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Pulsed Ejector Wave Propagation Test Rig - 2002 Entry

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

The National Oceanic and Atmospheric Administration (NOAA) Wave Propagation Laboratory (WPL) presently operates five dual-channel microwave radiometers, one triple-channel microwave radiometer, and one six-channel microwave radiometer. The dual-channel radiometers operate at frequencies of 20.6 or 23.87 GHz and 31.4 or 31.65 GHz. The triple-channel radiometer operates at 20.6, 31.65, and 90.0 GHz. The six-channel radiometer operates at frequencies of 20.6, 31.65, 52.85, 53.85, 55.45, and 58.8 GHz. Recent brightness temperature measurements and attenuation values from some of the above radiometers are presented. These radiometric measurements, taken in different locations throughout the world, have given WPL a diverse set of measurements under a variety of atmospheric conditions. We propose to do a more complete attenuation analysis on these measurements in the future. In addition, a new spinning reflector was installed recently for the dual-channel radiometer at the Platteville, Colorado site. This reflector will extend our measurement capabilities during precipating conditions. Locating the three-channel and portable dual-channel radiometers at or near Greeley, Colorado to support the Advanced Communications Technology Satellite (ACTS) program is discussed.

Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.

A theoretical propagation model that represents the scattering properties of an inhomogeneous rain often found on a satellite communications link is presented. The model includes the scattering effects of an arbitrary distribution of particle type (rain or ice), particle shape, particle size, and particle orientation within a given rain cell. An associated rain propagation prediction program predicts attenuation, isolation and phase shift as a function of ground rain rate. A frequency independent synthetic storm algorithm is presented that models nonuniform rain rates present on a satellite link. Antenna effects are included along with a discussion of rain reciprocity. The model is verified using the latest available multiple frequency data from the CTS and COMSTAR satellites. The data covers a wide range of frequencies, elevation angles, and ground site locations.

We have developed an effective two-stage time-integration technique for elastodynamics and acoustic wave propagation problems solved with explicit and implicit time-integration methods and different space-discretization methods. For the first time, we have quantified the range of spurious oscillations for different space-discretization methods and have effectively filtered the spurious oscillations at the filtering stage. We have developed new finite elements with reduced dispersion for explicit time-integration methods as well as an analytical procedure for the selection of the size of time increments for the stage of basic computations and the filtering stage for the new finite elements with reduced numerical dispersion. The solution of 1D, 2D and 3D benchmark wave propagation problems showed that the new technique yields accurate and non-oscillatory results without interaction between computer code and user and reduces the computation time by a factor of 10-1000 and more compared with the standard finite element approaches. A surprisingly good agreement between experiments by group of Dr. Foley from AFRL/RWMF, Eglin and the simulations with the new numerical technique has been obtained for wave propagation in the components of the Hopkinson Pressure Bar.

C-HEMP is a two-dimensional finite-difference computer program for treating stress waves propagation, in either planar or axisymmetric flow, caused by impacts or explosive detonation. It was designed, implemented, and tested at SRI International under a three-year contract for the U.S. Army Ballistic Research Laboratory to develop a computational model for armor penetration. The manual for the C-HEMP stress wave propagation code consists of two volumes. This first volume contains the descriptions and derivations of the code. Keywords: Two dimensional, Wave propagation code, Armor penetration, Explosive detonation, Computational model, Micromechanical model, Shear banding, Brittle fracture, Ductile fracture.

