We introduce numerical methods and algorithms to estimate the main parameters of fractal-like particle aggregates from their optical structure factor (i.e. light scattering diagrams). The first algorithm is based on a direct and simple method, but its applicability is limited to aggregates with large size parameter and intermediate fractal dimension. The second algorithm requires to build calibration curves based on accurate particle agglomeration and particle light scattering models. It allows analyzing the optical structure factor of much smaller aggregates, regardless of their fractal dimension and the size of the single particles. Therefore, this algorithm as well as the introduction of a criterial curve to detect the different scattering regimes, are thought to be powerful tools to perform reliable and reproducible analysis.
Sound diffusers, in particular those based on changes in the phase of the reflected wave (Schroeder diffusers), have recently gained greatly in popularity in acoustics as an effective means to eliminate defects and improve the acoustic performance of interiors. This paper draws attention to a possibility of shaping acoustic parameters of sound diffusers and fundamental errors made in applying diffusers. Also, an often neglected issue of sound absorption by diffusers has been tackled. The presented results of laboratory measurements indicate a great significance of the diffusers' rigidity and geometry on their absorption coefficient at low frequencies. The effect of arrangement of elements on the diffusion coefficient was analysed for two types of elements based on the prime number N = 7.
An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.
The paper considers the application of statistical properties of backscattered ultrasonic signal for assessment of the trabecular bone status. Computer simulations were conducted to investigate the properties of the ultrasound pulse-echo signal, as it is received on the transducer surface after scattering in trabecular bone. The micro-architecture of trabecular bone was modeled by a random distribution of long and thin cylindrical scatterers of randomly varying diameters and mechanical properties, oriented perpendicular to the ultrasound beam axis. The received echo signal was calculated as a superposition of echoes from all the scatterers present in the scattering volume. The simulated signal envelope was used for statistical processing to compute various parameters like the mean amplitude, the amplitude MSR defined as the ratio of the mean to the standard deviation and the amplitude histogram. Results indicated that while for the well-defined trabeculae properties within the simulated bone structure the signal envelope values are Rayleigh distributed the significant departures from Rayleigh statistics may be expected as the thickness of trabeculae become random. The influence of the variation of mechanical properties of the bone tissue building the trabeculae on the bone backscattered signal parameters was not observed.
Fabric covering is often used by designers, as it can easily mask acoustic structures that do not match an interior. However, in the case of sound diffusers based on change in the phase of the reflected wave, the use of fabric covering is not without its effect on acoustics. It reduces the effectiveness of these structures and raises acoustic absorption. In the paper, the authors analyzed the acoustical properties of a selected fabric used to cover sound diffusers. Sound absorption and scattering coefficients for a system composed of sound diffusers and a fabric situated at different distances d were measured. The results were compared to the sound absorption predicted on the basis of Kuttruff’s and Mechel’s theoretical models. Analysis of the results indicates that the fabric has a significant influence on the system’s acoustic parameters. It is also observed, that fabric applied directly on a phase grating diffuser, produces higher absorption than when it is at some distance from it.
The paper focuses on the problem of test signal selection in determining the sound scattering coefficient in accordance with ISO 17497-1. Research shows that the use of MLS signal is preferred in this procedure. The sine sweep signal, despite its advantages, presents certain limitations if the sample is moving during measurement. An attempt has been made to develop a method that allows for minimization of error, demonstrating the dependence of the obtained values of the sound scattering coefficient on the rotational speed of the turntable and type of test signal. Conditions for the application of the sine sweep signals in continuous and discrete measurements were defined.
The paper presents the verification of a solution to the narrow sound frequency range problem of flat reflective panels. The analytical, numerical and experimental studies concerned flat panels, panels with curved edges and also semicircular elements. There were compared the characteristics of sound reflected from the studied elements in order to verify which panel will provide effective sound reflection and also scattering in the required band of higher frequencies, i.e. above the upper limit frequency. Based on the conducted analyzes, it was found that among some presented solutions to narrow sound frequency range problem, the array composed of panels with curved edges is the most preferred one. Nevertheless, its reflection characteristic does not meet all of the requirements, therefore, it is necessary to search for another solution of canopy which is effective over a wide frequency range.
We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.
