Singular Source Research Articles

Romanizing Chinese: word–tone relations in Athanasius Kircher’s China illustrata

Abstract When Matteo Ricci and the Jesuit missionaries landed in China in the late 16th century, they heard a language they could not readily reproduce in their own tongue. Unlike Latin and the Romance languages, Chinese is a tone language, in which the meaning of a word varies according to its relative pitch level. In order to Romanize Chinese, the Jesuits applied their knowledge of music theory and assigned solmization syllables to the Chinese tones. Although their manuscript musical dictionary remains lost, the essence of it is preserved in print in the most widely disseminated treatise on China of the time: China illustrata (1667), by the Jesuit polymath Athanasius Kircher. To date, sinologists have generally dismissed Kircher’s musical Chinese as unintelligible. Musicologists, meanwhile, having long poured over Kircher’s Musurgia universalis (1650), have yet to offer a detailed critique of China illustrata. In reapproaching this singular source in Sino-Western history, this article argues that the Jesuits’ musical representation of the Chinese language should not be rejected a priori. Kircher’s cryptic description of Chinese can, in fact, be clarified by a letter from Beijing in which a Jesuit spelled out the Chinese tones in musical staff notation. A musical analysis of the lead illustration in China illustrata—the Nestorian Stele of Xi’an—indicates that the Jesuits’ solmizations were closer approximations of Chinese than one might assume. Off-tone though it might at first appear, China illustrata is a valuable record of how the Jesuits Romanized Chinese.

On the nucleation of cracks near stress sources with weak singularities

Analytical expressions are obtained for the configuration force and the value of elastic energy relaxation at the nucleation of a microcrack in a small neighborhood of an arbitrary singular stress source. When analyzing the conditions of crack nucleation at sources with weak divergences of the stress fields, ideas about the instantaneous nucleation of a crack of finite length are used. Simultaneous fulfillment of stress and energy conditions is considered as a criterion for the nucleation of such a crack. Within the framework of these representations, in the configuration space of the system parameters (geometric characteristics and strength of mesodefects, the value of external stress), the regions in which crack nucleation is possible in the case of a combined mesodefect, which is a superposition of the dipole of wedge disclinations and planar shear mesodefect, are determined. It is shown that the nucleation of the crack is significantly facilitated by the instability of the shear mesodefect.

Acoustic sensitivity analysis for 3D structure with constant cross-section using 2.5D singular boundary method

In this paper, a 2.5D singular boundary method (SBM) in conjunction with the direct differentiation method (DDM) and adjoint variable method (AVM) are formulated for the sensitivity analysis of 3D longitudinally invariant structures. The assumption of a constant cross-section in the longitude direction enables it possible to decouple the 3D system into 2D problems at every wavenumber, and thus makes it a 2.5D-problem. The 2D sensitivity problem is solved by a boundary-type method, SBM. The SBM solves a problem with a linear combination of the fundamental solutions with respect to boundary collocation points. The fundamental solution makes the SBM available for exterior problems without the artificial truncated boundary. The source singularity issue of fundamental solution is overcome by a simple analytical formula and its derivatives. Numerical experiments present the accuracy, efficiency and feasibility of the proposed methods, and indicate that the proposed methods can be considered as an effective alternative in 3D problems with a longitudinally invariant cross-section.

Distributed source scheme for Poisson equation using finite element method

The finite-element method (FEM) is one of the most versatile numerical techniques to solve partial differential equations (PDEs). The approximations in FEM result in numerous errors and various techniques are available to reduce the errors. Distributed Source Scheme (DSS) is a recently proposed method to reduce error around a single source of field which obeys the Poisson equation using the 3-D finite-difference method (FDM). DSS achieves this feat by introducing pseudo sources around the singular source. In this article, the proposed method is studied for single and bulk sources using 2-D FEM along with experimental validation. The numerical solution from FEM is compared with the approximate solution from integral equations over the whole computational domain for the error analysis. The error due to boundary values are isolated by considering the solution of integral equations on boundary elements in FEM. The maximum error in the numerical solution of a single source is reduced from 4.96% to 3.28×10−4% using DSS and to 0.55% using Truncated Distributed Source Scheme (TDSS) with a truncation number of 5. The mean difference in numerical and approximate potential at the boundaries of bulk sources is reduced from 1.21×105 Volt to 2.69×104 Volt using DSS.

