurements are computable and most likely useful given a velocity vector field. Further studies, particularly by medical professionals, need to be done to analyse the effects of the measurements and verify its usefulness by comparison to the same measurements in real, not simulated, patients. Some specific studies are proposed to address this. With the triple decomposition implemented some basic analysis was done. High levels of shear were observed in certain areas, particularly around the papillary muscles, where strain was also present.

One of the important considerations in radio link analysis is the signal degradation that accompanies rainfall in a link’s path. Random scattering by rain can adversely affect a propagating wave in two ways. First, it results in attenuation and depolarization of the coherent field which is associated with the forward propagating wave. ln addition to this, random scattering gives rise to an incoherent field component that can further degrade the signal in a manner similar to multipath. This dissertation presents an analysis of the coherent and incoherent effects of rain scatter at millimeter-wave frequencies. Within it, the scattering properties of individual spherical and non-spherical are quantified. Spherical raindrops are treated using the Mie theory and non-spherical ones analyzed with Waterman’s Extended Boundary Condition Method. Computed values of forward scattering amplitudes and scattering cross-sections for both spherical and non-spherical raindrops at 80, 45, 70 and 90 GHz are presented; the computer programs used to obtain the scattering data are also provided. Following the analysis of individual raindrops scatterers, the Foldy·Lax Twersky integral equations for coherent field and incoherent intensity are used to derive the coherent and incoherent outputs of a generic radio receiver. In doing so, the effects of scattering in an antenna’s far-field and radiating near field (Fresnel Region) are analyzed. Through this analysis, it is shown that the expected system outputs are essentially the same in either case. Using the computed raindrop scattering parameters and models developed for the coherent and Incoherent system outputs, specific cases are Iooked at for 30, 45, 70 and 90 GHz operation and theoretical data presented. The data consists of the predicted attenuation and Isolation of the coherent signal and the ratio of coherent to Incoherent power In the presence of rain. From the latter it Is found that during heavy rainfall, the Incoherent effects can be appreciable and should be taken into account. / Ph. D.

