Improved convergence of fast integral equation solvers for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface

In recent years, several fast solvers for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by penetrable inhomogeneous obstacles, have been proposed. While many of these fast methodologies exhibit rapid convergence for smoothly varying scattering configurations, the rate for most of them reduce to either linear or quadratic when material properties are allowed to jump across the interface. A notable exception to this is a recently introduced Nystr\"{o}m scheme [J. Comput. Phys., 311 (2016), 258--274] that utilizes a specialized quadrature in the boundary region for a high-order treatment of the material interface. In this text, we present a solution framework that relies on the specialized boundary integrator to enhance the convergence rate of other fast, low order methodologies without adding to their computational complexity of $O(N \log N)$ for an $N$-point discretization. In particular, to demonstrate the efficacy of the proposed framework, we explain its implementation to enhance the order to convergence of two schemes, one introduced by Duan and Rokhlin [J. Comput. Phys., 228(6) (2009), 2152--2174] that is based on a pre-corrected trapezoidal rule while the other by Bruno and Hyde [J. Comput. Phys., 200(2) (2004), 670--694] which relies on a suitable decomposition of the Green's function via Addition theorem. In addition to a detailed description of these methodologies, we also present a comparative performance study of the improved versions of these two and the Nystr\"{o}m solver in [J. Comput. Phys., 311 (2016), 258--274] through a wide range of numerical experiments

An efficient high-order Nystr\"om scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface

This text proposes a fast, rapidly convergent Nystr\"{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of $O(N \log N)$ for an $N$-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance in terms of both speed and accuracy are presented in this paper

Experimental demonstration of 25 GHz wideband chaos in symmetric dual port EDFRL

We study dynamics of chaos in dual port erbium-doped fiber ring laser (EDFRL). The laser consists of two erbium-doped fibers, intracavity filters at 1549.30 nm, isolators, and couplers. At both ports, the laser transitions into the chaotic regime for pump currents greater than 100 mA via period doubling route. We calculate the Lyapunov exponents using Rosenstein’s algorithm. We obtain positive values for the largest Lyapunov exponent (≈0.2) for embedding dimensions 5, 7, 9 and 11 indicating chaos. We compute the power spectrum of the photocurrents at the output ports of the laser. We observe a bandwidth of ≈ 25 GHz at both ports. This ultra wideband nature of chaos obtained has potential applications in high speed random number generation and communication

Performance analysis of a compact heat exchanger

Compact heat exchangers are one of the most critical components of many cryogenic components; they are characterized by a high heat transfer surface area per unit volume of the exchanger. The heat exchangers having surface area density (β) greater than 700 m2/m3 in either one or more sides of two-stream or multi stream heat exchanger is called as a compact heat exchanger. Plate fin heat exchanger is a type of compact heat exchanger which is widely used in automobiles, cryogenics, space applications and chemical industries. The plate fin heat exchangers are mostly used for the nitrogen liquefiers, so they need to be highly efficient because no liquid nitrogen is produced, if the effectiveness of heat exchanger is less than 87%. So it becomes necessary to test the effectiveness of these heat exchangers before putting them in to operation

Effect of Attention and Self-Supervised Speech Embeddings on Non-Semantic Speech Tasks

Human emotion understanding is pivotal in making conversational technology mainstream. We view speech emotion understanding as a perception task which is a more realistic setting. With varying contexts (languages, demographics, etc.) different share of people perceive the same speech segment as a non-unanimous emotion. As part of the ACM Multimedia 2023 Computational Paralinguistics ChallengE (ComParE) in the EMotion Share track, we leverage their rich dataset of multilingual speakers and multi-label regression target of 'emotion share' or perception of that emotion. We demonstrate that the training scheme of different foundation models dictates their effectiveness for tasks beyond speech recognition, especially for non-semantic speech tasks like emotion understanding. This is a very complex task due to multilingual speakers, variability in the target labels, and inherent imbalance in the regression dataset. Our results show that HuBERT-Large with a self-attention-based light-weight sequence model provides 4.6% improvement over the reported baseline.Comment: Accepted to appear at ACM Multimedia 2023 Multimedia Grand Challenges Trac

Improved convergence of fast integral equation solvers for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface

In recent years, several fast solvers for the solution of the Lippmann–Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by penetrable inhomogeneous obstacles, have been proposed. While many of these fast methodologies exhibit rapid convergence for smoothly varying scattering configurations, the rate for most of them reduce to either linear or quadratic when material properties are allowed to jump across the interface. A notable exception to this is a recently introduced Nyström scheme (Anand et al., 2016 [22]) that utilizes a specialized quadrature in the boundary region for a high-order treatment of the material interface. In this text, we present a solution framework that relies on the specialized boundary integrator to enhance the convergence rate of other fast, low order methodologies without adding to their computational complexity of O(N log N) for an N-point discretization. In particular, to demonstrate the efficacy of the proposed framework, we explain its implementation to enhance the order to convergence of two schemes, one introduced by Duan and Rokhlin (2009) [13] that is based on a pre-corrected trapezoidal rule while the other by Bruno and Hyde (2004) [12] which relies on a suitable decomposition of the Green's function via Addition theorem. In addition to a detailed description of these methodologies, we also present a comparative performance study of the improved versions of these two and the Nyström solver in Anand et al. (2016) [22] through a wide range of numerical experiments