Calculation Of Propagation Research Articles

Shape Sensing Based on Longitudinal Strain Measurements Considering Elongation, Bending, and Twisting

The inherent flexibility, the small dimensions as well as the curvilinear shape of continuum robots makes it challenging to precisely measure their shape. Optical fibers with Bragg gratings (FBGs) provide a powerful tool to reconstruct the centerline of continuum robots. We present a theoretical model to determine the shape of such a sensor array based on longitudinal strain measurements and incorporating bending, twisting, and elongation. To validate our approach, we conduct several simulations by calculating arbitrary shapes based on the Cosserat rod theory. Our algorithm showed a maximum mean relative shape deviation of 0.04%, although the sensor array was twisted up to 78°. Because we derive a closed-form solution for the strain curvature twist model, we also give analytical sensitivity values for the model, which can be used in the calculation of error propagation.

Multiple-scale uncertainty optimization design of hybrid composite structures based on neural network and genetic algorithm

A multiple-scale uncertainty optimization design framework is established for hybrid composite structures, where the stacking sequence and material patches are optimized simultaneously considering micro-scale uncertainty material and strength parameters. Firstly, the uncertainty propagation and performance calculation are implemented based on the finite-element method and classical laminated plate theory, and an adaptive neural network model is constructed to quantify the uncertainties of the natural frequency, reliability index and total cost. Furthermore, the uncertainty optimization design function for the hybrid composite structure is constructed, which maximizes the natural frequency under constraints of the reliability index and total cost, the stacking sequences and material patches are optimized using an adaptive genetic algorithm. In comparison with the determinate optimization results and optimum staking sequence with single materials in two examples with different in-plane loads and cost constraints, the proposed methodology improves the natural frequency by 2.14%–18.61% with the constraints of the reliability index and total cost under multiple scale uncertainties.

Exploiting a holographic polarization microscope for rapid autofocusing and 3D tracking.

We report a fast autofocusing and accurate 3D tracking scheme for a digital hologram (DH) that intrinsically exploits a polarization microscope setup with two off-axis illumination beams having different polarization. This configuration forms twin-object images that are recorded in a digital hologram by angular and polarization multiplexing technique. We show that the separation of the two images on the recording plane follows a linear relationship with the defocus distance and indicates the defocus direction. Thus, in the entire field of view (FOV), the best focus distance of each object can be directly retrieved by identifying the respective separation distance with a cross-correlation algorithm, at the same time, 3D tracking can be performed by calculating the transverse coordinates of the two images. Moreover, we estimate this linear relationship by utilizing the numerical propagation calculation based on a single hologram, in which the focus distance of one of the objects in the FOV is known. We proved the proposed approach in accurate 3D tracking through multiple completely different experimental cases, i.e., recovering the swimming path of a marine alga (tetraselmis) in water and fast refocusing of ovarian cancer cells under micro-vibration stimulation. The reported experimental results validate the proposed strategy's effectiveness in dynamic measurement and 3D tracking without multiple diffraction calculations and any precise knowledge about the setup. We claim that it is the first time that a holographic polarization multiplexing setup is exploited intrinsically for 3D tracking and/or fast and accurate refocusing. This means that almost any polarization DH setup, thanks to our results, can guarantee accurate focusing along the optical axis in addition to polarization analysis of the sample, thus overcoming the limitation of the poor axial resolution.

Comparative testing of MOST and Mac-Cormack numerical schemes to calculate tsunami wave propagation

The problem of fast, reliable, and accurate calculation of tsunami wave propagation is addressed. Based on the shallow water approximation, two numerical approaches to calculate tsunami wave propagation are compared at the same computational mesh. To evaluate precision of numerical solutions the available exact solutions (for the cases of sloping and parabolic bottom) are used. Results of several numerical tests are presented. Time required to obtain tsunami wave height maxima distribution is briefly discussed, too.

Normalized SPH without boundary deficiency and its application to transient solid mechanics problems

Smoothed particle hydrodynamics (SPH) method is a powerful tool for modeling solid mechanics problems, especially for large deformation problems. However, it suffers from boundary deficiency and difficulty of boundary condition treatment. In this work, a normalized SPH method is proposed to overcome these problems. The method is based on a newly developed normalized particle approximation. To derive this particle approximation, a normalized kernel approximation which is accurate for derivatives of linear functions everywhere in a problem domain is constructed, and all integral terms of the normalized kernel approximation including boundary terms are discretized by particle summations. The normalized particle approximation is free of matrix inversion, consequently attractive in computational stability and simplicity compared with other corrective particle approximations. Its approximation accuracy is demonstrated by calculating derivatives of test functions. Based on this particle approximation, the formulation of the normalized SPH method for transient solid mechanics problems is derived. Moreover, a direct method of treating traction boundary conditions is presented by making use of the boundary term of the normalized particle approximation. The accuracy and capability of the normalized SPH method are validated by the calculation of elastic wave propagation in solids and compared with commonly used SPH method.

