Isotropic Propagation Research Articles

Enhancement of inductance along metallic mesh wires in three-dimensional quasi-isotropic metamaterials using high-ε dielectric particles for impedance-matching with free space

In this paper, we consider cube-shaped unit cells including high-ε dielectric cubes under magnetic dipole-like resonance placed at the center and metallic mesh wires for negative permittivity to construct three-dimensional quasi-isotropic metamaterials in the microwave region. Basically, such structures suffer from their low wave impedance due to inclusion of high-ε materials. To reduce effective permittivity of the composite structures, we propose to insert additional inductance into the metallic mesh. For the insertion of lumped inductors along the wires, dispersion diagram and the Bloch-impedance are numerically estimated, and converted to effective permittivity and permeability. The numerical simulation results clearly show almost 3-D isotropic propagation characteristics in a specific frequency region and enhancement of the Bloch-impedance close to free space in the left-handed region. The lumped inductors are replaced by meander-line strip patterns for practical configurations. The metallic patterned structures also achieve the enhanced Bloch impedance that is well-matched to free space.

Investigation on the resolution of a micro cone beam CT scanner scintillating detector using Monte Carlo methods

The impact of several physical quantities on the spatial resolution of an X-ray scintillating pixel detector for a micro cone beam CT (µCBCT) is investigated and discussed.The XtremeCT from SCANCO Medical AG was simulated using the EGSnrc/EGS++ Monte Carlo (MC) framework and extensively benchmarked in a previous work. The resolution of the detector was determined by simulating a titanium knife-edge to obtain the edge spread function (ESF) and the modulation transfer function (MTF). Propagation of the scintillation light through the scintillator and its coupling into the fiber optics system was taken into account.The contribution of particles scattered in the main scanner components to the detector signal is very low and does not affect the spatial resolution of the detector. The resolution obtained from the energy deposition in the scintillator without any blurring due to the propagation of the scintillation light into the fiber optics array was 31 µm. By assuming isotropic light propagation in the scintillator, the resolution degraded to 360 µm. A simple light propagation model taking into account the impact of the scintillator’s columnar microstructures was developed and compared with the MANTIS Monte Carlo simulation package. By reducing the width of the model’s light propagation kernel by a factor of 2 compared to the isotropic case, the detector resolution can be improved to 83 µm, which corresponds well to the measured resolution of 86 µm.The resolution of the detector is limited mainly by the propagation of the scintillation light through the scintillator layer. It offers the greatest potential to improve the resolution of the µCBCT imaging system.

Sound transmission loss through triple-walled cylindrical shells with porous layers.

Sound transmission loss through triple-walled sandwich cylindrical shells in the presence of an external mean flow is analytically examined. Love's theory and a simplified method based on Biot's theory are considered to describe the motions of thin isotropic shells and wave propagation in the porous material cores, respectively. The random incidence transmission loss in a diffuse field is calculated numerically by considering the limiting incidence angle due to the total internal reflection. The analytical model and numerical code are validated against both experimental and analytical results reported by previous studies. The transmission loss of triple-walled structure in the diffuse sound field is compared with its double-walled counterpart at the same weight. The results generally show a superior performance in the sound insulation for the triple-walled shell, considerably at mid-high and high frequencies, in comparison with its double-walled counterpart at the same weight. The effects of sandwich shell configuration and air gap depth are also investigated on the sound transmission loss.

Lens Design for Computing With Anisotropic Spin Waves

We present the design and micromagnetic simulations of lenses for spin waves with anisotropic dispersion. Spin waves are attractive candidates for on-chip wave-computing devices. These, in general, require means of generation, manipulation, and detection of spin waves; here, we address manipulation of spin waves. Most wave-computing algorithms proposed so far require isotropic wave propagation, since it is the easiest to handle, and well-established concepts from optics can be used. Spin waves in in-plane magnetized magnetic films are, in general, anisotropic, and this magnetization direction is often favorable from practical perspectives. We investigated the possibility of using anisotropic spin waves in designs based on the Fourier transforming property of a lens.

On the solid-state dewetting of polycrystalline thin films: Capillary versus grain growth approach

Solid-state dewetting of polycrystalline silver thin films was investigated with in situ and real time Environmental Scanning Electron Microscopy at High Temperature (HT-ESEM) in different annealing atmospheres: secondary vacuum or oxygen-rich (partial pressure ≥100 Pa) environment. A model where oxygen plays a key role is proposed to explain the very different observed morphologies; oxygen favours hole creation and isotropic hole propagation as well as grain selection. But, whatever the atmosphere, dewetting does not proceed through the propagation of a rim but instead involves the growth of specific grains and shrinkage of others. Models based on macroscopic curvature to account for the propagation speed of the dewetting front fail to fit the present observations. This points to a paramount role of the grain size and stability in the dewetting morphology.