A numerical method is described by which theoretical formulas governing the propagation of symmetric and antisymmetric waves in elastic plate theory may be evaluated. Vital to evaluating the formulas is the availability of a means for solving transcendental equations. A generalized iterative rootfinder that was developed for this purpose is described. This rootfinder provides the investigator having access to computing facilities with a reliable means for solving transcendental equations. Dispersion curves for both the flexural and extensional waves in rubber, steel, and beryllium plates are calculated and plotted. These curves approach a real value k for the ratio of the Rayleigh to shear wave speeds. Values of this quantity calculated from the exact elasticity theory were compared with those obtained from an approximate formula given by Victorov. In addition, the inflection and the maximum points of the strain distribution throughout a free plate were calculated. It was found that inflection points in the strain distribution do not exist at all frequencies. In addition to a description and flow chart of the iterative rootfinder method, the significant graphs, equations, and computer programs that arose when computing the dispersion curve calculations are included. (Author)

Theoretical predictions of weak shocks and Prandtl-Meyer expansions in unsteady flow and three-dimensional steady supersonic flow

Formation of shock wave in two dimensional flow field and method for predicting shape and strength of shock wave

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Propagation of large-amplitude plane waves was studied in rock specimens from 1/2 to 12 inches thick using in-material piezoresistive stress gages. Sioux quartzite, charcoal black granite, and Coconino sandstone were examined. Good records were obtained in the granite experiments, allowing separation of the precursor from the main wave to be observed at five successive locations in a single experiment. It is concluded that time-dependent effects on wave propagation in quartzite and granite are not significant over these distances. Two experiments in granite, with open cracks, one dry and one water- filled, displayed the effect of the crack in erasing the precursor. The erasure was more complete than expected by simple theory, especially in the case of the water-filled crack.

Literature on longitudinal wave propagation in cylindrical shells is reviewed.

The ability to simulate a reentry vehicle plasma layer and the radio wave interaction with that layer, is crucial to the design of aerospace vehicles when the analysis of radio communication blackout is required. Results of aerothermal heating, plasma generation and electromagnetic wave propagation over a reentry vehicle are presented in this paper. Simulation of a magnetic window radio communication blackout mitigation method is successfully demonstrated.

The purpose of the investigation is to study the interaction between an obliquely incident, plane electromagnetic wave and a plane, semi infinite dielectric medium, the dielectric constant of which contains a space- and time- varying component. Let us first consider a medium, the dielectric constant of which is periodically fluctuating only in time. It can then be shown that one gets parametric resonance when the angular frequency, w1, of the incident electro-magnetic wave is equal to half the angular frequency, w2, of the forced, or pumped, variations in the disturbed medium. However, when the disturbance is propagating, this resonance condition becomes altered. We find, that in order to get resonance effects certain relations depending on the angle of incidence and the phase velocities of the incident and pump-wave, predicted by Rydbeck, must be fulfilled. The harmonic time variation of the dielectric medium produces transmitted and reflected waves (non-linear modes) on the characteristic frequencies w1 = nw2, where n 0, 1, 2 ... The angles of reflection and transmission will be functions of the propagation parameters of the two waves as expressed by a generalization of Snell's law. The investigation, finally, also includes the case where losses are taken into account.

This report summarizes the mechanical and electrical characteristics of instrumentation designed to be flown in a Black Brant rocket along with another payload developed by AFCRL. The experiments for which the instrumentation is used are: (a) an A-C conductivity probe which measures the impedance between an insulated section of the nose cone and the body of the rocket at two different frequencies; and (b) a propagation experiment which measures the field strength, along two axes of the rocket, of a low frequency wave transmitted from the ground to the rocket. A block diagram of the system used to perform the experiments is given.

The long propagation paths involved in radio and stellar occultations by turbulent planetary atmospheres require that the classical, weak scattering scintillation theory be expanded to account for the inhomogeneous ambient atmosphere upon which the turbulence is superimposed. Such coupling between the turbulent and the ambient components of refractivity reduces the scintillation index by less than a factor of two in shallow radio occultations. For stellar occultations the reduction varies between this value for very small projected stellar radii, to approximately a factor of 3.6 when the projected stellar radius above the planetary limb greatly exceeds the radius of the free-space Fresnel zone at this distance. More profound changes are found in the scintillation power spectrum, the shape of which depends strongly on both occultation depth and geometry when coupling to the inhomogeneous background is properly accounted for. Second-order, systematic propagation effects calculated from both geometrical optics and a wave-optical formulation show that the average phase velocity is increased in the presence of turbulence. The finite wavelength dependence of the phase path bias implies that an initially non-dispersive medium becomes slightly dispersive by the addition of turbulence. Atmospheric profiles derived from occultations by turbulent planetary atmospheres differ only slightly from those of the corresponding non-turbulent atmosphere when the weak scattering condition is satisfied.

