Shape optimization of an acoustic horn is performed with the goal to minimize the portion of the wave that is reflected. The analysis of the acoustical properties of the horn is performed using a finite element method for the Helmholtz equation.The optimization is performed employing a BFGS Quasi-Newton algorithm, where the gradients are provided by solving the associated adjoint equations. To avoid local solutions to the optimization problem corresponding to irregular shapes of the horn, a filtering technique is used that applies smoothing to the design updates and the gradient. This smoothing technique can be combined with Tikhonov regularization. However, experiments indicate that regularization is redundant for the optimization problems we consider here. However, the use of smoothing is crucial to obtain sensible solutions. The smoothing technique we use is equivalent to choosing a representation of the gradient of the objective function in an inner product involving second derivatives along the design boundary.Optimization is performed for a number of single frequencies as well as for a band of frequencies. For single frequency optimization, the method shows particularly fast convergence with indications of super-linear convergence close to optimum. For optimization on a range of frequencies, a design was achieved providing a low and even reflection throughout the entire frequency band of interest.

The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an ( ) perturbation, where is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier-Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model.

The human body can act as a medium for the transmission of electromagnetic waves in the wireless body sensor networks context. However, there are transmission losses in biological tissues due to the presence of water and salts. This Letter focuses on lateral intra-body microwave communication through different biological tissue layers and demonstrates the effect of the tissue thicknesses by comparing signal coupling in the channel. For this work, the authors utilise the R-band frequencies since it overlaps the industrial, scientific and medical radio (ISM) band. The channel model in human tissues is proposed based on electromagnetic simulations, validated using equivalent phantom and ex-vivo measurements. The phantom and ex-vivo measurements are compared with simulation modelling. The results show that electromagnetic communication is feasible in the adipose tissue layer with a low attenuation of ∼2 dB per 20 mm for phantom measurements and 4 dB per 20 mm for ex-vivo measurements at 2 GHz. Since the dielectric losses of human adipose tissues are almost half of ex-vivo tissue, an attenuation of around 3 dB per 20 mm is expected. The results show that human adipose tissue can be used as an intra-body communication channel.

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