Knowledge-Building Approach for Tsunami Impact Analysis Aided by Citizen Science

Large tsunami events are devastating even though the impacts are limited to coastal areas. Knowledge is the key to minimize the losses from natural disasters by more proactive and better preparation. Targeting on natural hazards mitigation in Asia, a collaboration among 10 Asian and 2 European countries based on deeper understanding approach has been conducted since 2015. Deeper understanding is to discover the physical mechanisms and drivers behind a hazard event. Innovative model and simulation facilities are developed correspondingly to achieve more accurate numerical simulations of the whole lifespan of the target event. Application framework composed by the knowledge, data, simulation facility, software tools and case studies is designed to provide advanced estimation of hazard risk and would be evolved progressively with more case studies and observation data. For tsunami, based on the COMCOT (COrnell Multi-grid Coupled Tsunami Model), the simulation portal (iCOMCOT) implementing parallelized tsunami wave propagation calculation over distributed cloud had been established. iCOMCOT system finished the simulation of whole lifecycle of the 2011 Great East Japan Earthquake Tsunami in one minute. In this regional collaboration, case studies on historical events and tsunami impact analysis were conducted. The goal is to capture the physical characteristics of tsunami as much as possible such as tsunami wave propagation, tsunami refraction, tsunami run-up on land, as well as their drivers and root causes. The whole processes of tsunami from its initiation to its impacts in selected locations then could be simulated accurately by iCOMCOT based on the scientific explorations and the revised models quantitatively. Sulawesi Tsunami (2018) case is presented to demonstrate the processes of deeper understanding approach and how to achieve the capacity building. At the same time, the ways to take advantages of citizen science are also explored. Citizen science model is valuable in supporting data collection such as data of run up height, inundation range, flow depth, disruption information, impact area, from publication, news report, and interviews of local people. According to experiences on case studies, suggestions to simplify and optimize the integration of citizen science model with deeper understanding approach to lower operation cost are provided.

Comparison of distributed memory algorithms for X-ray wave propagation in inhomogeneous media.

Calculations of X-ray wave propagation in large objects are needed for modeling diffractive X-ray optics and for optimization-based approaches to image reconstruction for objects that extend beyond the depth of focus. We describe three methods for calculating wave propagation with large arrays on parallel computing systems with distributed memory: (1) a full-array Fresnel multislice approach, (2) a tiling-based short-distance Fresnel multislice approach, and (3) a finite difference approach. We find that the first approach suffers from internode communication delays when the transverse array size becomes large, while the second and third approaches have similar scaling to large array size problems (with the second approach offering about three times the compute speed).

Simulation of plasma instabilities artificially induced in the equatorial ionosphere

Based on a proposed high-resolution numerical simulation, a qualified development of ionospheric instability triggered by chemical release is first presented in this paper. First, the upwelling, pinching, penetrating, and bifurcating processes of artificial instability are overall produced with electron density patterns generated by using this model. This high-resolution simulation method is first used in artificial instability rather than similar previous work involving natural cases. The numerical method provides a clearer prospect on the development of artificially induced instability. Second, aside from the morphology, statistical characteristics of the electron density fluctuations are obtained and used to verify the effect of instability. The variance and the power spectral density (PSD) of artificial instability are first analyzed in detail by using data extracted from simulations. The empirical PSD of the generated natural irregularities yields Shkarofsky's spectrum, which is deemed to be the general spectrum of the ionospheric plasma. It is interesting that the PSD of artificially initiated electron density fluctuation is found to be in good agreement with Shkarofsky's spectrum. This consistency indicates the occurrence of irregularities in nonlinear simulation and applicability of the simulations to extended studies. Finally, as the electron density fluctuation shown in simulation varies along the altitude, the multiple phase screen (MPS) method is ready for scintillation calculation of the diagnostic radio propagation. Validity of the scintillation calculation by using the MPS reveals that the electron density predicted by instability simulation could be useful for further studies involving both natural and artificial instabilities in the ionosphere. It is shown that the high-resolution simulation model proposed could be useful for further studies involving both natural and artificial instabilities in the ionosphere.

