Application of partial areas method in the problem of sound radiation by a sphere in a waveguide with soft acoustically boundaries

The paper considers the features of the formation of an acoustic field by a spherical source with complicated properties in a regular plane-parallel waveguide, which is of practical importance in marine instrumentation and oceanographic research. The calculation algorithm is based on the use of the Helmholtz equation and the Fourier method for each partial region and the conjugation conditions on their boundaries. The presented calculation allows one to get rid of the idealized boundary conditions on the source surface, with the subsequent determination of the excitation coefficients of the waveguide modes within the framework of the Sturm-Liouville problem. In this case, the attraction of the boundary conditions on the surface and the bottom of the sea, as well as the Sommerfeld conditions, makes it possible to obtain the real distribution of the field in the vertical sections of the waveguide. The obtained frequency dependences of the pressure and vibrational velocity components show their amplitude-phase differences, which reach 90 degrees, which partially explains the appearance of singular points in the intensity field in a regular waveguide. It has been determined that multiple reflections of sound waves from the boundaries of the working space and the space of the waveguide cause oscillations of the pressure components with a change in the amplitude level up to 6 dB. It was found that with an increase in the size of the source, a kind of resonance is formed in the working space, the frequency of which depends on the depth of the sea and corresponds to the region kr=x=5.8. It was found that when the acoustic field is formed in the working space, the frequency response of the impedance components is represented as a multiresonant dependence formed on the basis of the frequency characteristics of the lower modes and their combinations. Experimental studies have shown that the results of calculations of the mode composition of the acoustic field of the emitter, obtained in the conditions of the pool, correspond to the spatial characteristics of the mode components of the acoustic field with an error of up to 3 dB

Corn plants as temporary acoustic barrier to limit the effects of noise pollution

Corn is a cereal imported into Europe from the Americas and is used for human and animal feed, but there are also industrial uses such as the production of ethanol, as a fuel for heating homes or to produce starch. Corn grows in the summer in areas where there is water. Corn is grown in many regions of the world and its production exceeds that of any other cereal in quantity. The corn plant can reach up to three meters in height, with a stem diameter of a few centimeters and with dense leaves longer than 30 cm and 10 cm wide. There are noisy activities where it is necessary to attenuate the noise produced to limit the effects of noise pollution. Some activities use temporary barriers depending on the processing cycle adopted. If noisy work is carried out during the summer season, corn rows of adequate width can be used as an acoustic barrier. In this paper, the possibility of using corn plants as an acoustic barrier is investigated. The acoustic measurements of the noise attenuation of corn rows of adequate width are described. Using a semi-spherical source placed on the ground, the acoustic attenuation due to the corn plants arranged in several rows for different distances from the sound source to the receiver was measured.

Derivation of Coulomb's Law Based on a Mechanical Model of Electromagnetic Field and a Spherical Source and Sink Model of Electric Charges

We suppose that vacuum is filled with a kind of continuously distributed matter which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Suppose that the time scale of a macroscopic observer is very large compares to the the Maxwelllian relaxation time of the $\Omega(1)$ substratum. Thus, the macroscopic observer concludes that the $\Omega(1)$ substratum behaves like a Newtonian-fluid. Inspired by H. A. Lorentz, we speculate that electric charges may be extremely small hard spherical sources or spherical sinks with finite radii. Based on the spherical source and spherical sink model of electric charges, we derive Coulomb's law of interactions between static electric charges in vacuum. Further, we derive a reduced form of the Lorentz's force law for static electric charges in vacuum.

Models of non-static and inhomogeneous gravitating source in Rastall gravity

In this paper, we have explored the non-static anisotropic gravitational collapse and expansion solutions in Rastall theory of gravity. The field equations have been formulated for the non-static and inhomogeneous gravitating source. The Misner–Sharp mass function, auxiliary solution and trapped condition have been used to obtained a trapped surface. The auxiliary solutions have been used to obtain the expansion and collapse solutions; these solutions depend on [Formula: see text] and parameter [Formula: see text] (which appears due to parametric form of metric components); also the range of parameter [Formula: see text] has been examined. The expansion scalar [Formula: see text] depends on parameter [Formula: see text], in the case of expansion [Formula: see text] for [Formula: see text], while for collapse [Formula: see text] with [Formula: see text]. Also, the dynamics of the gravitating spherical source has been discussed graphically with the effects of Rastall parameter [Formula: see text]. For the physically reasonable fluid, the validity of energy conditions has been discussed for expansion and collapse solutions with the various values of [Formula: see text].

