Numerical modelling of industrial microwave heating

The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh. In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

A descriptive approach for power system stability and security assessment

Power system dynamic analysis and security assessment are becoming more significant today due to increases in size and complexity from restructuring, emerging new uncertainties, integration of renewable energy sources, distributed generation, and micro grids. Precise modelling of all contributed elements/devices, understanding interactions in detail, and observing hidden dynamics using existing analysis tools/theorems are difficult, and even impossible. In this chapter, the power system is considered as a continuum and the propagated electomechanical waves initiated by faults and other random events are studied to provide a new scheme for stability investigation of a large dimensional system. For this purpose, the measured electrical indices (such as rotor angle and bus voltage) following a fault in different points among the network are used, and the behaviour of the propagated waves through the lines, nodes, and buses is analyzed. The impact of weak transmission links on a progressive electromechanical wave using energy function concept is addressed. It is also emphasized that determining severity of a disturbance/contingency accurately, without considering the related electromechanical waves, hidden dynamics, and their properties is not secure enough. Considering these phenomena takes heavy and time consuming calculation, which is not suitable for online stability assessment problems. However, using a continuum model for a power system reduces the burden of complex calculations

Computer simulation of underground blast response of pile in saturated soil

This paper treats the blast response of a pile foundation in saturated sand using explicit nonlinear finite element analysis, considering complex material behavior of soil and soil–pile interaction. Blast wave propagation in the soil is studied and the horizontal deformation of pile and effective stresses in the pile are presented. Results indicate that the upper part of the pile to be vulnerable and the pile response decays with distance from the explosive. The findings of this research provide valuable information on the effects of underground explosions on pile foundation and will guide future development, validation and application of computer models.

Load bearing improves the limits of agreement for repeated in vivo measures of the speed of sound in human Achilles tendon

Axial acoustic wave propagation has been widely used in evaluating the mechanical properties of human bone in vivo. However, application of this technique to monitor soft tissues, such as tendon, has received comparatively little scientific attention. Laboratory-based research has established that axial acoustic wave transmission is not only related to the physical properties of equine tendon but is also proportional to tensile load to which it is exposed (Miles et al., 1996; Pourcelot et al., 2005). The reproducibility of the technique for in vivo measurements in human tendon, however, has not been established. The aim of this study was to evaluate the limits of agreement for repeated measures of the speed of sound (SoS) in human Achilles tendon in vivo. Methods: A custom built ultrasound device, consisting of an A-mode 1MHz emitter and two regularly spaced receivers, was used to measure the SoS in the mid-portion of the Achilles tendon in ten healthy males and ten females (mean age: 33.8 years, range 23-56 yrs; height: 1.73±0.08 m; weight: 68.4±15.3 kg). The emitter and receivers were held at fixed positions by a polyethylene frame and maintained in close contact with the skin overlying the tendon by means of elasticated straps. Repeated SoS measurements were taken with the subject prone (non-weightbearing and relaxed Achilles tendon) and during quiet bipedal and unipedal stance. In each instance, the device was detached and repositioned prior to measurement. Results: Limits of agreement for repeated SoS measures during non-weightbearing and bipedal and unipedal stance were ±53, ±28 and ±21 m/s, respectively. The average SoS in the non-weightbearing Achilles tendon was 1804±198 m/s. There was a significant increase in the average SoS during bilateral (2122±135 m/s) (P < 0.05) and unilateral (2221±79 m/s) stance (P < 0.05). Conclusions: Repeated SoS measures in human Achilles tendon were more reliable during stance than under non-weightbearing conditions. These findings are consistent with previous research in equine tendon in which lower variability in SoS was observed with increasing tensile load (Crevier-Denoix et al, 2009). Since the limits of agreement for Achilles tendon SoS are nearly 5% of the changes previously observed during walking and therapeutic heel raise exercises, acoustic wave transmission provides a promising new non-invasive method for determining tendon properties during sports and rehabilitation related activities.

Blast induced ground shock effects on pile foundations

Due to increased number of terrorist attacks in recent years, loads induced by explosions need to be incorporated in building designs. For safer performance of a structure, its foundation should have sufficient strength and stability. Therefore, prior to any reconstruction or rehabilitation of a building subjected to blast, it is important to examine adverse effects on the foundation caused by blast induced ground shocks. This paper evaluates the effects of a buried explosion on a pile foundation. It treats the dynamic response of the pile in saturated sand, using explicit dynamic nonlinear finite element software LS-DYNA. The blast induced wave propagation in the soil and the horizontal deformation of pile are presented and the results are discussed. Further, a parametric study is carried out to evaluate the effect of varying the explosive shape on the pile response. This information can be used to evaluate the vulnerability of piled foundations to credible blast events as well as develop guidance for their design.