The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareal's wave propagation characteristics with the aim to better understand what causes the well documented stability problems for hyperbolic equations. The analysis shows that the instability is caused by convergence of the amplification factor to the exact value from above for medium to high wave numbers. Phase errors in the coarse propagator are identified as the culprit, which suggests that specifically tailored coarse level methods could provide a remedy.

This paper presents multiwavelength observations of a flare-generated type II radio burst. The kinematics of the shock derived from the type II closely match a fast EUV wave seen propagating through coronal arcade loops. The EUV wave was closely associated with an impulsive M1.0 flare without a related coronal mass ejection, and was triggered at one of the footpoints of the arcade loops in active region NOAA 12035. It was initially observed in the AIA 335 \AA\ images with a speed of ~800 km/s and accelerated to ~1490 km/s after passing through the arcade loops. A fan-spine magnetic topology was revealed at the flare site. A small, confined filament eruption (~340 km/s) was also observed moving in the opposite direction to the EUV wave. We suggest that breakout reconnection in the fan-spine topology triggered the flare and associated EUV wave that propagated as a fast shock through the arcade loops.

We present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, non-linearly to the field strength. We work in the context of Maxwell' s theory in the low frequency limit and obtain a geometrical representation of light paths for each case presented. The isotropic case and artificial birefringence caused by an external electric field are analyzed as an application of the formalism and the effective geometry associated to the wave propagation is exhibited.

We present a complete study of the ergodic theorem for the difficult problem of non-linear wave propagations through cylindrical measures /path integrals and the famous Ruelle-Amrein-Geogerscu-Enss (R.A.G.E.) theorem on the caracterization of continuous spectrum of self-adjoint operators.

We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biot's model in an infinite bilayered medium, with a plane interface. We adopt the Cagniard-De Hoop's technique. This report is devoted to the calculation of analytical solutions in two dimensions. The solutions we present here have been used to validate numerical codes.

We experimentally and theoretically analyze the propagation of weak signal field pulses under the conditions of electromagnetically induced transparency (EIT) in hot Rb vapor, and study the effects of resonant four-wave mixing (FWM). In particular, we demonstrate that in a double-$\Lambda$ system, formed by the strong control field with the weak resonant signal and a far-detuned Stokes field, both continuous-wave spectra and pulse propagation dynamics for the signal field depend strongly on the amplitude of the seeded Stokes field, and the effect is enhanced in optically dense atomic medium. We also show that the theory describing the coupled propagation of the signal and Stokes fields is in good agreement with the experimental observations.

The description of stress-time history acting on a buried structure is a major source of error in the analysis of underground structures to weapons loadings. The stress wave propagating spherically from the weapon is attenuated as it travels from the source. This attenuation is a function of the inelastic response of the soil, and results in an increase in the loading rise time or decrease in the loading rate. Since the inelastic soil response is a function of the loading rate, a wave propagation analysis should be conducted to determine the stresses on the structure. At the interface between the soil and structure, the stress is modified further by soil-structure interaction effects. Thus, the stress on the structure is a function of both the structural and soil properties as well as the distance traveled by the stress wave. These related phenomena can be included in a numerical analysis, but the accuracy depends on the constitutive representation of the materials. One-dimensional wave propagation experiments and impact tests with various soils are reviewed, and the attenuation as a function of the soil stress-strain response is discussed. Keywords include: Dynamic loads, Hardened structures, Explosive effects, Underground structures, Conventional weapons, Dynamic structural response, and Interaction.