Diffuse interface-lattice Boltzmann modeling for heat and mass transfer with Neumann boundary condition in complex and evolving geometries

In this research, a diffuse interface-lattice Boltzmann method is developed to model heat and mass transfer problems with Neumann boundary condition in complex and evolving geometries. In this model, the physical domain with curved and moving boundaries is extended to a larger and regular domain based on the concept of fictitious domain. The Neumann boundary condition is incorporated into the jump conditions of field variable at the inner interface. Then a unified convection-diffusion equation of field variable with two singular source terms is built. Using the smoothing technique, a diffuse interface equation is obtained. Moreover, an energy method is presented to derive the diffuse interface equation in a special case. We utilized a multiple-relaxation-time lattice Boltzmann scheme to numerically solve the diffuse interface equation. A simple example with analytical solutions validates the numerical accuracy of the present model. Finally, several thermal convection and mass transport problems are also simulated. The numerical results denotes the validity of the proposed diffuse interface model.

On a nonlinear fractional differential equation with a weakly singular source

This paper is devoted to the study of a nonlinear fractional differential equation with a weakly singular source in Banach space. Using Bielecki type norm, we show that the problem has a unique solution. Furthermore, we introduce a result of the new Ulam- Hyers type stability for the main equation.

Helmholtz-equation solution in nonsmooth media by a physics-informed neural network incorporating quadratic terms and a perfectly matching layer condition

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep-learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is still room for improvement on this front. For example, PINN can lead to inaccurate solutions when PDE coefficients are nonsmooth and describe structurally complex media. Thus, we solve the acoustic and visco-acoustic scattered-field (Lippmann-Schwinger) wave equation in the frequency domain with PINN instead of the wave equation to remove the source singularity. We first illustrate that nonsmooth velocity models lead to inaccurate wavefields when no boundary conditions are implemented in the loss function. Then, we add the perfectly matched layer (PML) conditions in the loss function to better couple the real and imaginary parts of the wavefield. Moreover, we design new neurons by replacing the classical affine function with a quadratic function in the argument of the activation function to better capture the nonsmooth features of the wavefields. We find that the PML condition and the quadratic functions improve the results including handling attenuation and discuss the reason for this improvement. We also illustrate that a network trained to predict a wavefield for a specific medium can be used as an initial model of the neural network for predicting other wavefields corresponding to PDE-coefficient alterations and improving the convergence speed accordingly. This pretraining strategy should find applications in iterative full-waveform inversion and time-lag target-oriented imaging when the model perturbation between two consecutive iterations or two consecutive experiments is small.

Scalable cryopreservation of infectious Cryptosporidium hominis oocysts by vitrification.

Cryptosporidium hominis is a serious cause of childhood diarrhea in developing countries. The development of therapeutics is impeded by major technical roadblocks including lack of cryopreservation and simple culturing methods. This impacts the availability of optimized/standardized singular sources of infectious parasite oocysts for research and human challenge studies. The human C. hominis TU502 isolate is currently propagated in gnotobiotic piglets in only one laboratory, which limits access to oocysts. Streamlined cryopreservation could enable creation of a biobank to serve as an oocyst source for research and distribution to other investigators requiring C. hominis. Here, we report cryopreservation of C. hominis TU502 oocysts by vitrification using specially designed specimen containers scaled to 100 μL volume. Thawed oocysts exhibit ~70% viability with robust excystation and 100% infection rate in gnotobiotic piglets. The availability of optimized/standardized sources of oocysts may streamline drug and vaccine evaluation by enabling wider access to biological specimens.

Suppression of Short Channel Effects for a SiC MOSFET Based on the S-MOS Cell Concept

This paper investigates the short channel effects (SCE) of the recently proposed Singular Point Source MOS (S-MOS) SiC MOSFET. The study was carried out using 2D and 3D TCAD simulations for a planar, trench and S-MOS 1200V SiC MOSFETs for the IV output characteristics up to 1200V and under short circuit transient conditions. The S-MOS device shows no SCE up to the rated voltage when compared to reference planar and trench devices which exhibit strong SCE. This is due to the appropriate P++ protection of the N++ source and the electric field shielding due to the narrow mesa dimensions between orthogonal trenches where the channel is located.

