Iterative Correction Research Articles

Functional Parametric Elasto-Dynamics for Efficient Multicomponent Design

In industrial settings, engineering products are often divided into separate components for detailed conception. They often require iterative corrections between different designers/teams to optimize the final product with all components assembled into a system. This article proposes a surrogate modeling approach with functional descriptions of parts in the model and aims to accelerate the design and optimization phase in real projects. The approach is applied to a vibration problem of a two-component plate structure, where the model estimates the dynamic behavior of the assembled system when only the properties of each individual part are available. A database is built using high-fidelity numerical simulations, and neural-network-based regressions provide reliable predictions on unseen data.

Form-finding analysis and optimization of cable membrane structure based on iterative correction of tension process

The current form-finding analysis of cable membrane structures does not consider the actual tensioning process, thus leading to a difference between the form-finding prestressed and tensioning working states. It will affect the morphology accuracy of membrane structures in use, especially in the field of space structures. This work proposes a form-finding optimization method based on the iterative correction of the tensioning process, which considers membrane stress and edge shape optimizations in order. The method focuses on two evaluation indices: the average membrane stress difference and the root mean square (RMS) of the position difference of the edge cables. This sequential optimization analysis is illustrated based on the examples of a sunshade structure for aerospace applications. The results show that these design requirements on the two evaluation indices can be satisfied after one membrane stress optimization and one edge shape optimization. Subsequently, the influence of the seams on the optimization analysis of tensile cable membranes is also investigated. Although seams increase the inhomogeneity of the membrane stress and edge shape difference, the proposed optimization framework based on the iterative correction of the tension process can still ensure that the design requirement can be satisfied. The work in this paper could form the basis for a high-precision study of tensile membrane structures in space.

A correlated sampling-based Monte Carlo simulation for fast CBCT iterative scatter correction.

In recent years, cone-beam computed tomography (CBCT) has played an important role in medical imaging. However, the applications of CBCT are limited due to the severe scatter contamination. Conventional Monte Carlo (MC) simulation can provide accurate scatter estimation for scatter correction, but the expensive computational cost has always been the bottleneck of MC method in clinical application. In this work, an MC simulation method combined with a variance reduction technique called correlated sampling is proposed for fast iterative scatter correction. Correlated sampling exploits correlation between similar simulation systems to reduce the variance of interest quantities. Specifically, conventional MC simulation is first performed on the scatter-contaminated CBCT to generate the initial scatter signal. In the subsequent correction iterations, scatter estimation is then updated by applying correlated MC sampling to the latest corrected CBCT images by reusing the random number sequences of the task-related photons in conventional MC. Afterward, the corrected projections obtained by subtracting the scatter estimation from raw projections are utilized for FDK reconstruction. These steps are repeated until an adequate scatter correction is obtained. The performance of the proposed framework is evaluated by the accuracy of the scatter estimation, the quality of corrected CBCT images and efficiency. Overall, the difference in mean absolute percentage error between scatter estimation with and without correlated sampling is 0.25% for full-fan case and 0.34% for half-fan case, respectively. In simulation studies, scatter artifacts are substantially eliminated, where the mean absolute error value is reduced from 15 to 2HU in full-fan case and from 53 to 13HU in half-fan case. Scatter-to-primary ratio is reduced to 0.02 for full-fan and 0.04 for half-fan, respectively. In phantom study, the contrast-to-noise ratio (CNR) is increased by a factor of 1.63, and the contrast is increased by a factor of 1.77. As for clinical studies, the CNR is improved by 11% and 14% for half-fan and full-fan, respectively. The contrast after correction is increased by 19% for half-fan and 44% for full-fan. Furthermore, root mean square error is also effectively reduced, especially from 78 to 4HU for full-fan. Experimental results demonstrate that the figure of merit is improved between 23 and 43 folds when using correlated sampling. The proposed method takes less than 25s for the whole iterative scatter correction process. The proposed correlated sampling-based MC simulation method can achieve fast and accurate scatter correction for CBCT, making it suitable for real-time clinical use.