The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weak- ened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff-Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical analysis is carried out for a steel shell filled with oil and immersed in seawater. The modules and phases of the scattering amplitudes versus the dimensionless wavenumber of the incident sound wave as well as directivity patterns of the scattered field are investigated taking into consideration the orientation of the slit on the elastic shell surface. The plots obtained show a considerable influence of the slit and viscous fluid filler on the diffraction process.
Ray tracing simulation of sound field in rooms is a common tool in room acoustic design for predicting impulse response. There are numerous commercial engineering tools utilising ray tracing simulation. A specific problem in the simulation is the modelling of diffuse reflections when contribution of individual surface is prevailing. The paper introduces modelling of scattering which is interesting when the whole impulse response of a room is not a goal but contribution of certain surface. The main goal of the project is to shape directivity characteristics of scattered reflection. Also, an innovative approach is suggested for converting the energy histogram information obtained by ray tracing into an “equivalent impulse response”. The proposed algorithm is tested by comparing the results with measurements in a real sound field, realised in a scaled model where a diffusing surface is hardware-implemented.
An original model based on first principles is constructed for the temporal correlation of acoustic waves propagating in random scattering media. The model describes the dynamics of wave fields in a previously unexplored, moderately strong (mesoscopic) scattering regime, intermediate between those of weak scattering, on the one hand, and diffusing waves, on the other. It is shown that by considering the wave vector as a free parameter that can vary at will, one can provide an additional dimension to the data, resulting in a tomographic-type reconstruction of the full space-time dynamics of a complex structure, instead of a plain spectroscopic technique. In Fourier space, the problem is reduced to a spherical mean transform defined for a family of spheres containing the origin, and therefore is easily invertible. The results may be useful in probing the statistical structure of various random media with both spatial and temporal resolution.
BC (Black Carbon), which can be found in the atmosphere, is characterized by a large value of the imaginary part of the complex refractive index and, therefore, might have an impact on the global warming effect. To study the interaction of BC with light often computer simulations are used. One of the methods, which are capable of performing light scattering simulations by any shape, is DDA (Discrete Dipole Approximation). In this work its accuracy was estimated in respect to BC structures using the latest stable version of the ADDA (vr. 1.2) algorithm. As the reference algorithm the GMM (Generalized Multiparticle Mie-Solution) code was used. The study shows that the number of volume elements (dipoles) is the main parameter that defines the quality of results. However, they can be improved by a proper polarizability expression. The most accurate, and least time consuming, simulations were observed for IGT_SO. When an aggregate consists of particles composed of ca. 750 volume elements (dipoles), the averaged relative extinction error should not exceed ca. 4.5%.
A trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher order scattering (multiple scattering) into the total scattering of ultrasound in a trabecular bone. The scattering due to the interconnections between thick trabeculae, usually neglected in trabecular bone models, has been also studied. The basic element in our model of the trabecular bone was an elastic cylinder with a various finite-length and diameter as well as orientation. The applied model was taking into account variation of both, elements size and their spatial configuration. The field scattered on the bone model was evaluated by solving numerically the integral form of the generalized Sturm-Liouville equation describing a scalar wave in inhomogeneous and lossy media. For the scattered fields calculated numerically the effective cross-sections were determined. The influence of absorption on the scattering coefficients was demonstrated. The results allowed to conclude that within the frequency range from 0.5 to 1.5 MHz contribution of the second order scattering to the effective backscattering cross-section is at least 500 times lower than that due to the first order scattering. It was noticed that for a frequency higher than 1.5 MHz fast growth of the backscattering (reflection) coefficients, calculated for the second order scattering, occurs.
The paper deals with the problem of acoustic correction in historic opera theatres with the auditorium layout in the form of a horseshoe with deep underbalcony cavities limited with a semicircular wall surface. Both geometry of the cavities and excessive sound absorption determine acoustic phenomena registered in this area of the hall. The problem has been observed in the Theatre of Opera and Ballet in Lviv, Ukraine, where acoustic tests were carried out, simulation calculations performed, and finally a diffusion panel worked out designed for the rear wall of the underbalcony space. Acoustic measurements carried out after installation of the diffusers revealed favourable changes in the sound strength factor G within the range of medium and high frequencies in the underbalcony and auditorium centre area. By replacing textile tapestry with diffusion panels, a significant reduction of sound absorption was achieved for the frequency range above 1 kHz and an increase of uniformity of acoustic parameters registered in the hall. The method presented in the paper can be applied in historic halls of the similar type as well as contemporary rooms where there is a need for correction of acoustic flaws related to sound focusing or the echo effect.