Analyzing the effect of dipping anisotropy on 3D marine controlled-source electromagnetic response based on a goal-oriented adaptive finite element method

This paper presents a goal-oriented adaptive edge-based finite element (FE) algorithm for modelling marine controlled-source electromagnetic (CSEM) responses in three-dimensional (3-D) dipping anisotropic conductive media. We adopt the secondary field formulation for quasi-static Maxwell's equations to avoid the source singularity. The algorithm is implemented on unstructured tetrahedral grids, which allow for the simulation of complex model geometries, including tilted electrical interfaces and bathymetry. We validate the adaptive finite element code against a one-dimensional (1-D) layered model with vertical anisotropy. Further, we compare the 3-D FE numerical solutions with those obtained by a 2-D FE code for a two-dimensional dipping anisotropic model. The modelling results from the new 3-D FE algorithm are in good agreement with both the analytical solutions derived from the 1-D code and the numerical results from the anisotropic 2-D FE algorithm. We then use the algorithm to simulate the marine CSEM responses over different anisotropic 3-D models, including an anisotropic reservoir, anisotropic surrounding sediments, and an anisotropic overburden, and performed a detailed analysis of the effect of VTI, HTI, and TTI anisotropy on 3-D marine CSEM response. The modelling results illustrate that marine CSEM responses are considerably influenced by various anisotropic parameters, but to different extents. The research on different types of anisotropy within different media can help us avoid the misinterpretation of marine CSEM data when processing and interpreting of the measured geophysical electromagnetic data.

End-to-End Detection of a Landing Platform for Offshore UAVs Based on a Multimodal Early Fusion Approach.

A perception module is a vital component of a modern robotic system. Vision, radar, thermal, and LiDAR are the most common choices of sensors for environmental awareness. Relying on singular sources of information is prone to be affected by specific environmental conditions (e.g., visual cameras are affected by glary or dark environments). Thus, relying on different sensors is an essential step to introduce robustness against various environmental conditions. Hence, a perception system with sensor fusion capabilities produces the desired redundant and reliable awareness critical for real-world systems. This paper proposes a novel early fusion module that is reliable against individual cases of sensor failure when detecting an offshore maritime platform for UAV landing. The model explores the early fusion of a still unexplored combination of visual, infrared, and LiDAR modalities. The contribution is described by suggesting a simple methodology that intends to facilitate the training and inference of a lightweight state-of-the-art object detector. The early fusion based detector achieves solid detection recalls up to 99% for all cases of sensor failure and extreme weather conditions such as glary, dark, and foggy scenarios in fair real-time inference duration below 6 ms.

A New 3D Marine Controlled-Source Electromagnetic Modeling Algorithm Based on Two New Types of Quadratic Edge Elements

This study proposes a new algorithm for a higher-order vector finite element method based on two new types of second-order edge elements to solve the electromagnetic field diffusion problem in a 3D anisotropic medium. To avoid source singularity in the quasistatic variant of Maxwell’s function, a secondary field formulation was adopted. The modeling domain was discretized using two types of quadratic edge hexahedral elements, which were obtained using the edge unification method to reduce variables on each side of two conventional quadratic edge elements. Compared with the traditional quadratic element, the number of unknowns that needed to be solved was significantly reduced. The sparse linear equation of the finite element system was solved using an open-source direct solver called MUMPS. The numerical results demonstrated that the proposed algorithm has the same level of accuracy as the conventional vector finite element method and has a significant advantage over it in terms of computational cost.

Non-degeneracy and uniqueness of solutions to general singular Toda systems on bounded domains

In this note we show non-degeneracy and uniqueness results for solutions of Toda systems associated to general simple Lie algebras with multiple singular sources on bounded domains. The argument is based on spectral properties of Cartan matrices and eigenvalue analysis of linearized Liouville-type problems. This seems to be the first result for this class of problems and it covers all the Lie algebras of any rank.