Error transport equations implementation for discontinuous Galerkin methods

The procedure for performing higher-order discretization error estimation for Discontinuous Galerkin (DG) methods using Error Transport Equations (ETE) is presented in this work. The results obtained using the linearized ETE and the nonlinear ETE are compared for several steady state inviscid test cases containing completely smooth cases and cases with singularities or discontinuities. Prior work with the linearized version of ETE achieved improved results by using a relinearization process. This process is generalized to the nonlinear version of ETE and is more appropriately termed iterative correction when applied to both the linear and nonlinear versions. For smooth test cases, the discretization error estimates show expected order of accuracy which is higher than the order of accuracy of the primal solution. This holds for both the linearized and the nonlinear ETE. Discontinuities and singularities in the solution cause trouble in the discretization error estimation process. Discussion is made on the behavior of the ETE error estimates for non-smooth test cases to figure out potential solutions to the existing problems.

N/O abundance ratio and the progenitor mass for the most luminous planetary nebulae of M 31

Context. Plasma diagnostics form the basis of investigation into the physico-chemical properties of line-emitting gaseous systems. Aims. To perform plasma diagnostics properly, it is essential to accurately correct the input spectrum for extinction because determining the degree of extinction is dependent on the physical properties of the line-emitting gas. Hence, both extinction correction and plasma diagnostics have to be performed simultaneously and self-consistently. Methods. By comparing the results of analyses performed for a sample of nine bright planetary nebulae in M 31, both with and without the fully iterative self-consistent simultaneous extinction correction and plasma diagnostics, we demonstrate how a seemingly benign initial assumption of the physical conditions of the line-emitting gas in extinction correction could compromise the results of the entire analyses in terms of the extinction, electron density and temperature, and ionic and elemental abundances. Results. While the electron density and temperature are relatively immune to the imposed inconsistent assumptions, the compromised extinction would cause systematic offsets in the extinction-corrected spectrum, and hence, line strengths, which consequently would impose adverse effects on the resulting ionic and elemental abundances, and other inferences made from the incorrect results. Conclusions. We find that this M 31 PN sample simply represents those around the high-mass end of the mass range for low-mass planetary nebula progenitor stars as expected from the existing theoretical models. It appears that the suspicion raised in the previous study – that these PNe could be anomalously nitrogen-overabundant for the expected progenitor mass range – is simply caused by the apparent underestimation in extinction that originates from the imposed inconsistent assumptions in extinction correction. In a larger context, the results of plasma diagnostics in the literature that are done without seeking simultaneous self-consistency with extinction corrections have to be handled with caution. Ideally, such previous results should be re-evaluated by always seeking simultaneous self-consistency.

Use of S-transform and a new multi-taper S-transform for spectral and coherence estimates: With application to characterize and simulate multivariate non-Gaussian wind pressure coefficient

Obtaining a long duration time series of wind pressure coefficient from wind tunnel tests may not be economically feasible for some projects, and simulated synthetic time series of wind pressure coefficient can be used. In this study, we propose a new multi-taper S-transform (ST), where the discrete prolate spheroidal sequences are used for tapering, and ST is applied to each tapered time series. The proposed multi-taper ST is simple and efficient. The simulation results indicate that the proposed transform provides an unbiased estimate of the power spectral density (PSD) function with small variability. It is also shown that the use of the temporally-averaged results from ST or the proposed multi-taper ST leads to an unbiased estimate of the coherence function. As an application, we use the obtained PSD and coherence, and marginal probability distribution function (PDF) from the time series of the wind pressure coefficient as the targets to simulate univariate and multivariate processes. For the simulation of the non-Gaussian processes, we use the iterative power and amplitude correction but include a digital filter to consider sample-to-sample variability in the PSD function. We show that the PSD and coherence functions and the marginal PDF from the samples match their targets.

Accuracy improvement of immersed boundary-lattice Boltzmann and finite element method by iterative velocity correction

In an analysis of the fluid–structure interaction (FSI) problem, the non-slip boundary condition at solid walls cannot be accurately satisfied by the conventional immersed boundary-lattice Boltzmann coupling schemes due to insufficient interpolation accuracy. To solve this problem, an improved iterative velocity correction procedure for the immersed boundary-lattice Boltzmann coupling scheme is proposed by introducing a modified velocity operator. The particle distribution function was modified at each time step, and the evolution governing equation of the multiple relaxation time-lattice Boltzmann method was performed. A numerical framework for coupling lattice Boltzmann and finite element methods for transient problems involving FSI was established, and the iterative velocity correction immersed boundary method was used for the partitioned approach. The solid structure was discretized with the finite element method, while the single-component fluid flows were simulated with the lattice Boltzmann method. An FSI benchmark model was employed to verify the efficiency of the proposed coupling method. The results show that the developed method guarantees the non-slip boundary condition and maintains the convergence rate of the conventional immersed boundary method. In viscous flow and strong shearing flow, the accuracy of both stationary and moving solid boundaries is obviously improved.

