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The two-dimensional grid-free compressed sensing method with planar microphone arrays is expected to achieve super-resolution direction-of-arrival (DOA) estimation for acoustic sources in the hemispherical space in front of array. The existing methods are not yet well compatible with arbitrary planar array geometries. In this paper, we aim to break this limitation and explore a novel method applicable to arbitrary planar array geometries. First, the covariance between source-induced signals at arbitrary two microphones is formulated as related to the two-dimensional inverse Fourier transform of the source strength. Then, a mathematical model with a source sparsity constraint is built in the continuous domain to denoise the covariances of measured signals, which can be solved by decoupled positive semidefinite programming. Finally, the DOAs are extracted from the solution of the mathematical model via a matrix pencil and pairing method. Simulation and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure. [ABSTRACT FROM AUTHOR]

Compressive beamforming with a planar microphone array can effectively estimate the two-dimensional directions-of-arrival and quantify the strengths of acoustic sources. Due to the superiorities of overcoming the basis mismatch issue of the conventional grid-based method and improving the performance of the single-snapshot grid-free method, the multiple-snapshot grid-free method has become the current research focus. Its existing atomic norm minimization (ANM) based strategy blocks high resolution because it cannot work well for sources with a small separation. This paper commits itself to remedying this drawback. After revealing the cause for this drawback, we present an iterative reweighted ANM (IRANM) approach. Both simulations and experiments demonstrate that compared with the ANM-based two-dimensional multiple-snapshot grid-free compressive beamforming, the IRANM-based one enjoys not only the enhanced resolution but also the stronger denoising ability and the higher identification accuracy. [ABSTRACT FROM AUTHOR]

• A grid-free compressive beamforming method is proposed based on prolate spheroidal wave functions. • It is compatible with arbitrary linear microphone arrays. • It can identify sources accurately, even using only a single snapshot. • The increase in snapshots helps the method perform better. Grid-free compressive beamforming is a new attractive method for acoustic source identification based on compressive sensing theory, which extracts the source information from the microphone array measurements without discretizing the target source region. In the framework of linear microphone array measurements, many studies have been carried out around this method. They have strict requirements on the distribution of microphones. Specifically, only the uniform arrays with equally spaced microphones and sparse arrays consisting of a selection of microphones from uniform arrays are available. In this paper, based on the prolate spheroidal wave functions, we propose a grid-free compressive beamforming method compatible with arbitrary linear microphone arrays. Some examples are conducted to demonstrate the correctness and superiority of the proposed method. Plenty of Monte Carlo simulations are performed to reveal the effects of source coherence, source separation, noise, and number of snapshots. This study helps to promote the popularization and application of grid-free compressive beamforming method and offers the possibility to improve the acoustic source identification performance by optimizing microphone distribution. [ABSTRACT FROM AUTHOR]

Highlights • A two-dimensional multiple-snapshot grid-free compressive beamforming method is proposed. • It can overcome the basis mismatch conundrum of the grid-based method. • It enjoys obvious advantages over the single-snapshot grid-free method. Abstract Compressive beamforming with planar microphone arrays can effectively achieve the two-dimensional direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. This paper focuses on developing a multiple-snapshot grid-free method and comparing it against the existing grid-based and single-snapshot grid-free ones. The minimization of the atomic norm of multiple-snapshot microphone pressure induced by acoustic sources and the matrix pencil and pairing method are utilized jointly. The former is utilized to denoise the measured pressure and therefore obtain the pressure from acoustic sources. The latter is utilized to estimate DOAs and quantify strengths. Both simulations and experiments demonstrate the advantages of the developed method. For sources that are active across multiple snapshots, it can overcome the basis mismatch conundrum of the grid-based compressive beamforming. When the sources are uncorrelated or partially correlated in both spatial and temporal dimensions, it outperforms the single-snapshot grid-free compressive beamforming in terms of denoising, DOA estimation and strength quantification accuracy and resolution. These advantages stand up whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is utilized. [ABSTRACT FROM AUTHOR]