The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed in this work. In this realistic situation both the incident and the scattered waves interact with these two elements, the surface and the array. The interaction between the excess attenuation effect, due to the destructive interference produced by the superposition of the incident wave and the reflected one by the surface, and the bandgap, due to the periodicity of the array, is fundamental for the design of devices to control the transmission of waves based on periodic arrays. The most obvious application is perhaps the design of Sonic Crystals Noise Barriers. Two different finite impedance surfaces have been analyzed in the work in order to observe the dependence of the wave propagation properties on the impedance of the surface.

We consider a recently derived kinetic model for weakly relativistic quantum plasmas. We find that that the effects of spin-orbit interaction and Thomas precession may alter the linear dispersion relation for a magnetized plasma in case of high plasma densities and/or strong magnetic fields. Furthermore, the ponderomotive force induced by an electromagnetic pulse is studied for an unmagnetized plasma. It turns out that for this case the spin-orbit interaction always give a significant contribution to the quantum part of the ponderomotive force.

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

In ocean wave-field evolution, nonlinear effects affect the propagation velocity of each wave component in the wave field, produce locked wave components, cause modulational instability development, and enable resonant wave-wave interactions. All of these influence the spatial and temporal variations of the sea surface shape. The nonlinear effects are dependent on wave spectrum parameters (such as wave steepness, bandwidth, and propagating direction) and propagation distance and evolution duration of the wave-field. The main objective of this project is to develop understanding and characterization of nonlinear effects in phase-resolved ocean surface wave-field evolution.

In order to meet the demanding accuracy requirements in the simulation of wave propagation phenomena, a numerical approach based on high-resolution spatial schemes is presented. The time-domain AFRL code, FDL3DI, solves either the time-dependent Maxwell's equations (for CEM) or the Euler equations (for acoustics) employing 6th-order accurate compact-differences and low-pass spatial filters of up to 10th-order accuracy. The solver has been made applicable to general curvilinear grids through the incorporation of a careful treatment of the coordinate transformation metrics. In addition, the method has been extended to multi-body scattering applications through the use of overset grids and high-order interpolation. A robust absorbing boundary condition exploiting the transfer function of the low-pass filter has been developed. To evaluate the solver, several benchmark problems have been considered. Application to communication through weakly ionized plasma has also been studied.

An investigation of inverse problems as basic problems in science, in which physical systems are to be identified on the basis of experimental observations. These problems are especially important in astrophysics and astronomy, for their objects of investigation are frequently not observable in a direct fashion. Solar and stellar structure, for example, is estimated from the study of spectra, while the structure of a planetary atmosphere may be deducted from measurements of reflected sunlight. This memorandum shows that a wide class of inverse problems may now be solved with high-speed computers and modern computational techniques.

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters.

The nature of fast magnetoacoustic and Alfv\'en waves is investigated in a zero $\beta$ plasma. This gives an indication of wave propagation in the low $\beta$ solar corona. It is found that for a two-dimensional null point, the fast wave is attracted to that point and the front of the wave slows down as it approaches the null point, causing the current density to accumulate there and rise rapidly. Ohmic dissipation will extract the energy in the wave at this point. This illustrates that null points play an important role in the rapid dissipation of fast magnetoacoustic waves and suggests the location where wave heating will occur in the corona. The Alfv\'en wave behaves in a different manner in that the wave energy is dissipated along the separatrices. For Alfv\'en waves that are decoupled from fast waves, the value of the plasma $\beta$ is unimportant. However, the phenomenon of dissipating the majority of the wave energy at a specific place is a feature of both wave types.

An analysis of the propagation of electromagnetic waves along a perfectly conducting wire parallel to a plane interface between dissimilar materials is presented. Particular emphasis is placed on determination of the significance of the first order Fourier components of current on the wire compared with the zero order current which has no azimuthal dependence around the wire. (Author)

An analysis of the propagation of electromagnetic waves along a perfectly conducting wire parallel to a plane interface between dissimilar materials is presented. Particular emphasis is placed on determination of the significance of the first order Fourier components of current on the wire compared with the zero order current which has no azimuthal dependence around the wire. (Author)

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps.