Sandwich constructions are the most commonly used structures in aircraft and navy industries, traditionally. These structures are made up of the face sheets and the core, where the face sheets will be taking the load and is connected to other structural members, while the soft core material, will be used to absorb energy during impact like situation. Thus, sandwich constructions are mainly employed in light weight structures where the high energy absorption capability is required. Generally the face sheets will be thin, made up of either metallic or composite material with high stiffness and strength, while the core is light in weight, made up of soft material. Cores generally play very crucial role in achieving the desired properties of sandwich structures, either through geometric arrangement or material properties or both. Foams are in extensive use nowadays as core material due to the ease in manufacturing and their low cost. They are extensively used in automotive and industrial field applications as the desired foam density can be fabricated by adjusting the mixing, curing and heat sink processes. Modeling of sandwich beams play a crucial role in their design with suitable finite elements for face sheets and core, to ensure the compatibility between degrees of freedom at the interfaces. Unless the mathematical model simulates the physics of the model in terms of kinematics, boundary and loading conditions, results predicted will not be accurate. Accurate models helps in obtaining an efficient design of sandwich beams. In Structural Health Monitoring studies, the responses under the impact loading will be captured by carrying out the wave propagation analysis. The loads applied will be for a shorter duration (in the orders of micro seconds), where higher frequency modes will be excited. Wavelengths at such high frequencies are very small and hence, in such cases, very fine mesh generally is employed matching the wavelength requirement of the propagating wave. Traditional Finite element softwares takes enormous time and computational e ort to provide the solution. Various possible models and modeling aspects using the existing Finite element tools for wave propagation analysis are studied in the present work. There exists a huge demand for an accurate, efficient and rapidly convergent finite elements for the analysis of sandwich beams. E orts are made in the present work to address these issues and provide a solution to the sandwich user community. Super convergent and Spectral Finite sandwich Beam Elements with metallic or composite face sheets and soft core are developed. As a philosophy, the sandwich beam finite element is constructed with the combination of two beams representing the face sheets (top and bottom) at their neutral axis. The core effects are captured at the interface boundaries in terms of shear stress and normal transverse stress. In the case of wave propagation analysis, the equations are coupled in time domain and spatial domain and solving them directly is a difficult task. In Spectral Finite Element Method(SFEM), the displacement functions are derived by solving the transformed governing equations in the frequency domain. By transforming them and forces from time domain to frequency domain, the coupled partial differential equations will become coupled ordinary differential equations. These equations in frequency domain, can be solved exactly as they are normally ordinary differential equation with constant coefficients with frequency entering as a parameter. These solutions will be used as interpolating functions for spectral element formulation and in this respect it differs from conventional FE method wherein mostly polynomials are used as interpolating functions. In addition, SFEM solutions are expressed in terms of forward and backward moving waves for all the degrees of freedom involved in the formulations and hence, SFEM provides faster and efficient solutions for wave propagation analysis. In the present work, strong form of the governing differential equations are derived for a given system using Hamilton's principle. Super Convergent elements are developed by solving the static part of the governing differential equations exactly and hence the stiffness matrix derived is exact for point static loads. For wave propagation analysis, as the mass is not exactly represented, these elements are required in the optimal numbers for getting good results. The number of these elements required are generally much lesser than the number of elements required using traditional finite elements since the stiffness distribution is exact. Spectral elements are developed by solving the governing equations exactly in the frequency domain and hence the dynamic stiffness matrix derived is exact for the dynamic loads. Hence, one element between any two joints is enough to solve the whole system under impact loads for simple structures. Developing FE for sandwich beams is quiet challenging. Due to small thickness, the face sheets can be modeled using 1D idealization, while modeling of large core requires 2-D idealization. Hence, most finite or spectral elements requires stitching of these two idealizations into 1-D idealization, which can be accomplished in a variety of ways, some of which are highlighted in this thesis. Variety of finite and spectral finite elements are developed considering Euler and Timoshenko beam theories for modeling the sandwich beams. Simple element models are built with rigid core in both the theories. Models are also developed considering the flexible core with the variation of transverse displacements across depth of the core. This has direct influence on shear stress variation and also transverse normal stress in the core. Simple to higher order models are developed considering different variations in shear stress and transverse normal stress across depth of the core. Development of super convergent finite Euler Bernoulli beam elements Eul4d (4 dof element), Eul10d (10 dof element) are explained along with their results in Chapter 2. Development of different super convergent finite Timoshenko beam elements namely Tim4d (4 dof), Tim7d (7 dof), Tim10d (10 dof) are explained in Chapter 3. Validation of Euler Bernoulli and Timoshenko elements developed in the present work is carried out with test cases available in the open literature for displacements and free vibration frequencies are presented in Chapter 2 and Chapter 3. The results indicates that all developed elements are performing exceedingly well for static loads and free vibration. Super convergence performance for the elements developed is demonstrated with related examples. Spectral elements based on Timoshenko theory STim7d, STim6d, STim6dF are developed and the wave propagation characteristics studies are presented in Chapter 4. Euler spectral elements are derived from Timoshenko spectral elements by enforcing in finite shear rigidity, designated as SEul7d, SEul6d, SEul6dF and are presented. E orts were made in this present work to model the horizontal cracks in top or bottom face sheets using the spectral elements and the methodology is presented in Chapter 4. Wave propagation analysis using general purpose software N AST RAN and the super convergent as well as spectral elements developed in this work, are discussed in detail in Chapter 5. Modeling aspects of sandwich beam in N AST RAN using various combination of elements available and the performance of four possible models simulated were studied. Validation of all four models in N AST RAN, Super convergent Euler, Timoshenko and Spectral Timoshenko finite elements was carried out by simulating a homogenous I beam by comparing the longitudinal and transverse responses. Studies were carried out to find out the response predictions of a sandwich beam with soft core and all the predictions were compared and discussed. The responses in case of cracks in top or bottom face sheets under the longitudinal and transverse loading were studied in this chapter. In Chapter 6, Parametric studies were carried out for bringing out the sensitiveness of the important specific parameters in overall behaviour and performance of a sandwich beam, using Super convergent and Spectral elements developed. This chapter clearly brings out the various aspects of design of sandwich beam such as material selection of core, geometrical configuration of overall beam and core. Effects of shear modulus, mass density on wave propagation characteristics, effects of thick or thin cores with reference to the face sheets and dynamic effects of core are highlighted. Wave propagation characteristics studies includes the study of wave numbers, group speeds, cut off frequencies for a given configuration and identification of frequency zone of operations. The recommendations for improvement in design of sandwich beams based on the parametric studies are made at the end of chapter. The entire thesis, written in seven Chapters, presents a unified treatment of sandwich beam analysis that will be very useful for designers working in the area.

We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable. The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space. / eSSENCE

This dissertation is divided up into two parts, each examining a distinct theme. The rst part of our work concerns itself with open quantum systems and the relaxation phenomena arising from the repeated application of an interaction Hamiltonian on systems composed of quantum harmonic oscillators. For the second part of our work, we shift gears and investigate the wave propagation in left-handed media, or materials with simultaneously negative electric permeability and magnetic permeability . Each of these two parts is complete within its own context. In the rst part of this dissertation, we introduce a relaxation-generating model which we use to study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to bipartite harmonic oscillator systems for some characteristic time interval . The two important time scales which enter our results are discussed in detail. We show that the relaxation time obtained by the application of this repeated interaction scheme is proportional to both the strength of interaction and to the characteristic time interval . Through discussing the implications of our model, we show that, for the case where the oscillator frequencies are equal, the initial Maxwell-Boltzmann distributions of the uncoupled parts evolve to a new Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann distributions, or quasi-stationary, non-equilibrium states. We further analyze the case in which the two oscillator frequencies are unequal and show how the application of the same model leads to a non-thermal steady state. The calculations are exact and the results are obtained through an iterative process, without using perturbation theory. In the second part of this dissertation, we examine the response of a plane wave incident on a at surface of a left-handed material, a medium characterized by simultaneously negative electric permittivity and magnetic permeability . We do this by solving Maxwell's equations explicitly. In the literature up to date, it has been assumed that negative refractive materials are necessarily frequency dispersive. We propose an alternative to this assumption by suggesting that the requirement of positive energy density can be relaxed, and discuss the implications of such a proposal. More speci cally, we show that once negative energy solutions are accepted, the requirement for frequency dispersion is no longer needed. We further argue that, for the purposes of discussing left-handed materials, the use of group velocity as the physically signi cant quantity is misleading, and suggest that any discussion involving it should be carefully reconsidered. / text