Iterative correction method of a retrace error in interferometry.

In interferometer measurements, the inconsistency of the optical range through which the reference and test lights pass introduces a retrace error in the phase measurement. In this study, we propose an iterative retrace error correction method in interferometry. A black-box model is established based on the linear and squared relationships between the retrace error and the tilt of the testing surface. The error correction phase is obtained using the least-squares method; thereafter, the global tilt is determined to iteratively correct the retrace error. The root mean square (RMS) of the residuals was > 3.2 × 10-5λ, >6.4 × 10-3λ, and >1.4 × 10-3λ in the simulation, experimentally computed retrace error correction in the planar measurement, and spherical measurement, respectively, proving that the retrace error can be effectively corrected.

Modern determinants and challenges of marketing management Ukrainian IT startup industry

The aim of the article. The aim of the article is to study the Ukrainian ecosystem of startups and highlight the determinants and challenges of marketing management of the national IT startup industry in modern conditions. The results of the analysis. It was revealed that in the conditions of increasing entropy at all levels of social systems, the development of the start-up industry becomes critical for adapting to external turbulences. The prerequisites and prospects for the development of the ecosystem of IT startups in Ukraine were analyzed. It is emphasized that the priorities of managing the national economy should shift in the direction of finding opportunities for active formation and use of the country's intellectual potential on the basis of effective marketing management of the start-up industry. The critical determinants of modern IT start-ups have been identified: the issue of choosing forms, methods and tools for marketing management of innovative projects The modern management challenges of the IT startup industry in Ukraine have been identified: insufficient financing at all stages and stages of the startup and requirements for transformation of sources of investment income; breaks in logistics chains with partners and suppliers; requirements of anti-crisis marketing and low-budget flexible PR; aggravation of the need for institutional support and legal support; relocation and optimization of project teams; adaptation of a client-oriented strategy to the turbulence of client needs; personnel management in conditions of shortage of personnel and lack of qualifications. The problems of transformation of target markets, relocation of teams, investment and support of financial sustainability of Ukrainian IT startups were considered. As a solution, it is proposed to use the tools of adaptive marketing management, correction of business models, the use of innovative sources of investment and personnel management. The role of IT startups as a catalyst of innovative transformations and digital transformations of all sectors of the country's economy, the basis for ensuring economic growth, is emphasized. The importance of ensuring an effective system of adaptive marketing management of IT startups as a driver of accelerated innovative development and national security of Ukraine is substantiated. Conclusions and direction for further research. IT startup is a company with a necessarily innovative component, which operates in conditions of extreme uncertainty and limited resources and is in search of a sustainable and scalable business model. That is why it is IT startups that have the role of leader and catalyst of social development in the digital economy. In order to find exactly the right sustainable and scalable business model, IT startups need effective marketing management, since the creation of a business model includes the implementation of marketing management tasks, namely: defining segments, product development, value proposition , sales channels, pricing, etc. The Ukrainian IT startup industry has a strong potential for development and should be considered as a driver of accelerating progress. In wartime conditions, the national IT startup industry is characterized by the relocation of teams, partial disintegration of teams, remote work, efforts of startups to help the country with their innovative solutions, the main focus on domestic and European markets. During this period of time, Ukrainian IT startups also faced many challenges such as: financial and investment, personnel and qualification, marketing and legal. Solving these problematic issues and challenges of marketing management of IT startups will be facilitated by iterative analysis and operational correction of business models for effective management of the marketing strategy in terms of finding new target markets, revising the value proposition, adjusting the marketing mix, as well as expanding the use of innovative sources of investment, intensifying participation international organizations, hiring and training new employees with less work experience.