Bell System Technical Journal, 28: 1. January 1949 pp 1-32. Propagation of TE01 Waves in Curved Wave Guides. (Albersheim, W.J.)

Bell System Technical Journal, 38: 1. January 1959 pp 119-139. Space-Charge Wave Harmonics and Noise Propagation in Rotating Electron Beams. (Rigrod, W.W.)

Propagation of high-frequency wave in periodic media is a challenging problem due to the existence of multiscale characterized by short wavelength, small lattice constant and large physical domain size. Conventional computational methods lead to extremely expensive costs, especially in high dimensions. In this paper, based on Bloch decomposition and asymptotic analysis in the phase space, we derive the frozen Gaussian approximation for high-frequency wave propagation in periodic media and establish its converge to the true solution. The formulation leads to efficient numerical algorithms, which are presented in a companion paper [Delgadillo, Lu and Yang, arXiv:1509.05552].

In the present work, we experimentally implement, numerically compute with and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally-resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly-localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of high-amplitude impacts without relying on damping in the system.

A localized perturbation of a magnetic flux tube produces a pair of wave trains that propagate in opposite directions along the tube. These wave packets disperse as they propagate, where the extent of dispersion depends on the physical properties of the magnetic structure, on the length of the initial excitation, and on its nature (e.g., transverse or axisymmetric). In Oliver et al. (2014) we considered a transverse initial perturbation, whereas the temporal evolution of an axisymmetric one is examined here. In both papers we use a method based on Fourier integrals to solve the initial value problem. Previous studies on wave propagation in magnetic wave guides have emphasized that the wave train dispersion is influenced by the particular dependence of the group velocity on the longitudinal wavenumber. Here we also find that long initial perturbations result in low amplitude wave packets and that large values of the magnetic tube to environment density ratio yield longer wave trains. To test the detectability of propagating transverse or axisymmetric wave packets in magnetic tubes of the solar atmosphere (e.g., coronal loops, spicules, or prominence threads) a forward modelling of the perturbations must be carried out. This is left for a future work.

This work is concerned with the Biot/squirt (BISQ) models for wave propagation in saturated porous media. We show that the models allow exponentially exploding solutions, as time goes to infinity, when the characteristic squirt-flow coefficient is negative or has a non-zero imaginary part. We also show that the squirt-flow coefficient does have non-zero imaginary parts for some experimental parameters. Because the models are linear, the existence of such exploding solutions indicates instability of the BISQ models. This result calls on a reconsideration of the widely used BISQ theory. Furthermore, we demonstrate that the 3D isotropic BISQ model is stable when the squirt-flow coefficient is positive. In particular, the original Biot model is unconditionally stable where the squirt-flow coefficient is 1.

We analyze plasma dispersion and scattering of fast radio bursts (FRBs) to identify the dominant locations of free electrons along their lines of sight and thus constrain the distances of the burst sources themselves. We establish the average $\tau$-DM relation for Galactic pulsars and use it as a benchmark for discussing FRB scattering. Though scattering times $\tau$ for FRBs are large in the majority of the 17 events we analyze, they are systematically smaller than those of Galactic pulsars that have similar dispersion measures (DMs). The lack of any correlation between $\tau$ and DM for FRBs suggests that the intergalactic medium (IGM) cannot account for both $\tau$ and DM. We therefore consider mixed models involving the IGM and host galaxies. If the IGM contributes significantly to DM while host galaxies dominate $\tau$, the scattering deficit with respect to the mean Galactic trend can be explained with a $\tau$-DM relation in the host that matches that for the Milky Way. However, it is possible that hosts dominate both $\tau$ and DM, in which case the observed scattering deficits require free electrons in the host to be less turbulent than in the Galaxy, such as if they are in hot rather than warm ionized regions. Our results imply that distances or redshifts of FRB sources can be significantly overestimated if they are based on the assumption that the extragalactic portion of DM is dominated by the IGM.