Detonation wave solutions to the scalar combustion models with a singular source term

This paper is concerned with detonation wave solutions of scalar combustion models with a singular source term to the Chapman–Jouguet (CJ) and the Zeldovich–von Neumann–Döring (ZND) reaction equations, respectively. The self-similar detonation wave solution to a Riemann initial-boundary value problem for the simplest CJ combustion model is constructed. The existence of a global in time classical solution to a free boundary value problem for the scalar ZND model is obtained by using the iterative method. Furthermore, we obtain that as the reaction rate goes to infinity, the detonation wave solution of the scalar ZND combustion model converges to a detonation wave solution of the corresponding CJ combustion model. The results are keeping with the fact that, in an actual spherical detonation process, the detonation front is propagated with a speed less than that derived from the CJ hypothesis, which is stated in Sec. 163 in the book Supersonic Flow and Shock Waves.

Technical Study of Deep Learning in Cloud Computing for Accurate Workload Prediction

Proactive resource management in Cloud Services not only maximizes cost effectiveness but also enables issues such as Service Level Agreement (SLA) violations and the provisioning of resources to be overcome. Workload prediction using Deep Learning (DL) is a popular method of inferring complicated multidimensional data of cloud environments to meet this requirement. The overall quality of the model depends on the quality of the data as much as the architecture. Therefore, the data sourced to train the model must be of good quality. However, existing works in this domain have either used a singular data source or have not taken into account the importance of uniformity for unbiased and accurate analysis. This results in the efficacy of DL models suffering. In this paper, we provide a technical analysis of using DL models such as Recurrent Neural Networks (RNN), Multilayer Perception (MLP), Long Short-Term Memory (LSTM), and, Convolutional Neural Networks (CNN) to exploit the time series characteristics of real-world workloads from the Parallel Workloads Archive of the Standard Workload Format (SWF) with the aim of conducting an unbiased analysis. The robustness of these models is evaluated using the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) error metrics. The findings of these highlight that the LSTM model exhibits the best performance compared to the other models. Additionally, to the best of our knowledge, insights of DL in workload prediction of cloud computing environments is insufficient in the literature. To address these challenges, we provide a comprehensive background on resource management and load prediction using DL. Then, we break down the models, error metrics, and data sources across different bodies of work.

A novel meshless method based on the virtual construction of node control domains for porous flow problems

In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing node control domains. By defining a connectable node cloud, this method uses the integral of the diffusion term and generalized finite-difference operators to derive overdetermined equations of the node control volumes. An empirical method of calculating reliable node control volumes and a triangulation-based method to determine the connectable point cloud are developed. The method focuses only on the volume of the node control domain rather than the specific shape, so the construction of node control domains is virtual and does not increase the computational cost. To our knowledge, this is the first study to construct node control volumes in the meshless framework, termed the node control domain-based meshless method (NCDMM), which can also be regarded as an extended finite-volume method (EFVM). Taking two-phase porous flow problems as an example, discrete NCDMM schemes satisfying local mass conservation are derived by integrating the generalized finite-difference schemes of governing equations on each node control domain. Finally, commonly used low-order finite-volume method (FVM)-based nonlinear solvers for various porous flow models can be directly employed in the proposed NCDMM, significantly facilitating general-purpose application. Theoretically, the proposed NCDMM has the advantages of previous meshless methods for discretizing computational domains with complex geometries, as well as the advantages of traditional low-order FVMs for stably handling a variety of porous flow problems with local mass conservation. Four numerical cases are implemented to test the computational accuracy, efficiency, convergence, and good adaptability to the calculation domain with complex geometry and various boundary conditions.

An inverse nano-cavity/-inhomogeneity problem with surface/interface effects in terahertz frequency range

In nondestructive evaluation, the maximum wavelength of the incident wave must be smaller than twice the perceptible obstacle size. Hence, in order to be able to detect a nanosize fiber of radius about a few nanometer, the frequency of the incident elastic wave should be in the order of 1012 Hz, i.e., in the terahertz frequency range. The present work addresses the possibility of application of elastic waves in terahertz frequency range to detect embedded circular nanosize inhomogeneity or nanocavity for which, respectively, the interface and surface effects are remarkable. Traditionally, singular sources method (SSM) and linear sampling method (LSM) have been utilized to treat inverse problems in the context of classical elasticity theory, where the surface/interface effects are not important. In the present paper these methods are extended to operate in the mathematical framework of surface/interface elasticity theory, suitable for capturing the surface/interface effects. In this framework the boundary conditions in contrast to the common Dirichlet and Neumann types involve the second derivative of the displacement field. The validity and uniqueness of the extended LSM and SSM in this framework will be established. An exact analysis emphasizing the importance of the consideration of surface/interface effects will also be given for the direct problem of SH waves scattering. In this work, the scatterer will be reconstructed solely based on data from the incident waves and the far-field pattern. Using the proposed theory, the size and location of the embedded nano-size cavity and nano-size inhomogeneity are detected. The surface effects of a nano-size cavity within a silver plate are more significant than the copper–silver interface effects in the case of a nano-size copper inhomogeneity embedded in a silver plate.