The paper presents a classification of the healthy skin and the skin lesions (basal cell carcinoma) basing on a statistics of the envelope of ultrasonic echoes. The echoes envelopes distributions were modeled using Rayleigh and K-distribution. The distributions were compared with empirical data to find which of them better models the statistics of the echo-signal obtained from the human skin. The results indicated that the K-distribution provides a better fit. Also, a characteristic parameter of the K-distribution, the effective number of scatterers (M), was investigated. The values of the M parameter, obtained for the skin cancer (basal cell carcinoma), were lower as compared to those obtained for the healthy skin. The results indicate that the statistical quantitative ultrasound parameters have a potential for extracting information useful for characterization of the skin condition.
Rapid development of computing and visualisation systems has resulted in an unprecedented capability to display, in real time, realistic computer-generated worlds. Advanced techniques, including three-dimensional (3D) projection, supplemented by multi-channel surround sound, create immersive environments whose applications range from entertainment to military to scientific. One of the most advanced virtual reality systems are CAVE-type systems, in which the user is surrounded by projection screens. Knowledge of the screen material scattering properties, which depend on projection geometry and wavelength, is mandatory for proper design of these systems. In this paper this problem is addressed by introducing a scattering distribution function, creating a dedicated measurement setup and investigating the properties of selected materials used for rear projection screens. Based on the obtained results it can be concluded that the choice of the screen material has substantial impact on the performance of the system
High−frequency acoustic measurements supplemented by a modern optical method, Laser Optical Plankton Counter (LOPC), allowed us to perform a comparative analysis through the application of a mathematical model. We have studied the correspondence between measured and modelled echoes from zooplankton aggregations consisted mainly of two Calanus species. Data were collected from the upper 50 m water layer within the hydrographical frontal zone on the West Spitsbergen Shelf. The application of a “high− −pass” model of sound scattering by fluid−like particles to the distribution of zooplankton sizes measured by LOPC resulted mostly in very good agreement between the measured (420 kHz BioSonics) and modelled values, except for cases with very low zooplankton abundance or with occurrence of stronger scatterers ( e.g. macrozooplankton, fish). An acoustic model validated for the elastic parameters of zooplankton confirmed that particles smaller than 1 mm in diameter, although highly abundant, did not contribute significantly to the sound scattering process at a frequency of 420 kHz. The implementation of diverse complementary methods has great potential to obtain high spatial and temporal resolution in zooplankton distribution studies; however, their compatibility has to be tested first.
Porous materials are used in many vibro-acoustic applications. Different models describe their perfor- mance according to material’s intrinsic characteristics. In this paper, an evaluation of the effect of the porous and geometrical parameters of a liner on the acoustic power attenuation of an axisymmetric lined duct was performed using multimodal scattering matrix. The studied liner is composed by a porous ma- terial covered by a perforated plate. Empirical and phenomenal models are used to calculate the acoustic impedance of the studied liner. The later is used as an input to evaluate the duct attenuation. By varying the values of each parameter, its influence is observed, discussed and deduced
In this work we present the design and the manufacturing processes, as well as the acoustics standardization tests, of an acoustic barrier formed by a set of multi-phenomena cylindrical scatterers. Periodic arrangements of acoustic scatterers embedded in a fluid medium with different physical properties are usually called Sonic Crystals. The multiple scattering of waves inside these structures leads to attenuation bands related to the periodicity of the structure by means of Bragg scattering. In order to design the acoustic barrier, two strategies have been used: First, the arrangement of scatterers is based on fractal geometries to maximize the Bragg scattering; second, multi-phenomena scatterers with several noise control mechanisms, as resonances or absorption, are designed and used to construct the periodic array. The acoustic barrier reported in this work provides a high technological solution in the field of noise control.
Mixed boundary-value problem for periodic baffles in acoustic medium is solved with help of the method developed earlier in electrostatics. The nice feature of the method is that the resulting matrices are relatively easy for computations and that the results satisfy exactly the energy conservation law. Illustrative numerical examples present the wave-beam steering (in the far-field) in a baffle system that may be considered as a model of one-dimensional ultrasonic transducer array.