Optimization of the iterative deconvolution correction method applied to ionization chamber response for small field dosimetry measurements

This study aims to optimize the iterative deconvolution correction of air-filled ionization chamber measurements with limited spatial resolution for photon beam dosimetry. The ionization chamber volume effect could be explained by the inhomogeneity of the absorbed dose in its sensitive volume, leading to a volume averaging effect acting as a convolution kernel K(x). Therefore, the “true” dose profile Pt(x) can be deduced by deconvolving measured 1D profiles Pm(x). The Semiflex 3D ionization chamber type PTW 31021 was studied for beams with flattening filter (WFF), while the SNC125c ionization chamber was investigated for flattening filter free (FFF) beams. The deconvolution distributions were compared for the first ionization chamber with reference dose profiles calculated by Monte Carlo simulation and for the second ionization chamber with reference measurements obtained using a diode EDGE detector, suitable for small field applications. The convolution kernel was assumed to be a sum of normalized Gaussian and Lorentz distributions parametrized by the pair (σicλic ). Good results were obtained with respect to the γ index 2.0%/0.5 mm criterion for the field sizes 6 × 6 mm2, 10 × 10 mm2 and 20 × 20 mm2. The highest agreement between reference and corrected measurement data was obtained by using the Gauss-Lorentz distribution parameters (1.92 mm, 0.80 mm) and (1.90 mm, 0.90 mm) for the ionization chambers Semiflex 3D type PTW 31021 and SNC125c, respectively.

Cube-Based Multitarget 3D Localization Using Bayesian Learning-Based Turbo Decoding in Wireless Sensor Networks

Wireless techniques have progressed beyond two-dimensional (2D) applications; in particular, three-dimensional (3D) localization in wireless sensor networks has attracted increasing attention. While many research works in 3D localization focused on the accuracy enhancement of schemes based on the sensors’ measurements, limited research works addressed the design of 3D localization schemes considering the narrowband signal restriction of sensors. Against this background, we propose a cube-based multitarget three-dimensional (3D) localization solution by exploiting sensors’ time-difference-of-arrival (TDOA) measurements. In particular, unlike the traditional TDOA based scheme, our scheme works in an asynchronous network. Our contributions are twofold. First, the distributed TDOA–based sensor arrays placed with a predefined method create a cube-based location system in 3D space. Second, we propose a turbo expectation propagation (EP)-based decoding algorithm (TED). EP computation is an efficient tool in Bayesian machine learning. With the assistance of the iterative sensor reliability correction (ISRC), we propose an improved algorithm referred to as ISRC-TED. Specifically, the ISRC-TED algorithm outperforms the TED algorithm by utilizing the decisions of the sensor array at every iteration to improve the decoding accuracy further. A reduced-complexity tree search–based decoding strategy for TED and ISRC-TED is also proposed. In simulations, the proposed TED and ISRC-TED algorithms were highly effective, even when the partial sensor network was in power-saving mode. For example, the proposed ISRC-TED algorithm had almost no localization performance loss when 10% of the sensors were in sleep mode.

Use of transform pairs to represent and simulate nonstationary non-Gaussian process with applications

We extend the use of the iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary non-Gaussian processes by considering five transform pairs, including the redundant and non-redundant transform pairs that could provide time–frequency or time-scale decomposition. We compare the performance of the IPAC algorithm to that of the spectral representation method (SRM) in terms of matching the prescribed power spectral density function (PSDF) and the marginal probability distribution function. We also extend and examine the IPAC algorithm to simulate concatenated nonstationary non-Gaussian processes. It is emphasized that the IPAC algorithm can be used with a power or energy distribution defined in a transform domain corresponding to a selected transform pair and without directly relying on the definition of the evolutionary process. Unlike SRM, the use of the IPAC algorithm to simulate the nonstationary non-Gaussian process does not require evaluating the underlying Gaussian PSDF. This is especially advantageous for cases when one is interested in estimating the reliability or performance of a structural system during its design life that is subjected to a number of nonstationary non-Gaussian excitations, each defined by a different PSDF.