Automatic determination of first-motion polarity and its application to focal mechanism analysis of microseismic events

A method for automatically determining first-motion polarities is developed, with a view to its application to the focal mechanism analysis of massive microseismic events caused by hydraulic fracturing. The method is based on two assumptions: the existence of a point source, which has negligible effects of fault finiteness and rupture directivity; and a laterally homogeneous structure, which has azimuthally isotropic propagation characteristics. Under these assumptions, the event waveforms recorded at each station share a common source time function shape, with varying amplitudes, that is dependent on the radiation pattern from the source. With respect to the reference waveform with the highest signal-to-noise ratio (SNR) among all the waveforms at each station for an event, the relative polarities of waveforms at other stations are estimated using cross correlation analysis. The absolute polarities of each waveform are then defined using the reference waveform, whose SNR can be further enhanced using the stacked waveforms after corrections of relative polarities and time lags between the reference and target waveforms have been made. Then, a grid-search algorithm can be incorporated to invert focal mechanisms using the automatically measured polarities for a given event. Since the procedure requires only the evaluation of a cross-correlation coefficient, it can be incorporated into an automated algorithm. The method is applied to determine the focal mechanism solutions of microseismic events occurring in a shale gas play where commercial production is ongoing. Two types of focal mechanism solutions are found to be dominant: vertical dip-slip, and strike-slip. The strike-slip events occur due to re-activation of natural fractures connecting cracks opened by hydraulic fracturing. For the vertical dip-slip events, it was observed that their strikes are consistent with the direction of maximum horizontal stress, which supports the theory that slips occur on the horizontal bedding planes due to the opening of vertical cracks generated by hydraulic fracturing.

Isotropic transmission of magnon spin information without a magnetic field.

Spin-wave devices (SWD), which use collective excitations of electronic spins as a carrier of information, are rapidly emerging as potential candidates for post-semiconductor non-charge-based technology. Isotropic in-plane propagating coherent spin waves (magnons), which require magnetization to be out of plane, is desirable in an SWD. However, because of lack of availability of low-damping perpendicular magnetic material, a usually well-known in-plane ferrimagnet yttrium iron garnet (YIG) is used with a large out-of-plane bias magnetic field, which tends to hinder the benefits of isotropic spin waves. We experimentally demonstrate an SWD that eliminates the requirement of external magnetic field to obtain perpendicular magnetization in an otherwise in-plane ferromagnet, Ni80Fe20 or permalloy (Py), a typical choice for spin-wave microconduits. Perpendicular anisotropy in Py, as established by magnetic hysteresis measurements, was induced by the exchange-coupled Co/Pd multilayer. Isotropic propagation of magnon spin information has been experimentally shown in microconduits with three channels patterned at arbitrary angles.

A 3-D Radio Irregularity Model (3DRIM) for Wireless Sensor Network

Localization in wireless sensor network will be adversely effected due to radio irregularity. This makes the localization procedure more complex and as a result most of the localization techniques are based on the regular radio patterns and isotropic propagation model. In order to address this problem, we propose a three dimensional radio irregularity model, that takes into account non-isotropic radio model along with radio irregularity and also considers the three dimensional aspects. For this proposed model three dimensional degree of irregularity (3-D DOI) is calculated by forming a practical test bed and finally with the simulations are carried out to validate the theoretical model and effect of increase in distance on 3-D DOI.

Modeling Elastic Wave Propagation Using $K$ -Space Operator-Based Temporal High-Order Staggered-Grid Finite-Difference Method

The traditional high-order staggered-grid finite-difference (SGFD) method has high-order accuracy in space, but only the second-order accuracy in time, which makes the traditional SGFD method suffer from a large temporal dispersion error during long-distance wave propagation. This paper develops temporal fourth- and sixth-order and spatial arbitrary evenorder SGFD schemes to model isotropic elastic wave propagation. The temporal high-order SGFD schemes have smaller temporal dispersion than the traditional temporal second-order scheme, and thus allow larger time steps to attain a similar accuracy. The developed temporal high-order SGFD schemes are applied to simulate a quasi-stress–velocity wave equation (QWE) that is derived in the framework of a $k$ -space approach. A split QWE (SQWE) is further developed, and numerical simulation of SQWE results in separated P (compressional)-wave and S (shear)-wave. Theoretical computational cost analysis verifies that the numerical simulation of QWE using the temporal fourthand sixth-order SGFD schemes is more efficient than the numerical simulation of the traditional stress–velocity wave equation using the traditional temporal second-order SGFD scheme in 2-D. In 3-D, the temporal fourth-order SGFD scheme still runs faster than the traditional temporal second-order scheme; however, the temporal sixth-order scheme is more efficient only when a longer stencil length than 12 is adopted. Numerical examples confirm the correctness of the developed elastic wave modeling schemes.

