A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Ultra-wideline 14N solid-state NMR as a method for differentiating polymorphs: glycine as a case study

Nitrogen-14 solid-state NMR (SSNMR) is utilized to differentiate three polymorphic forms and a hydrochloride (HCl) salt of the amino acid glycine. Frequency-swept Wideband, Uniform Rate, Smooth Truncated (WURST) pulses were used in conjunction with Carr-Purcell Meiboom-Gill refocusing, in the form of the WURST-CPMG pulse sequence, for all spectral acquisitions. The ¹⁴N quadrupolar interaction is shown to be very sensitive to variations in the local electric field gradients (EFGs) about the ¹⁴N nucleus; hence, differentiation of the samples is accomplished through determination of the quadrupolar parameters CQ and ηQ, which are obtained from analytical simulations of the ¹⁴N SSNMR powder patterns of stationary samples (i.e., static NMR spectra). Additionally, differentiation of the polymorphs is also possible via the measurement of ¹⁴N effective transverse relaxation time constants, T^eff2(¹⁴N). Plane-wave density functional theory (DFT) calculations, which exploit the periodicity of crystal lattices, are utilized to confirm the experimentally determined quadrupolar parameters as well as to determine the orientation of the ¹⁴N EFG tensors in the molecular frames. Several signal-enhancement techniques are also discussed to help improve the sensitivity of the ¹⁴N SSNMR acquisition method, including the use of selective deuteration, the application of the BRoadband Adiabatic INversion Cross-Polarization (BRAIN-CP) technique, and the use of variable-temperature (VT) experiments. Finally, we examine several cases where ¹⁴N VT experiments employing Carr-Purcell-Meiboom-Gill (CPMG) refocusing are used to approximate the rotational energy barriers for RNH3⁺ groups.

Numerical calculation of diffraction coefficients from building edges using FDTD method

Finite Difference Time Domain (FDTD) Method and software are applied to obtain diffraction waves from modulated Gaussian plane wave illumination for right angle wedges and Fast Fourier Transform (FFT) is used to get diffraction coefficients in a wideband in the illuminated lit region. Theta and Phi polarization in 3-dimensional, TM and TE polarization in 2-dimensional cases are considered respectively for soft and hard diffraction coefficients. Results using FDTD method of perfect electric conductor (PEC) wedge are compared with asymptotic expressions from Uniform Theory of Diffraction (UTD). Extend the PEC wedges to some homogenous conducting and dielectric building materials for diffraction coefficients that are not available analytically in practical conditions. ^

Determining polarization dependent diffraction coefficients from building edges using FDTD method

Electromagnetic waves in suburban environment encounter multiple obstructions that shadow the signal. These waves are scattered and random in polarization. They take multiple paths that add as vectors at the portable device. Buildings have vertical and horizontal edges. Diffraction from edges has polarization dependent characteristics. In practical case, a signal transmitted from a vertically polarized high antenna will result in a significant fraction of total power in the horizontal polarization at the street level. Signal reception can be improved whenever there is a probability of receiving the signal in at least two independent ways or branches. The Finite-Difference Time-Domain (FDTD) method was applied to obtain the two and three-dimensional dyadic diffraction coefficients (soft and hard) of right-angle perfect electric conductor (PEC) wedges illuminated by a plane wave. The FDTD results were in good agreement with the asymptotic solutions obtained using Uniform Theory of Diffraction (UTD). Further, a material wedge replaced the PEC wedge and the dyadic diffraction coefficient for the same was obtained.

Non-invasive method for detecting changes in soil moisture using wireless sensor networks