Building geometrically realistic representations of geological heterogeneity in reservoir models is a challenging task that is limited by the inflexibility of pre-defined pillar or cornerpoint grids. The surface-based modelling workflow uses grid-free surfaces that allows efficient creation of geological models without the limitations of pre-defined grids. Surface-based reservoir modelling uses a boundary representation approach in which all heterogeneity of interest (structural, stratigraphic, sedimentological, diagenetic) is modelled by its bounding surfaces, independent of any grid. Volumes bounded by these surfaces are internally homogeneous and, thus, no additional facies or petrophysical modelling is performed within these geological domains and no grid or mesh discretisation is needed during modelling. Any heterogeneity to be modelled within such volumes is incorporated by adding surfaces. Surfaces and curves are modelled using a parametric non-uniform rational B-splines (NURBS) description. These surfaces are efficient to generate and manipulate, and allow fast creation of multiple realisations of geometrically realistic reservoir models. Multiple levels of surface hierarchy are introduced to allow modelling of all features of interest at the required level of detail; surfaces at one hierarchical level are constructed so as to truncate or conform to surfaces of a higher hierarchical level. This procedure requires the joining, terminating and stacking of surfaces to ensure that models contain "watertight" surface-bounded volumes. NURBS curves are used to represent well trajectories accurately, including multi-laterals or side-tracks. Once all surfaces and wells have been generated, they are combined into a reservoir model that takes into account geological relationships between surfaces and preserves realistic geometries. [ABSTRACT FROM AUTHOR]

In this work, a new grid-free global optimization algorithm that combined the image source model(ISM) and state transition algorithm(STA) was proposed to realize the sound source localization in reverberant environments. The simulation results show that only first-order mirror sources being kept can ensure localization accuracy. Compared with de-reverberation beamforming, the localization results of the proposed algorithm have no sidelobes and smaller mainlobes. Compared with the differential evolution(DE) algorithm, STA can converge to smaller fitness values, which can achieve more accurate sound source localization in reverberant environments. Meanwhile, the proposed algorithm can be applied to both single-source and multi-source localization in practical scenarios. The experimental results show that the proposed algorithm can locate the sound source accurately in reverberant environments. • A 3D grid-free de-reverberation sound sources localization algorithm is proposed. • It shows no sidelobes and smaller mainlobes than the de-reverberation beamforming. • It achieves more accurate results than the differential evolution algorithm. [ABSTRACT FROM AUTHOR]

• Two-dimensional grid-free compressive beamforming for spherical arrays is proposed. • It can avoid basis mismatch defect and enjoys significant accuracy superiority. • It can identify sources accurately and panoramically, even only with one snapshot. • The increase in snapshots helps the method perform better. Compressive beamforming based on microphone array measurements and compressive sensing theory is an emerging and practical acoustic source identification technology. The grid-free compressive beamforming that treats the target source region as a continuum has attracted tremendous attention due to the advantage of circumventing the basis mismatch defect caused by the gridding. The grid-free methods have been developed for the linear and the planar microphone array measurements to identify sources in a local region. In contrast, for the spherical microphone array measurements suitable for 360° panoramic identification, the current research mainly focuses on grid-based methods. In this paper, we propose a two-dimensional grid-free compressive beamforming method with spherical microphone arrays. First of all, the relationship between the spherical harmonic function vector and the two-dimensional Fourier basis function vector is determined. Then, the mathematical model relating the measured sound pressures to the source distribution is built under a continuous setting. Next, a source sparsity constraint is imposed based on the total variation norm to solve the mathematical model, and its dual problem is deduced. Subsequently, the dual problem is solved by positive semidefinite programming. Finally, the DOAs of sources are estimated through polynomial rooting and utilizing the dual optimal variables, and the source strengths are quantified via least-square fitting. An experimental case is conducted to examine the practicability and superiority of the proposed method to the existing grid-based compressive beamforming method. Plenty of Monte Carlo simulations are carried out to disclose the influence of the source coherence, the angular distance between sources, the noise, the number of snapshots and the number of microphones. This study offers a new approach for the accurate and 360° panoramic identification of acoustic sources. [ABSTRACT FROM AUTHOR]