Blast response and failure analysis of pile foundations subjected to surface explosion

This paper presents the response of pile foundations to ground shocks induced by surface explosion using fully coupled and non-linear dynamic computer simulation techniques together with different material models for the explosive, air, soil and pile. It uses the Arbitrary Lagrange Euler coupling formulation with proper state material parameters and equations. Blast wave propagation in soil, horizontal pile deformation and pile damage are presented to facilitate failure evaluation of piles. Effects of end restraint of pile head and the number and spacing of piles within a group on their blast response and potential failure are investigated. The techniques developed and applied in this paper and its findings provide valuable information on the blast response and failure evaluation of piles and will provide guidance in their future analysis and design.

Performance of buried tunnels subjected to surface blast incorporating fluid structure interaction

This paper uses finite element techniques to investigate the performance of buried tunnels subjected to surface blasts incorporating fully coupled Fluid Structure Interaction and appropriate material models which simulate strain rate effects. Modelling techniques are first validated against existing experimental results and then used to treat the blast induced shock wave propagation and tunnel response in dry and saturated sands. Results show that the tunnel buried in saturated sand responds earlier than that in dry sand. Tunnel deformations decrease with distance from explosive in both sands, as expected. In the vicinity of the explosive, the tunnel buried in saturated sand suffered permanent deformation in both axial and circumferential directions, whereas the tunnel buried in dry sand recovered from most of the axial deformation. Overall, response of the tunnel in saturated sand is more severe for a given blast event and shows the detrimental effect of pore water on the blast response of buried tunnels. The validated modelling techniques developed in this paper can be used to investigate the blast response of tunnels buried in dry and saturated sands.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Ion-acoustic surface waves on a dielectric-dusty plasma interface

The theory of ion-acoustic surface wave propagation on the interface between a dusty plasma and a dielectric is presented. Both the constant and variable dust-charge cases are considered. It is found that massive negatively charged dust grains can significantly affect the propagation and damping of the surface waves. Application of the results to surface-wave generated plasmas is discussed. © 1998 IEEE.

Ion-acoustic waves in a complex plasma with negative ions

A wave propagation in a complex dusty plasma with negative ions was considered. The relevant processes such as ionization, electron attachment, diffusion, positive-negative ion recombination, plasma particle collisions, as well as elastic Coulomb and inelastic dust-charging collisions were taken self-consistently. It was found that the equilibrium of the plasma as well as the propagation of ion waves were modified to various degrees by these effects.

Effect of soil properties on the response of pile to underground explosion

This paper develops and presents a fully coupled non-linear finite element procedure to treat the response of piles to ground shocks induced by underground explosions. The Arbitrary Lagrange Euler coupling formulation with proper state material parameters and equations are used in the study. Pile responses in four different soil types, viz, saturated soil, partially saturated soil and loose and dense dry soils are investigated and the results compared. Numerical results are validated by comparing with those from a standard design manual. Blast wave propagation in soils, horizontal pile deformations and damages in the pile are presented. The pile damage presented through plastic strain diagrams will enable the vulnerability assessment of the piles under the blast scenarios considered. The numerical results indicate that the blast performance of the piles embedded in saturated soil and loose dry soil are more severe than those in piles embedded in partially saturated soil and dense dry soil. Present findings should serve as a benchmark reference for future analysis and design.

Frequency independence of ultrasound transit time spectroscopy

Recent studies have shown that ultrasound transit time spectroscopy (UTTS) is an alternative method to describe ultrasound wave propagation through complex samples as an array of parallel sonic rays. This technique has the potential to characterize bone properties including volume fraction and may be implemented in clinical systems to predict osteoporotic fracture risk. In contrast to broadband ultrasound attenuation, which is highly frequency dependent, we hypothesise that UTTS is frequency independent. This study measured 1 MHz and 5 MHz broadband ultrasound signals through a set of acrylic step-wedge samples. Digital deconvolution of the signals through water and each sample was applied to derive a transit time spectrum. The resulting spectra at both 1 MHz and 5 MHz were compared to the predicted transit time values. Linear regression analysis yields agreement (R2) of 99.23% and 99.74% at 1 MHz and 5 MHz respectively indicating frequency independence of transit time spectra.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.