Calculation of Hydroacoustic Propagation and Conversion to Seismic Phases at T-Stations

The International Monitoring System (IMS) hydroacoustic network consists of six hydrophone stations and 5 T-stations. The IMS T-stations are high-frequency seismic stations (sample rates of 100 Hz) situated on islands or coastal stations and intended primarily to capture impulsive signals from in-water explosions. However, while there are numerous recordings of impulsive-like signals from in-water explosions at the hydrophone stations, recordings of this type of signal at the T-stations are rare. This is because the conversion of the hydroacoustic to a seismic signal as it propagates from ocean to land is inefficient, characterized both by complex geologic and topographic features and by strong attenuation. To improve the understanding of this signal conversion at T-stations, we performed numerical calculations using the spectral element code SPECFEM2D, modelling the acoustic signal as it propagates from the deep ocean through the ocean/land interface and finally, as an elastic signal, to the T-station. Environmental information from a variety of sources was gathered to construct the earth and ocean models used in the calculations. The goal of this work is to provide a set of calculated waveforms to complement the limited set of observed waveforms and to assist in the characterization of arrivals from explosion-generated hydroacoustic waves recorded at the T-stations.

Exclusive detection of cerebral hemodynamics in functional near-infrared spectroscopy by reflectance modulation of the scalp surface.

.Significance: Functional near-infrared spectroscopy (fNIRS) is a technique for detecting regional hemodynamic responses associated with neural activation in the cerebral cortex. The absorption changes due to hemodynamic changes in the scalp cause considerable signal contamination in the fNIRS measurement. A method for extracting hemodynamic changes in the cerebral tissue is required for reliable fNIRS measurement.Aim: To exclusively detect cerebral functional hemodynamic changes, we developed an fNIRS technique using reflectance modulation of the scalp surface.Approach: The theoretical feasibility of the proposed method was proven by a simulation calculation of light propagation. Its practical feasibility was evaluated by a phantom experiment and brain activation simulation mimicking human fNIRS experiments.Results: The simulation calculation revealed that the partial path length of the scalp was changed by reflectance modulation of the scalp surface. The influence of absorption change in the superficial layer was successfully reduced by the proposed method, using only measurement data, in the phantom experiment. The proposed method was applicable to human experiments of standard designs, achieving statistical significance within an acceptable experimental time-frame.Conclusions: Removal of the scalp hemodynamic effect by the proposed technique will increase the quality of fNIRS data, particularly in measurements in neonates and infants that typically would require a dense optode arrangement.

A TMF crack propagation model considering time dependency and load sequence effects

Due to increasing temperatures and mechanical loads in aero engine turbine components, the prediction of thermomechanical life requires accurate crack propagation calculations under thermomechanical Fatigue (TMF) conditions. Based on a linear elastic crack propagation model which considers pure cyclic crack propagation behavior only, a crack propagation model was developed to accurately predict TMF crack propagation life. It is considering short crack behavior by an El Haddad approach, time dependent effects by a combined creep and oxidation model, as well as cyclic and static time dependent load sequence effects described by a modified Willenborg model. Furthermore, an approach was developed to calculate the time dependent threshold behavior. The model can be applied to arbitrary mission profiles.A total of 29 parameters are required to describe all considered effects. As an example, these were calibrated by isothermal cyclic crack propagation, threshold and creep crack propagation tests on Inconel 718 at three temperatures. TMF crack propagation tests were carried out to validate the capability of the model. It is shown that the calculated crack propagation rates and thresholds, and consequently the predicted crack propagation life, match the measured data very well for isothermal as well as for TMF conditions.

A Comparison of Different Wave Modelling Techniques in An Open-Source Hydrodynamic Framework

Modern design for marine and coastal activities places increasing focus on numerical simulations. Several numerical wave models have been developed in the past few decades with various techniques and assumptions. Those numerical models have their own advantages and disadvantages. The proper choice of the most useful numerical tool depends on the understanding of the validity and limitations of each model. In the past years, REEF3D has been developed into an open-source hydrodynamic numerical toolbox that consists of several modules based on the Navier–Stokes equations, the shallow water equations and the fully nonlinear potential theory. All modules share a common numerical basis which consists of rectilinear grids with an immersed boundary method, high-order finite differences and high-performance computing capabilities. The numerical wave tank of REEF3D utilises a relaxation method to generate waves at the inlet and dissipate them at the numerical beach. In combination with the choice of the numerical grid and discretisation methods, high accuracy and stability can be achieved for the calculation of free surface wave propagation and transformation. The comparison among those models provide an objective overview of the different wave modelling techniques in terms of their numerical performance as well as validity. The performance of the different modules is validated and compared using several benchmark cases. They range from simple propagations of regular waves to three-dimensional wave breaking over a changing bathymetry. The diversity of the test cases help with an educated choice of wave models for different scenarios.

Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan

In order to speed up the calculation of tsunami wave propagation, the field-programmable gate array (FPGA) microchip is used. This makes it possible to achieve valuable performance gain with a modern regular personal computer. The two half-step MacCormack scheme was used herein for numerical approximation of the shallow water system. We studied the distribution of tsunami wave maximal heights along the coast of the southern part of Japan. In particular, the dependence of wave maximal heights on the particular tsunami source location was investigated. Synthetic 100 × 200 km sources have realistic parameters corresponding to this region. As observed numerically, only selected parts of the entire coast line are subject to dangerous tsunami wave amplitudes. The particular locations of such areas strongly depend on the location of the tsunami source. However, the extreme tsunami heights in some of those areas can be attributed to local bathymetry. The proposed hardware acceleration to compute tsunami wave propagation can be used for rapid (say, in a few minutes) tsunami wave danger evaluation for a particular village or industrial unit on the coast.

GPU implementation of curved-grid finite-difference modelling for non-planar rupture dynamics

SUMMARYA deep understanding of earthquake physics requires a large amount of numerical simulations on seismic wave propagation and dynamic rupture. However, the corresponding intensive computational expense of simulations at traditional CPU (central processing unit) platforms make related researches time-consuming. There are many mature graphics processing unit (GPU) programs that can dramatically accelerate the calculation of seismic wave propagation. Unfortunately, there are few discussions about GPU implementations for rupture dynamics. In this work, we extend our 3-D curved-grid finite-difference method (CG-FDM) for rupture dynamics to the GPU platform using the CUDA (compute unified device architecture) programming language. By taking advantage of the new features of the NVIDIA Volta architecture, we implement the GPU-based program for rupture dynamics that is not only efficient but also easy to maintain. The GPU-based CG-FDM program is two orders of magnitude faster than our previous serial CPU-based program and still has a considerable advantage compared with the parallel one. The reliability and correctness of the program are carefully examined by the comparisons of the benchmarks from the ‘Southern California Earthquake Center/U.S. Geological Survey (SCEC/USGS) Dynamic Earthquake Rupture Code Verification Exercise’. The performance improvements of the GPU-based CG-FDM can save a lot of computing time, allowing researchers to perform much more numerical simulations of rupture dynamics to reveal more details of earthquake physics.

A bicomplex finite element method for wave propagation in homogeneous media

PurposeThe purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be applied for wave propagation problems in various environments.Design/methodology/approachIn this paper, the bicomplex number system is introduced and accordingly the differential equation for time-harmonic Maxwell’s equations in homogeneous media is derived in detail. Besides that, numerical simulations of wave propagation are performed and compared to the traditional approach based on classical FEM related to the Helmholtz equation. The appropriate error norm is investigated for different discretizations.FindingsThe results show that the use of bicomplex analysis in FEM leads to the higher accuracy of the electromagnetic field determination compared to the traditional Helmholtz approach. By using the bicomplex-valued formulation, the complex-valued electric and magnetic fields can be found directly and no additional FEM calculations are necessary to get the whole field.Originality/valueThe direct bicomplex formulation overcomes the use of the second order derivatives, which leads to the higher accuracy. In general, accurate calculations of the wave propagation in FEM is still an open problem and the approach described in this paper is a contribution to this class of problems.

Frequency-domain hot-wire sensor and 3D model for thermal conductivity measurements of reactive and corrosive materials at high temperatures.

High temperature solids and liquids are becoming increasingly important in next-generation energy and manufacturing systems that seek higher efficiencies and lower emissions. Accurate measurements of thermal conductivity at high temperatures are required for the modeling and design of these systems, but commonly employed time-domain measurements can have errors from convection, corrosion, and ambient temperature fluctuations. Here, we describe the development of a frequency-domain hot-wire technique capable of accurately measuring the thermal conductivity of solid and molten compounds from room temperature up to 800 °C. By operating in the frequency-domain, we can lock into the harmonic thermal response of the material and reject the influence of ambient temperature fluctuations, and we can keep the probed volume below 1 µl to minimize convection. The design of the microfabricated hot-wire sensor, electrical systems, and insulating wire coating to protect against corrosion is covered in detail. Furthermore, we discuss the development of a full three-dimensional multilayer thermal model that accounts for both radial conduction into the sample and axial conduction along the wire and the effect of wire coatings. The 3D, multilayer model facilitates the measurement of small sample volumes important for material development. A sensitivity analysis and an error propagation calculation of the frequency-domain thermal model are performed to demonstrate what factors are most important for thermal conductivity measurements. Finally, we show thermal conductivity measurements including model data fitting on gas (argon), solid (sulfur), and molten substances over a range of temperatures.