Adaptive-Energy-Sharing-Based Energy Management Strategy of Hybrid Sources in Electric Vehicles

The energy utilization of the transportation industry is increasing tremendously. The battery is one of the primary energy sources for a green and clean mode of transportation, but variations in driving profiles (NYCC, Artemis Urban, WLTP class-1) and higher C-rates affect the battery performance and lifespan of battery electric vehicles (BEVs). Hence, as a singular power source, batteries have difficulty in tackling these issues in BEVs, highlighting the significance of hybrid-source electric vehicles (HSEVs). The supercapacitor (SC) and photovoltaic panels (PVs) are the auxiliary power sources coupled with the battery in the proposed hybrid electric three-wheeler (3W). However, energy management strategies (EMS) are critical to ensure optimal and safe power allocation in HSEVs. A novel adaptive Intelligent Hybrid Source Energy Management Strategy (IHSEMS) is proposed to perform energy management in hybrid sources. The IHSEMS optimizes the power sources using an absolute energy-sharing algorithm to meet the required motor power demand using the fuzzy logic controller. Techno-economic assessment wass conducted to analyze the effectiveness of the IHSEMS. Based on the comprehensive discussion, the proposed strategy reduces peak battery power by 50.20% compared to BEVs. It also reduces the battery capacity loss by 48.1%, 44%, and 24%, and reduces total operation cost by 60%, 43.9%, and 23.68% compared with standard BEVs, state machine control (SMC), and frequency decoupling strategy (FDS), respectively.

Wave Radiation from Bottom Vibrations in Open-Channel Flow with Uniform Vorticity

The linearized water-wave radiation problem for a 2D oscillating source in an inviscid shear flow with a free surface is investigated analytically. The singular source is located at the bottom, with constant fluid depth. The velocity of the basic flow varies linearly with depth, assuming uniform vorticity. The far-field surface waves radiated out from the 2D bottom source are calculated, based on Euler’s equation of motion with the application of radiation conditions. The present analysis extends the work by Tyvand and Sveen to include a nonzero surface flow. Doppler effects will arise in a system at rest with the undisturbed free surface. Resonance with zero group velocity will occur at a critical Froude number for the surface flow. In the presence of a basic surface flow, there are in total four radiated waves when the surface flow is subcritical. With supercritical flow, there are only two emitted waves, with downstream propagation. The critical Froude number depends on the surface velocity, the shear rate and the oscillation frequency of the bottom source.

Limiting profile of the blow-up solutions for the fourth-order nonlinear Emden-Fowler equation with a singular source

We consider the anisotropic Emden-Fowler equation with exponential nonlinearity in fourth-dimensional with a singular source, given by \begin{document}$ \begin{equation*} \left\{\begin{array}{rclll}\Delta(a(x)\Delta u)-V(x)\,div(a(x)\nabla\,u) & = & \rho^{4} a(x)\,e^{u} -32 \pi^2\;\alpha\,a(x)\,\delta_{p}&\mbox{in} \; \; \Omega\subset \mathbb R^{4}\\\\u = \Delta u & = &0 &\mbox{on} \; \; \partial\Omega. \end{array} \right. \end{equation*} $\end{document} The leading part $ \Delta $ is, usually, called Laplacian operator. $ V = V(|x|) $ is a smooth bounded radial potential and $ a = a(|x|) $ is a given smooth radial function over $ \bar{\Omega} $, called the Schrödinger wave function. Namely, we extend the result of [8] by allowing the presence in the equation a singular source given by Dirac measure with pole at point $ p $ and a generalization in higher dimensional, of the interest problem treated in [11]. We construct a family of solutions $ u_{\rho} $ that concentrate at $ p $ as $ \rho $ tends to $ 0 $.