An Improved Aerosol Optical Depth Retrieval Algorithm for Multiangle Directional Polarimetric Camera (DPC)

The DPC is a multiangle sensor that detects atmospheric parameters. However, the retrieval of high-precision and high-spatial-resolution aerosol products from the DPC remains a great challenge due to the ill-posed nature of the problem. Thus, a novel aerosol optical depth (AOD) retrieval algorithm was proposed using visible surface reflectance relationships (VISRRs). The VISRR algorithm accounts for the surface anisotropy and needs neither a shortwave infrared band nor a surface reflectance database that can retrieve AOD over dark and bright land cover. Firstly, moderate-resolution imaging spectroradiometer (MODIS) surface reflectance (MYD09) products were used to derive the preceding surface reflectance relationships (SRRs), which are related to surface types, scattering angle, and normalized difference vegetation index (NDVI). Furthermore, to solve the problem of the NDVI being susceptible to the atmosphere, an innovative method based on an iterative atmospheric correction was proposed to provide a realistic NDVI. The VISRR algorithm was then applied to the thirteen months of DPC multiangle data over the China region. AOD product comparison between the DPC and MODIS showed that they had similar spatial distribution, but the DPC had both high spatial resolution and coverage. The validation between the ground-based sites and the retrieval results showed that the DPC AOD performed best, with a Pearson correlation coefficient (R) of 0.88, a root mean square error (RMSE) of 0.17, and a good fraction (Gfrac) of 62.7%. Then, the uncertainties regarding the AOD products were discussed for future improvements. Our results revealed that the VISRR algorithm is an effective method for retrieving reliable, simultaneously high-spatial-resolution and full-surface-coverage AOD data with good accuracy.

A framework for conditional simulation of nonstationary non-Gaussian random field and multivariate processes

We propose a conditional simulation framework for the nonstationary/nonhomogeneous non-Gaussian/Gaussian field and multivariate processes. There are three distinct stages within the proposed framework. The first one is to sample directly the unconditional nonstationary non-Gaussian field or multivariate processes without resorting to the underlying Gaussian characteristics. The second stage maps the unconditional samples and the conditions (i.e., observations) to the Gaussian space and uses them to find the conditional mean and covariance. In the final stage, the conditional samples by considering the effect of the conditioning are generated in Gaussian space and mapped back to the original non-Gaussian field. The efficiency of the framework relies on the efficient unconditional simulation algorithms (i.e., the iterative rank-dependent shuffling algorithm, and the iterative power and amplitude correction algorithm), and the reuse of the unconditional samples for the conditional simulation. The conditional samples match the conditional mean and conditional variance–covariance. The framework can directly apply to the random field and multivariate processes defined by the marginal probability distribution function and the covariance-variance information, or the time–frequency dependent PSD function. The framework is illustrated using several examples.

A Buffer-Based Adaptive Bitrate Approach in Wireless Networks With Iterative Correction

Most providers of video streaming are interested in improving quality of user experience across various wireless network circumstances. Many buffer-based ABR algorithms have been proposed to adjust the bitrate according to the buffer occupancy at the client player. Though keeping the buffer occupancy stable, such ABR algorithms cannot provide satisfied responsiveness to bandwidth dynamics. To solve the problem, we propose an ABR algorithm BBA+ that iteratively corrects the mapping function between bitrate and buffer occupancy according to network throughput. The results show that BBA+ effectively improves the average bitrate and reduces the rebuffering ratio.

Impact of beam-hardening corrections on proton relative stopping power estimates from single- and dual-energy CT.

A major contributing factor to proton range uncertainty is the conversion of computed tomography (CT) Hounsfield units (HU) to proton relative stopping power (RSP). This uncertainty is heightened in the presence of X‐ray beam‐hardening artifact (BHA), which has two manifestations: cupping and streaking, especially in and near bone tissue. This uncertainty can affect the accuracy of proton RSP calculation for treatment planning in proton radiotherapy. Dual‐energy CT (DECT) and iterative beam‐hardening correction (iBHC) both show promise in mitigating CT BHA. This present work attempts to analyze the relative robustness of iBHC and DECT techniques on both manifestations of BHA.The stoichiometric method for HU to RSP conversion was used for single‐energy CT (SECT) and DECT‐based monochromatic techniques using a tissue substitute phantom. Cupping BHA was simulated by measuring the HU of a bone substitute plug in wax/3D‐printed phantoms of increasing size. Streaking BHA was simulated by placing a solid water plug between two bone plugs in a wax phantom. Finally, the effect of varying calibration phantom size on RSP was calculated in an anthropomorphic head phantom.The RSP decreased −0.002 cm–1 as phantom size increased for SECT but remained largely constant when iBHC applied or with DECT techniques. The RSP varied a maximum of 2.60% in the presence of streaking BHA in SECT but was reduced to 1.40% with iBHC. For DECT techniques, the maximum difference was 2.40%, reduced to 0.6% with iBHC. Comparing calibration phantoms of 20‐ and 33‐cm diameter, maximum voxel differences of 5 mm in the water‐equivalent thickness were observed in the skull but reduced to 1.3 mm with iBHC. The DECT techniques excelled in mitigating cupping BHA, but streaking BHA still could be observed. The use of iBHC reduced RSP variation with BHA in both SECT and DECT techniques.