An air-to-air missile launched from a fighter aircraft needs to be stable at launch to enable safe separation from the aircraft, and less stable in the terminal phase of its flight to become highly maneuverable to intercept the targets. A study has been carried out to estimate the effect of the aircraft flow field on the longitudinal stability of the missile using an in-house developed 3-D grid-free Euler solver. Initially, the missiles are placed in the captive location in the launcher of the aircraft. One of the missiles is then moved to various pre-determined locations ahead of the wing of the aircraft, keeping the other missile at the captive location. The centre of pressure and stability margin of the missile is determined at these locations. It is observed that the presence of aircraft has a substantial effect on the longitudinal stability of the missile. The centre of pressure of the missile is seen to move aft as it leaves the launcher. As the missile moves, the centre of pressure reaches a maximum aft position and then moves forward till it reaches a position where the missile is free from the influence of the aircraft. It is observed that as the missile moves away from the region of strong influence of the aircraft, its aerodynamic characteristics approach asymptotically to that of the isolated missile. [ABSTRACT FROM AUTHOR]

A common approach to modeling kinetic problems in plasma physics is to represent the plasma as a set of Lagrangian macro-particles which interact through long-range forces. In the well-known particle-in-cell (PIC) method, the particle charges are interpolated to a mesh and the fields are obtained using a fast Poisson solver. The advantage of this approach is that the electrostatic forces can be evaluated in time O(N log N), where N is the number of macro-particles, but the scheme has difficulty resolving steep gradients and handling nonconforming domains unless a sufficiently fine mesh is used. The current work describes a grid-free alternative, the boundary integral/treecode (BIT) method. Using Green's theorem, we express the solution to Poisson's equation as the sum of a volume integral and a boundary integral which are computed using particle discretizations. The treecode replaces particle-particle interactions by particle-cluster interactions which are evaluated by Taylor expansions. In addition, the Green's function is regularized and adaptive particle insertion is implemented to maintain resolution. Like PIC, the operation count is O(N log N), but BIT avoids using a regular grid, so it can potentially resolve steep gradients and handle complex domains more efficiently. We applied BIT to several bounded plasma problems including a one-dimensional (1-D) sheath in direct current (dc) discharges, 1-D virtual cathode, cold two-stream instability, two-dimensional (2-D) planar and cylindrical ion optics, and particle dynamics in a Penning-Malmberg trap. Some comparisons of BIT and PIC were performed. These results and ongoing work will be reviewed. [ABSTRACT FROM AUTHOR]

We present expressions for approximating the velocity and vortex stretching vectors induced by a far-field collection of point vortices and we propose a set of recurrence relations to properly evaluate these expressions. Expressed as truncated series of spherical harmonics, these approximations are used in the context of O (N log ⁡ N) and O (N) -type fast multipole methods to reduce the computational cost of the advection step in three-dimensional grid-free vortex methods. These methods typically rely on operator splitting to handle diffusion and convection separately. In our implementation, the convection step employs a second order Runge-Kutta time integration scheme, where the particles velocities and vortex stretching vectors are computed using a fast multipole method that employs the proposed expressions. To model diffusion, we introduce an extension of the smoothed redistribution scheme to 3D unbounded flows. We check the accuracy of the expressions by inspecting the convergence of the velocity and the vortex stretching vectors as a function of the expansion order. The performance of the grid-free three-dimensional vortex method is assessed by simulating the collision of two vortex rings, over a long period of time, for different values of Reynolds number covering the range 500 − 2000. • A 3D grid-free vortex method is presented. • Convection implements an RK2 scheme that employs the fast multipole method. • Non-singular expressions for the velocity and vortex stretching vectors are presented. • Diffusion is modeled using an efficient extension to 3D of the redistribution method. • Performance is assessed by simulating the collision of two vortex rings Re=500-2000. [ABSTRACT FROM AUTHOR]