Experimental and Theoretical Photoemission Study of Indole and Its Derivatives in the Gas Phase

The valence and core-level photoelectron spectra of gaseous indole, 2,3-dihydro-7-azaindole, and 3-formylindole have been investigated using VUV and soft X-ray radiation supported by both an ab initio electron propagator and density functional theory calculations. Three methods were used to calculate the outer valence band photoemission spectra: outer valence Green function, partial third order, and renormalized partial third order. While all gave an acceptable description of the valence spectra, the last method yielded very accurate agreement, especially for indole and 3-formylindole. The carbon, nitrogen, and oxygen 1s core-level spectra of these heterocycles were measured and assigned. The double ionization appearance potential for indole has been determined to be 21.8 ± 0.2 eV by C 1s and N 1s Auger photoelectron spectroscopy. Theoretical analysis identifies the doubly ionized states as a band consisting of two overlapping singlet states and one triplet state with dominant configurations corresponding to holes in the two uppermost molecular orbitals. One of the singlet states and the triplet state can be described as consisting largely of a single configuration, but other doubly ionized states are heavily mixed by configuration interactions. This work provides full assignment of the relative binding energies of the core level features and an analysis of the electronic structure of substituted indoles in comparison with the parent indole.

A set of basis functions to improve numerical calculation of Mie scattering in the Chandrasekhar-Sekera representation

Numerical calculations of light propagation in random media demand the multiply scattered Stokes intensities to be written in a common fixed reference. In multiple-scattering schemes, a particularly useful way to perform automatically these basis transformations between reference frames is to write the scattered intensities in the Chandrasekhar-Sekera representation. The main drawback with this representation is the necessity of numerical tests to deal with the limiting situations of the small particle (Rayleigh) and forward/backward scattering. Here, a new set of basis functions is presented to describe the scattering of light by spherical particles (Mie scattering) in the Chandrasekhar-Sekera representation. These basis functions can be implemented in a new algorithm to calculate the Mie scattering amplitudes, which leads straightforwardly to all the scattering quantities. In contrast to the traditional implementation, this set of basis functions implies to natural numerical convergence to the above mentioned limiting cases, which are thoroughly discussed.

REEF3D::FNPF—A Flexible Fully Nonlinear Potential Flow Solver

Abstract In situations where the calculation of ocean wave propagation and impact on structures are required, fast numerical solvers are desired in order to find relevant wave events. Computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) emphasize on the hydrodynamic details such as fluid–structure interaction, which make them less ideal for the event identification due to the large computational resources involved. Therefore, a computationally efficient numerical wave model is needed to identify the events both for offshore deep-water wave fields and coastal wave fields where the bathymetry and coastline variations have strong impact on wave propagation. In the current paper, a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD-based NWTs. The resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. This allows the grid to follow the irregular bottom variation with great flexibility. The free surface boundary conditions are discretized using fifth-order weighted essentially non-oscillatory (WENO) finite difference methods and the third-order total variation diminishing (TVD) Runge–Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypre’s stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the message passing interface (MPI) communication protocol. The numerical results agree well with the experimental measurements in all tested cases and the model proves to be efficient and accurate for both offshore and coastal conditions.

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator.

Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital ERIs (AO-ERIs) is the bottleneck of second-order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition to generate efficiently the required MO-ERIs. The key point of the presented algorithms is to keep track of integrals through partial contractions performed on three-center AO-ERIs; these contractions are stored in RAM instead of the AO-ERIs. Two implementations are provided, an in-core, which reduces the arithmetic and memory scaling factors as compared to the four-center AO-ERIs contraction method, and a semidirect, which overcomes memory limitations by evaluating antisymmetrized MO-ERIs in batches. On the numerical side, the proposed approach is fast and stable. The bad effects due to ill conditioning, namely, several negative and close to zero eigenvalues due to machine round off errors of the matrix associated with the density fitting process, are effectively controlled by means of a modified Cholesky factorization that avoids the matrix inversion needed to perform the asymmetrical density fitting implementation. The numerical experience presented shows that the in-core implementation is highly competitive to perform calculations on medium and large basis sets, while the semidirect implementation has small variations in time by changes in the available memory. The general applicability is illustrated on a set of selected relatively large-size molecules.