A portable non-invasive microwave based head imaging system using compact metamaterial loaded 3D unidirectional antenna for stroke detection

A metamaterial (MTM) loaded compact three-dimensional antenna is presented for the portable, low-cost, non-invasive microwave head imaging system. The antenna has two slotted dipole elements with finite arrays of MTM unit cell and a folded parasitic patch that attains directional radiation patterns with 80% of fractional bandwidth. The operating frequency of the antenna is 1.95–4.5 GHz. The optimization of MTM unit cell is performed to increase the operational bandwidth, realized gain, and efficiency of the antenna within the frequency regime. It is also explored to improve radiation efficiency and gain when placed to head proximity. One-dimensional mathematical modelling is analyzed to precisely estimate the power distribution that validates the performance of the proposed antenna. To verify the imaging capability of the proposed system, an array of 9 antennas and a realistic three-dimensional tissue-emulating experimental semi-solid head phantom are fabricated and measured. The backscattered signal is collected from different antenna positions and processed by the updated Iterative Correction of Coherence Factor Delay-Multiply-and-Sum beamforming algorithm to reconstruct the hemorrhage images. The reconstructed images in simulation and experimental environment demonstrate the feasibility of the proposed system as a portable platform to successfully detect and locate the hemorrhages inside the brain.

A semi-analytical benchmark for the Stefan problem in arbitrary dimension – assessing accuracy of enthalpy-based methods

PurposeThis paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.Design/methodology/approachThe class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.FindingsThis study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.Practical implicationsThe proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.Originality/valueWhile the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

Projection method for the fluctuating hydrodynamics equations

Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into the classical Navier–Stokes equations, which need to be solved numerically. In this paper, we present a novel projection-based method for solving the incompressible fluctuating hydrodynamics (FHD) equations. By analyzing the equilibrium structure factor spectrum of the velocity field for the linearized FHD equations, we investigate how the inherent splitting errors affect the numerical solution of the stochastic partial differential equations in the presence of non-periodic boundary conditions, and how iterative corrections can reduce these errors. Our computational examples demonstrate both the capability of our approach to reproduce correctly stochastic properties of fluids at small scales as well as its potential use in the simulations of multi-physics problems.

Manual for Calibrating Sound Speed and Poisson’s Ratio of (Split) Hopkinson Bar via Dispersion Correction Using Excel® and Matlab® Templates

This manual presents a procedure to calibrate the one-dimensional sound speed (co) and Poisson’s ratio (ν) of a (split) Hopkinson bar using the open-source templates written in Excel® and Matlab® for dispersion correction. The Excel® template carries out the Fourier synthesis and one-time dispersion correction of a traveling elastic pulse under a given set of co and ν. The MATLAB® template performs the Fourier synthesis and iterative dispersion correction of a traveling elastic pulse for a range of co and ν sets. In the case of the iterative dispersion correction, a set of co and ν is assumed at each iteration step, and the sound speed vs. frequency (cdc vs. fdc) relationship necessary for dispersion correction is obtained under the assumed set by solving the Pochhammer–Chree equation. Subsequently, dispersion correction is carried out by using the cdc vs. fdc relationship. The co and ν values of the bar are determined in the iteration process when the dispersion-corrected pulse profiles are reasonably consistent with the measured ones at two travel distances (2103 and 4000 mm) in the bar. In the case of the experimental profile considered herein, the ν and co values were calibrated to six and four decimal places, respectively. The calibration algorithm is described with the tips for using the open-source templates, which are available online in a publicly accessible repository.