A Frequency-Shift Method to Measure Shear-Wave Attenuation in Soft Tissues.

In vivo quantification of shear-wave attenuation in soft tissues may help to better understand human tissue rheology and lead to new diagnostic strategies. Attenuation is difficult to measure in acoustic radiation force elastography because the shear-wave amplitude decreases due to a combination of diffraction and viscous attenuation. Diffraction correction requires assuming a cylindrical wavefront and an isotropic propagation medium, which may not be the case in some applications. In this paper, the frequency-shift method, used in ultrasound imaging and seismology, was adapted for shear-wave attenuation measurement in elastography. This method is not sensitive to diffraction effects. For a linear frequency dependence of the attenuation, a closed-form relation was obtained between the decrease in the peak frequency of the gamma-distributed wave amplitude spectrum and the attenuation coefficient of the propagation medium. The proposed method was tested against a plane-wave reference method in homogeneous agar-gelatin phantoms with 0%, 10%, and 20% oil concentrations, and hence different attenuations of 0.117, 0.202, and 0.292 [Formula: see text]/Hz, respectively. Applicability to biological tissues was demonstrated with two ex vivo porcine liver samples (0.79 and 1.35 [Formula: see text]/Hz) and an in vivo human muscle, measured along (0.43 [Formula: see text]/Hz) and across (1.77 [Formula: see text]/Hz) the tissue fibers. In all cases, the data supported the assumptions of a gamma-distributed spectrum for the source and linear frequency attenuation for the tissue. This method provides tissue attenuation, which is relevant diagnostic information to model viscosity, in addition to shear-wave velocity used to assess elasticity. Data processing is simple and could be performed automatically in real time for clinical applications.

Performance of continuous mass-lumped tetrahedral elements for elastic wave propagation with and without global assembly

We consider isotropic elastic wave propagation with continuous mass-lumped finite elements on tetrahedra with explicit time stepping. These elements require higher-order polynomials in their interior to preserve accuracy after mass lumping and are only known up to degree 3. Global assembly of the symmetric stiffness matrix is a natural approach but requires large memory. Local assembly on the fly, in the form of matrix-vector products per element at each time step, has a much smaller memory footprint. With dedicated expressions for local assembly, our code ran about 1.3 times faster for degree 2 and 1.9 times for degree 3 on a simple homogeneous test problem, using 24 cores. This is similar to the acoustic case. For a more realistic problem, the gain in efficiency was a factor 2.5 for degree 2 and 3 for degree 3. For the lowest degree, the linear element, the expressions for both the global and local assembly can be further simplified. In that case, global assembly is more efficient than local assembly. Among the three degrees, the element of degree 3 is the most efficient in terms of accuracy at a given cost.

High-Energy Neutron Concentration Far from a Source

The concentration of neutron radiation far from a source is discussed. A new method is proposed for solving this problem by choosing from among the scattered neutrons the ones that have acquired the required direction of flight and energy. The material along which such a neutron will travel must possess a small neutron cross section at the given energy. Materials consisting of isotopes with a large resonance cross section, for example, 56Fe, meet the requirements. The method discussed for concentrating high-energy neutrons makes it possible to increase their concentration more than 1000-fold in the detection area far from the source compared with isotropic propagation away from the source in all directions with equal probability.

Synchronization and Propagation of Global Sleep Spindles.

Sleep spindles occur thousands of times during normal sleep and can be easily detected by visual inspection of EEG signals. These characteristics make spindles one of the most studied EEG structures in mammalian sleep. In this work we considered global spindles, which are spindles that are observed simultaneously in all EEG channels. We propose a methodology that investigates both the signal envelope and phase/frequency of each global spindle. By analysing the global spindle phase we showed that 90% of spindles synchronize with an average latency time of 0.1 s. We also measured the frequency modulation (chirp) of global spindles and found that global spindle chirp and synchronization are not correlated. By investigating the signal envelopes and implementing a homogeneous and isotropic propagation model, we could estimate both the signal origin and velocity in global spindles. Our results indicate that this simple and non-invasive approach could determine with reasonable precision the spindle origin, and allowed us to estimate a signal speed of 0.12 m/s. Finally, we consider whether synchronization might be useful as a non-invasive diagnostic tool.