Immersive visualisation of intracardiac blood flow in virtual reality on a patient with HLHS

Funding Acknowledgements Type of funding sources: Other. Main funding source(s): NIHR i4i funded 3D Heart project Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z] onbehalf 3D Heart Project Background/Introduction: Virtual Reality (VR) for surgical and interventional planning in the treatment of Congenital Heart Disease (CHD) is an emerging field that has the potential to improve planning. Particularly in very complex cases, VR permits enhanced visualisation and more intuitive interaction of volumetric images, compared to traditional flat-screen visualisation tools. Blood flow is severely affected by CHD and, thus, visualisation of blood flow allows direct observation of the cardiac maladaptions for surgical planning. However, blood flow is fundamentally 3D information, and viewing and interacting with it using conventional 2D displays is suboptimal. Purpose To demonstrate feasibility of blood flow visualisation in VR using pressure and velocity obtained from a computational fluid dynamic (CFD) simulation of the right ventricle in a patient with hypoplastic left heart syndrome (HLHS) as a proof of concept. Methods We extend an existing VR volume rendering application to include CFD rendering functionality using the Visualization Toolkit (VTK), an established visualisation library widely used in clinical software for visualising medical imaging data. Our prototype displays the mesh outline of the segmented heart, a slicing plane showing blood pressure on the plane within the heart, and streamlines of blood flow from a spherical source region. Existing user tools were extended to enable interactive positioning, rotation and scaling of the pressure plane and streamline origin, ensuring continuity between volume rendering and CFD interaction and, thus, ease of use. We evaluated if rendering and interaction times were low enough to ensure a comfortable, interactive VR experience. Our performance benchmark is a previous study showing VR is acceptable to clinical users when rendering speed is at least 90 fps. Results CFD simulations were successfully rendered, viewed and manipulated in VR, as shown in the Figure. Evaluating performance, we found that visualisation of the mesh and streamlines was at an acceptably high and stable frame rate, over 150fps. User interactions of moving, rotating or scaling the mesh or streamlines origin did not significantly reduce this frame rate. However, rendering the pressure slicing plane reduced frame rate by an unacceptable degree, to less than 10fps. Conclusion Visualisation of and interaction with CFD simulation data was successfully integrated into an existing VR application. This aids in surgery and intervention planning for defects heavily relying on blood flow simulation, and lays a foundation for a platform for clinicians to test interventions in VR. Pressure plane rendering performance will require significant optimisation, potentially addressed by updating the pressure plane data separately from the main, VR rendering. Abstract Figure. An example render of CFD simulation

Four Years of Continuous Seafloor Displacement Measurements in the Campi Flegrei Caldera

We present 4 years of continuous seafloor deformation measurements carried out in the Campi Flegrei caldera (Southern Italy), one of the most hazardous and populated volcanic areas in the world. The seafloor sector of the caldera has been monitored since early 2016 by the MEDUSA marine research infrastructure, consisting of four instrumented buoys installed where sea depth is less than 100 m. Each MEDUSA buoy is equipped with a cabled, seafloor module with geophysical and oceanographic sensors and a subaerial GPS station providing seafloor deformation and other environmental measures. Since April 2016, the GPS vertical displacements at the four buoys show a continuous uplift of the seafloor with cumulative measured uplift ranging between 8 and 20 cm. Despite the data being affected by environmental noise associated with sea and meteorological conditions, the horizontal GPS displacements on the buoys show a trend coherent with a radial deformation pattern. We use jointly the GPS horizontal and vertical velocities of seafloor and on-land deformations for modeling the volcanic source, finding that a spherical source fits best the GPS data. The geodetic data produced by MEDUSA has now been integrated with the data flow of other monitoring networks deployed on land at Campi Flegrei.

Renewed Inflation of Krafla Caldera, Iceland, since 2018: Sensitivity of Ground Deformation to lateral variation in Earth structure and architecture of the magmatic system explored with the Finite Element Method