There are several popular soil moisture measurement methods today such as time domain reflectometry, electromagnetic (EM) wave, electrical and acoustic methods. Significant studies have been dedicated in developing method of measurements using those concepts, especially to achieve the characteristics of noninvasiveness. EM wave method provides an advantage because it is non-invasive to the soil and does not need to utilise probes to penetrate or bury in the soil. But some EM methods are also too complex, expensive, and not portable for the application of Wireless Sensor Networks; for example satellites or UAV (Unmanned Aerial Vehicle) based sensors. This research proposes a method in detecting changes in soil moisture using soil-reflected electromagnetic (SREM) wave from Wireless Sensor Networks (WSNs). Studies have shown that different levels of soil moisture will affects soil’s dielectric properties, such as relative permittivity and conductivity, and in turns change its reflection coefficients. The SREM wave method uses a transmitter adjacent to a WSNs node with purpose exclusively to transmit wireless signals that will be reflected by the soil. The strength from the reflected signal that is determined by the soil’s reflection coefficients is used to differentiate the level of soil moisture. The novel nature of this method comes from using WSNs communication signals to perform soil moisture estimation without the need of external sensors or invasive equipment. This innovative method is non-invasive, low cost and simple to set up. There are three locations at Brisbane, Australia chosen as the experiment’s location. The soil type in these locations contains 10–20% clay according to the Australian Soil Resource Information System. Six approximate levels of soil moisture (8, 10, 13, 15, 18 and 20%) are measured at each location; with each measurement consisting of 200 data. In total 3600 measurements are completed in this research, which is sufficient to achieve the research objective, assessing and proving the concept of SREM wave method. These results are compared with reference data from similar soil type to prove the concept. A fourth degree polynomial analysis is used to generate an equation to estimate soil moisture from received signal strength as recorded by using the SREM wave method.

Diffraction of a cylindrical pulse by a metallic half plane

A direct transform technique is applied to the initial and boundary value problem involving diffraction of a cylindrical pulse by a half plane, on which impedance type of boundary conditions must be met by the total field. The solution to the time harmonic incident plane wave is deduced as a particular case of the general time-dependent problem considered here and we avoid the Wiener–Hopf technique which leads to very complicated factorization and which masks the role of the impedance factor Z′ (a small quantity) in the expression for the scattered field.

On kuhnels 9-vertex complex projective plane

We present an elementary combinatorial proof of the existence and uniqueness of the 9-vertex triangulation of C P2. The original proof of existence, due to Kuhnel, as well as the original proof of uniqueness, due to Kuhnel and Lassmann, were based on extensive computer search. Recently Arnoux and Marin have used cohomology theory to present a computer-free proof. Our proof has the advantage of displaying a canonical copy of the affine plane over the three-element field inside this complex in terms of which the entire complex has a very neat and short description. This explicates the full automorphism group of the Kuhnel complex as a subgroup of the automorphism group of this affine plane. Our method also brings out the rich combinatorial structure inside this complex.

Characterization of Clean and Fouled Rail Track Ballast Subsurface Using Seismic Surface Survey Method: Model and Field Studies

The efficiency of track foundation material gradually decreases due to insufficient lateral confinement, ballast fouling, and loss of shear strength of the subsurface soil under cyclic loading. This paper presents characterization of rail track subsurface to identify ballast fouling and subsurface layers shear wave velocity using seismic survey. Seismic surface wave method of multi-channel analysis of surface wave (MASW) has been carried out in the model track and field track for finding out shear wave velocity of the clean and fouled ballast and track subsurface. The shear wave velocity (SWV) of fouled ballast increases with increase in fouling percentage, and reaches a maximum value and then decreases. This character is similar to typical compaction curve of soil, which is used to define optimum and critical fouling percentage (OFP and CFP). Critical fouling percentage of 15 % is noticed for Coal fouled ballast and 25 % is noticed for clayey sand fouled ballast. Coal fouled ballast reaches the OFP and CFP before clayey sand fouled ballast. Fouling of ballast reduces voids in ballast and there by decreases the drainage. Combined plot of permeability and SWV with percentage of fouling shows that after critical fouling point drainage condition of fouled ballast goes below acceptable limit. Shear wave velocities are measured in the selected location in the Wollongong field track by carrying out similar seismic survey. In-situ samples were collected and degrees of fouling were measured. Field SWV values are more than that of the model track SWV values for the same degree of fouling, which might be due to sleeper's confinement. This article also highlights the ballast gradation widely followed in different countries and presents the comparison of Indian ballast gradation with international gradation standards. Indian ballast contains a coarser particle size when compared to other countries. The upper limit of Indian gradation curve matches with lower limit of ballast gradation curves of America and Australia. The ballast gradation followed by Indian railways is poorly graded and more favorable for the drainage conditions. Indian ballast engineering needs extensive research to improve presents track conditions.