Approximations to seismic AVA responses: Validity and potential in glaciological applications

Amplitude-variation-with-angle (AVA) methods establish the seismic properties of material either side of a reflective interface, and their use is growing in glaciology. The AVA response of an interface is defined by the complex Knott-Zoeppritz (K-Z) equations, numerous approximations to which we typically assume weak interface contrasts and isotropic propagation, inconsistent with the strong contrasts at glacier beds and the vertically transverse isotropic (VTI) fabrics were associated with englacial reflectivity. We considered the validity of a suite of approximate K-Z equations for the exact P-wave reflectivity [Formula: see text] of ice overlying bedrock, sediment and water, and englacial interfaces between isotropic and VTI ice. We found that the approximations of Aki-Richards, Shuey, and Fatti match exact glacier bed reflectivity to within [Formula: see text], smaller than the uncertainty in typical glaciological AVA analyses, but only for maximum incident angle [Formula: see text] limited to 30°. A stricter limit of [Formula: see text] offered comparable accuracy to a hydrocarbon benchmark case of shale overlying gas-charged sand. The VTI-compliant Rüger approximation accurately described englacial reflectivity, to within [Formula: see text], and it can be modified to give a quadratic expression in [Formula: see text] suitable for curve-matching operations. Having shown the circumstances under which AVA approximations were valid for glaciological applications, we have suggested that their interpretative advantages can be exploited in the future AVA interpretations.

Influence of the Shape of Explosive Charge on the Blast Wave Propagation

For several decades, a blast wave due to explosive detonation has been investigated extensively. Base on a significant amount of experimental data, the blast wave propagation has been predicted at specific conditions. However, only spherical shape of explosive has been considered in most studies. Recently, it was noted that the shape of explosive influences the blast wave propagation significantly. In this study, a finite element analysis was carried out to investigate the effect of the shape of explosive on the blast wave propagation. Two different shapes of explosive were compared in blast wave propagation; spherical and cylindrical shape. It was found that the spherical and cylindrical shape blast show different characteristics in the blast wave propagation. The spherical blast showed the isotropic wave propagation as verified by experimental data. However, the cylindrical blast showed more concentrated and faster propagation in the axial direction

The Thinnest Path Problem

We formulate and study the thinnest path problem for secure communication in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission powers. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer √(n/2) and n/2√(n-1) approximation ratios for general directed hypergraphs (which can model nonisotropic signal propagation in space) and constant approximation ratios for ring hypergraphs (which result from isotropic signal propagation). We also consider the thinnest path problem in 1-D networks and 1-D networks embedded in a 2-D field of eavesdroppers with arbitrary unknown locations (the so-called 1.5-D networks). We propose a linear-complexity algorithm based on nested backward induction that obtains the optimal solution for both 1-D and 1.5-D networks. This algorithm does not require the knowledge of eavesdropper locations and achieves the best performance offered by any algorithm that assumes complete location information of the eavesdroppers.

Dynamic Analysis of Elevated Water Storage Tanks due to Ground Motions’ Rotational and Translational Components

Rotational components of ground motion including rocking and torsional components have rarely been accounted for in designing and analyzing water storage tanks. In this paper, the effects of these components on the dynamic response of water storage tanks are studied. The rotational components of ground motion acceleration have been obtained using an improved approach from the corresponding available translational components based on the transversely isotropic elastic wave propagation and classical elasticity theories. Based on this approach, it becomes possible to consider the frequency-dependent wave velocities and incident wave angle to generate the rotational components. For this purpose, the translational components of four earthquakes have been selected to generate their relative rotational components based on SV and SH wave incidence. The translational and computed rotational motions were then applied to the concrete elevated water storage tank with different water elevations considering fluid–structure interaction using the finite element method. The linear responses of these structures considering the full six components of the ground motion show that the rotational components of ground motion can affect the displacement and reaction force of the structure, depending on the frequency of structure and predominant frequencies of translational and rotational components of ground motion.