<p>The Krafla volcanic area in Northern Volcanic Zone of Iceland was characterized by deflation starting in 1989, suggesting a general pressure decrease and/or volume contraction at depth, which then exponentially decayed until having no significant deformation since around 2000.  In summer 2018, the volcano behaviour changed to inflation as observed both by Global Navigation Satellite System (GNSS) geodesy  and Sentinel-1 satellite radar interferometry (InSAR). Inflation since 2018 occurs at a rate of 10-14 mm/yr, centered in the middle of the caldera. No significant change in seismicity has occurred in the area in 2018, but seismic moment release ocurrs at a higher rate since middle 2019. Gravity stations in the area were remeasured in November 2019 for allowing comparison with earlier observations, and for providing reference for later studies. Initial modelling of the geodetic data is carried out assuming that the deformation is caused by a spherical source of pressure in an uniform elastic half-space. The result suggests that the deformation can be broadly explained by a single source of magma inflow at depth around 3.9-7.5 km, with the best-fit value around 4-4.5 km. We also apply the Finite Element Method (FEM) to additionally consider modification of the deformation field caused by Earth’s elastic heterogeneities and the uncertain geometry and  depth of the magma source. A set of FEM models are built with the COMSOL Multiphysics software in a 50x50 km domain where we test three different geometries of the source: a spherical source (radius 1000 km), a prolate ellipsoid,  and an oblate ellipsoid (sill-like) source, at 2.5, 4.0 and 5.5 km of depth. We also build a model to test how the vertical and horizontal displacements may be influenced by different elastic properties (e.g. Young’s modulus; about an order of magnitude different within a caldera boundary) for these sources. The results show that lateral variations in material properites can have a significant influence on ground deformation. Low-value Young’s inside caldera boundaries compared to higher values outside caldera boundaries will in particular influence the vertical displacement: the vertical displacement is about half of of what it is the original modelling.  The ratio of vertical to horizontal displacements will thus also be modified. This can in turn influence the inferred magma source geometry as it depends on the displacement ratios. The outcome of our study will provide better constrain for the elastic properties in Krafla area, and help understand the magma intrusion rate in the area.</p>

Post-eruptive volcano inflation following major magma drainage: Interplay between models of viscoelastic response influence and models of magma inflow at Bárðarbunga caldera, Iceland, 2015-2018

<p>Unrest at Bárðarbunga after a caldera collapse in 2014-2015 includes elevated seismicity beginning about six months after the eruption ended, including nine Mw>4.5 earthquakes. The earthquakes occurred mostly on the northern and southern parts of a caldera ring fault. Global Navigation Satellite System (GNSS, in particular, Global Positioning System; GPS) and Interferometric Synthetic Aperture Radar (InSAR) geodesy are applied to evaluate the spatial and temporal pattern of ground deformation around Bárðarbunga caldera outside the icecap, in 2015-2018, when deformation rates were relatively steady. The aim is to study the role of viscoelastic relaxation following major magma drainage versus renewed magma inflow as an explanation for the ongoing unrest.</p><p>The largest horizontal velocity is measured at GPS station KISA (3 km from caldera rim), 141 mm/yr in direction N47<sup>o</sup>E relative to the Eurasian plate in 2015-2018. GPS and InSAR observations show that the velocities decay rapidly outward from the caldera. We correct our observations for Glacial Isostatic Adjustment and plate spreading to extract the deformation related to volcanic activity. After this correction, some GPS sites show subsidence.</p><p>We use a reference Earth model to initially evaluate the contribution of viscoelastic processes to the observed deformation field. We model the deformation within a half-space composed of a 7-km thick elastic layer on top of a viscoelastic layer with a viscosity of 5 x 10<sup>18</sup> Pa s, considering two co-eruptive contributors to the viscoelastic relaxation: “non-piston” magma withdrawal at 10 km depth (modelled as pressure drop in a spherical source) and caldera collapse (modelled as surface unloading). The other model we test is the magma inflow in an elastic half-space. Both the viscoelastic relaxation and magma inflow create horizontal outward movements around the caldera, and uplift at the surface projection of the source center in 2015-2018. Viscoelastic response due to magma withdrawal results in subsidence in the area outside the icecap. Magma inflow creates rapid surface velocity decay as observed.</p><p>We explore further two parameters in the viscoelastic reference model: the viscosity and the "non-piston" magma withdrawal volume. Our comparison between the corrected InSAR velocities and viscoelastic models suggests a viscosity of 2.6×10<sup>18</sup> Pa s and 0.36 km<sup>3</sup> of “non-piston” magma withdrawal volume, given by the optimal reduced Chi-squared statistic. When the deformation is explained using only magma inflow into a single spherical source (and no viscoelastic response), the optimal model suggests an inflow rate at 1×10<sup>7</sup> m<sup>3</sup>/yr at 700 m depth. A magma inflow model with more model parameters is also a possible explanation, including sill inflation at 10 km together with slip on caldera ring faults. Our reference Earth model and the two end-member models suggest that there is a trade-off between the viscoelastic relaxation and the magma inflow, since they produce similar deformation signals outside the icecap. However, to reproduce details of the observed deformation, both processes are required. A viscoelastic-only model cannot fully explain the fast velocity decay away from the caldera, whereas a magma inflow-only model cannot explain the subsidence observed at several locations.</p>