The enhancement technologies of wireless body area network improved the health monitoring system. Previous work have been designed the implantable chip printed antenna at 4.8 GHz. This paper is continuing the investigation where the antenna wave propagation in term of attenuation and polarization were studied. The antenna is implanted in human hand voxel model from CST Microwave Studio Software. The performances of the antenna are evaluated in term of return loss, gain and efficiency. Results show that the rate attenuation for the propagation is approximately 0.16 dB up to 0.42 dB. All the results will be guidelines in designing implantable antennas in futures.

The enhancement technologies of wireless body area network improved the health monitoring system. Previous work have been designed the implantable chip printed antenna at 4.8 GHz. This paper is continuing the investigation where the antenna wave propagation in term of attenuation and polarization were studied. The antenna is implanted in human hand voxel model from CST Microwave Studio Software. The performances of the antenna are evaluated in term of return loss, gain and efficiency. Results show that the rate attenuation for the propagation is approximately 0.16 dB up to 0.42 dB. All the results will be guidelines in designing implantable antennas in futures.

SHALWV is a numerical model that simulates shallow-water wave growth, propagation, and decay in a directional spectrum over an arbitrary bathymetry. It is a time-dependent model requiring a primary input of the wind speed and wind direction at each grid point. Part I of this report contains an overview of SHALWV consisting of the model description, the theoretical background, and the model applications and limitations. Part II provides the information necessary to execute the model, such as model conventions, model input, and model output. The loose-leaf format is to facilitate documentation of future enhancements to the model. (Author)

Knowledge of the elastic properties of composite materials can be an invaluable tool for both the quality assurance of manufacturing techniques and design verification. Recent advances in ultrasonic velocity measurements have demonstrated the ability to recover elastic properties in anisotropic laminates. A simplified experimental setup was investigated to recover the elastic properties based upon the flexural wave propagation in anisotropic laminates. The initial objective of this thesis was to verify flexural wave propagation in composite laminates through the comparison of experimental and theoretical phase velocities. In the second part of this thesis, the experimental phase velocities were used to calculate the elastic properties of the material by inverting the governing equations. The initial method used to recover elastic constants was successful in the recovery of a partial set of the bending and extensional stiffnesses. The inability to recover all bending stiffnesses dictated the investigation of a second method. This method used an iterative method based upon a nonlinear Newton's method to recover the bending stiffnesses. This method did not converge due to the ill conditioning of the solution matrix. Although this method did not converge, it is believed that more robust methods suggest herein would converge to the proper solution.

This report describes the fundamental physics and basic numerical algorithms that form the basis of a range-dependent microwave propagation model. The model accounts for the effects of nonhomogeneous atmospheric refractivity fields, finite surface conductivity and variable surface terrain elevation. Both vertical and horizontal field polarization and general antenna radiation patterns are included in the analysis. The electromagnetic field propagation is modeled using the splitstep Fourier parabolic wave equation (SSFPE) algorithm, modified to account for an impedance-type boundary condition. The various approximations used in developing the SSFPE algorithm are discussed, along with local and global error estimates. Parabolic wave equation, Microwave propagation, Variable terrain microwave propagation, Pattern propagation factor.

The Effects of the Ionosphere on Radio-wave Propagation (1950) Includes a brief history of the electron microscope. Demonstrates the use and the importance of the electron microscope and the techniques in using it.

This article is from PLoS ONE , volume 9 . Abstract We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.

The unsteady flow field around an oscillating cascade of flat plates is studied using a time marching Euler code. Exact solutions based on linear theory serve as model problems to study pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step is demonstrated. Results show that an approximate non-reflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer than cases using reflective boundary conditions. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates does a better job of capturing the unsteady flow field than cases using uniform grids as long as the CFL number is less than one for a sufficient portion of the grid. Results for various stagger angles and oscillation frequencies show good agreement with linear theory as long as the grid is properly resolved.