Multidimensional HLLC Riemann solver for unstructured meshes – With application to Euler and MHD flows

The goal of this paper is to formulate genuinely multidimensional HLL and HLLC Riemann solvers for unstructured meshes by extending our prior papers on the same topic for logically rectangular meshes Balsara (2010, 2012) [4,5]. Such Riemann solvers operate at each vertex of a mesh and accept as an input the set of states that come together at that vertex. The mesh geometry around that vertex is also one of the inputs of the Riemann solver. The outputs are the resolved state and multidimensionally upwinded fluxes in both directions.A formulation which respects the detailed geometry of the unstructured mesh is presented. Closed-form expressions are provided for all the integrals, making it particularly easy to implement the present multidimensional Riemann solvers in existing numerical codes. While it is visually demonstrated for three states coming together at a vertex, our formulation is general enough to treat multiple states (or zones with arbitrary geometry) coming together at a vertex. The present formulation is very useful for two-dimensional and three-dimensional unstructured mesh calculations of conservation laws. It has been demonstrated to work with second to fourth order finite volume schemes on two-dimensional unstructured meshes. On general triangular grids an arbitrary number of states might come together at a vertex of the primal mesh, while for calculations on the dual mesh usually three states come together at a grid vertex.We apply the multidimensional Riemann solvers to hydrodynamics and magnetohydrodynamics (MHD) on unstructured meshes. The Riemann solver is shown to operate well for traditional second order accurate total variation diminishing (TVD) schemes as well as for weighted essentially non-oscillatory (WENO) schemes with ADER (Arbitrary DERivatives in space and time) time-stepping. Several stringent applications for compressible gasdynamics and magnetohydrodynamics are presented, showing that the method performs very well and reaches high order of accuracy in both space and time. The present multidimensional Riemann solver is cost-competitive with traditional, one-dimensional Riemann solvers. It offers the twin advantages of isotropic propagation of flow features and a larger CFL number.Please see http://www.nd.edu/~dbalsara/Numerical-PDE-Course for a video introduction to multidimensional Riemann solvers.

A finite Element Model for the Electrical Activity in Human Cardiac Tissues

Biosimulation models of the heart action potential have become a very useful tool. It provides better understanding for the complex biophysical phenomena related to electrical activity in the heart s uch as cardiac arrhythmias. At cellular level, the electrical activity of cardiac tissues may be simulated by solving a system of ordinary deferential equations (ODEs) describing the electrical behavior of the cell membrane. Because the biophysical processes underlying this phenomenon are non-linear and change very rapidly, the ODE system is a challenge to be solved numerically. Furthermore, the implementation of these models is a hard task for commercial finite element software. In this paper a finite element formulation, model a nd code generation of monodomain equation has been conducted. The developed code is coupled with the modified FitzHugh-Nag umo (FHN) cell electrophysiological model in order to have isotropic excitation propagation starting from cell level to complete hea rt level. MTALAB programming language was used to build the proposed standalone finite element code. A two dimensional spec imen of heart tissues is simulated to show the behavior of the excitation propagation and the repolarization phase for isotropic electric al activity. Simulation results of the cardiac action potential have shown good agreements with the experimental measurements obtained from published literature.

Low Delay MAC Scheduling for Frequency-Agile Multi-Radio Wireless Networks

Recent trends suggest that cognitive radio based wireless networks will be frequency agile and the nodes will be equipped with multiple radios capable of tuning across large swaths of spectrum. The MAC scheduling problem in such networks refers to making intelligent decisions on which communication links to activate at which time instant and over which frequency band. The challenge in designing a low-complexity distributed MAC, that achieves low delay, is posed by two additional dimensions of cognitive radio networks: interference graphs and data rates that are frequency-band dependent, and explosion in number of feasible schedules due to large number of available frequency-bands. In this paper, we propose MAXIMALGAIN MAC, a distributed MAC scheduler for frequency agile multi-band networks that simultaneously achieves the following: (i) optimal network-delay scaling with respect to the number of communicating pairs, (ii) low computational complexity of O(log2(maximum degree of the interference graphs)) which is independent of the number of frequency bands, number of radios per node, and overall size of the network, and (iii) robustness, i.e., it can be adapted to a scenario where nodes are not synchronized and control packets could be lost. Our proposed MAC also achieves a throughput provably within a constant fraction (under isotropic propagation) of the maximum throughput. Due to a recent impossibility result, optimal delay-scaling could only be achieved with some amount of throughput loss [30]. Extensive simulations using OMNeT++ network simulator shows that, compared to a multi-band extension of a state-of-art CSMA algorithm (namely, Q-CSMA), our asynchronous algorithm achieves a 2.5x? reduction in delay while achieving at least 85% of the maximum achievable throughput. Our MAC algorithms are derived from a novel local search based technique.