On the Role of Higher-Order Evanescent Modes in End-Offset Inlet and End-Centered Outlet Elliptical Flow-Reversal Chamber Mufflers

This paper deals with the role of the higher-order evanescent modes generated at the area discontinuities in the acoustic attenuation characteristics of an elliptical end-chamber muffler with an end-offset inlet and end-centered outlet. It has been observed that with an increase in length, the muffler undergoes a transition from being acoustically short to acoustically long. Short end chambers and long end chambers are characterized by transverse plane waves and axial plane waves, respectively, in the low-frequency range. The nondimensional frequency limit k(0)(D-1/2) or k(0)R(0) as well as the chamber length to inlet/outlet pipe diameter ratio, i.e., L/d(0), up to which the muffler behaves like a short chamber and the corresponding limit beyond which the muffler is acoustically long are determined. The limits between which neither the transverse plane-wave model nor the conventional axial plane-wave model gives a satisfactory prediction have also been determined, the region being called the intermediate range. The end-correction expression for this muffler configuration in the acoustically long limit has been obtained using 3-D FEA carried on commercial software, covering most of the dimension range used in the design exercise. Development of a method of combining the transverse plane wave model with the axial plane wave model using the impedance Z] matrix is another noteworthy contribution of this work.

Recent advances in muffler acoustics

Exhaust noise in engines has always been a major source of automotive noise. Challenges for muffler design have been constraints on size, back pressure, and, of course, the cost. Designing for sufficient insertion loss at the engine firing frequency and the first few harmonics has been the biggest challenge. Most advances in the design of efficient mufflers have resulted from linear plane wave theory, making use of the transfer matrix method. This review paper deals with evaluating approximate source characteristics required for prediction of the unmuffled intake and exhaust noise, making use of the electroacoustical analogies. In the last few years, significant advances have been made in the analysis of variable area perforated ducts, transverse plane wave analysis of short elliptical as well as circular chambers, double-tuned expansion chambers and concentric tube resonators, catalytic converters, diesel particulate filters, air cleaners, etc. The development of long strand fibrous materials that can be used in hot exhaust systems without binders has led to the use of combination mufflers in exhaust systems. Breakthroughs have been achieved in the prediction and control of breakout noise from the elliptical and circular muffler shell as well as the end plates of typical mufflers. Diesel particulate filters and inlet air cleaners have also been modeled acoustically. Some of these recent advances are the subject of this review paper.

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as E-f, the fibroblast resting-membrane potential, the fibroblast conductance G(f), and the MF gap-junctional coupling G(gap). Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as G(gap), G(f), and E-f, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of G(gap), for zero-sided and one-sided couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of G(gap), and, eventually, we observe that conduction failure occurs for low values of G(gap). In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling G(gap) or E-f. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Efficient Adaptive Mesh Refinement for MoM-based Package-Board 3D Full-wave Extraction

The accurate solution of 3D full-wave Method of Moments (MoM) on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretizations may not be fine enough to capture rapid spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates large number of solution variables and therefore requires an unnecessarily large matrix solution. In this work, a suitable refinement criterion for MoM based electromagnetic package-board extraction is proposed and the advantages of the adaptive strategy are demonstrated from both accuracy and speed perspectives.

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

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

Stress Wave Propagation in a Gradient Elastic Medium

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equation of motion, together with the internal material length, has been derived. Various dispersion relations have been determined. We present explicit expressions for the relationship between various wave speeds, wavenumber and internal material length.

Ab initio investigation of the elasticity and stability of aluminium

On the basis of the pseudopotential plane-wave (PP-PW) method in combination with the local density functional theory (LDFT), complete stress-strain curves for the uniaxial loading and uniaxial deformation along the [001] and [111] directions, and the biaxial proportional extension along [010] and [001] for aluminium are obtained. During the uniaxial loading, certain general behaviours of the energy versus the stretch and the load versus the stretch are confirmed; in each case, there exist three special unstressed structures: f.c.c., b.c.c., and f.c.t. for [001]; f.c.c., s.c., and b.c.c. for [111]. Using stability criteria, we find that all of these states are unstable, and always occur together with shear instability, except the natural f.c.c. structure. A Pain transformation from the stable f.c.c. structure to the stable b.c.c. configuration cannot be obtained by uniaxial compression along any equivalent [001] and [111] direction. The tensile strengths are similar for the two directions. For the higher energy barrier of the [111] direction, the compressive strength is greater than that for the [001] direction. With increase in the ratio of the biaxial proportional extension, the stress and tensile strength increase; however, the critical strain does not change significantly. Our results add to the existing ab initio database for use in fitting and testing interatomic potentials.