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Intuitively, one would expect a more skillful forecast if predicting weather averaged over one week instead of the weather averaged over one day, and similarly for different spatial averaging areas. However, there are few systematic studies of averaging and forecast skill with modern forecasts, and it is therefore not clear how much improvement in forecast performance is produced via averaging. Here we present a direct investigation of averaging effects, based on data from operational numerical weather forecasts. Data is analyzed for precipitation and surface temperature, for lead times of roughly 1 to 7 days, and for time- and space-averaging diameters of 1 to 7 days and 100 to 4500 km, respectively. For different geographic locations, the effects of time- or space-averaging can be different, and while no clear geographical pattern is seen for precipitation, a clear spatial pattern is seen for temperature. For temperature, in general, time averaging is most effective near coastlines, also effective over land, and least effective over oceans. Based on all locations globally, time averaging was less effective than one might expect. To help understand why time averaging may sometimes be minimally effective, a stochastic model is analyzed as a synthetic weather time series, and analytical formulas are presented for the decorrelation time. In effect, while time averaging creates a time series that is visually smoother, it does not necessarily cause a substantial increase in the predictability of the time series.

Background: The imaging photoplethysmography (iPPG) method is a non-invasive, non-contact measurement method that uses a camera to detect physiological indicators. On the other hand, wearing a mask has become essential today when COVID-19 is rampant, which has become a new challenge for heart rate (HR) estimation from facial videos recorded by a camera.Objective: The aim is to propose an iPPG-based method that can accurately estimate HR with or without a mask.Methods: First, the facial regions of interest (ROI) were divided into two sub-ROIs, and the original signal was obtained through spatial averaging with different weights according to the result of judging whether wearing a mask or not, and the CDF, which emphasizes the main component signal, was combined with the improved POS suitable for real-time HR estimation to obtain the noise-removed BVP signal.Results: For self-collected data while wearing a mask, MAE, RMSE, and ACC were 1.09 bpm, 1.44 bpm, and 99.08%, respectively.Conclusion: Experimental results show that the proposed framework can estimate HR stably in real-time in both cases of wearing a mask or not. This study expands the application range of HR estimation based on facial videos and has very practical value in real-time HR estimation in daily life. [ABSTRACT FROM AUTHOR]

Investigating the impact of field plot size on the performance of estimation models for forest inventory attributes could help optimize the technical schemes for an operational airborne LiDAR-assisted forest resource inventory. However, few studies on the topic have focused on subtropical forests. In this study, 104 rectangular plots of 900 m2 (subdivided into nine quadrats with an area of 10 × 10 m) in subtropical planted forests (Chinese fir, pine, eucalyptus, and broad-leaved forest, 2–56 years old) were used to establish four datasets with six different plot sizes (100, 200, 300, 400, 600, and 900 m2) by combining quadrats. The differences in the LiDAR-derived metrics and forest attributes between plots of different sizes were statistically analyzed. Based on the multivariate power models with stable structures, the differences in estimation accuracies of the stand volume (VOL) and basal area (BA) using plot data of different sizes were compared. The results indicated that: (1) the mean differences in LiDAR-derived metrics of the plots of different sizes in all forest types were small, and most of them had no statistically significant differences (α = 0.05) between the plots of different sizes and the 900 m2 plots; however, the standard deviation of the difference increased rapidly with decreasing plot size; (2) except for the maximal tree height of the plots, the other forest attributes, including the mean tree height, diameter at breast height, BA, and VOL of all forest types, showed no statistically significant differences between the plots of different sizes and the 900 m2 plots; and (3) with increasing plot size, the accuracies of VOL and BA estimations improved markedly, and the effects of plot size on the estimation accuracies of the different forest attributes and different forest types were essentially the same. Spatial averaging resulted in the variations in the independent variables (LiDAR variables) and dependent variables (forest attributes) decreasing gradually with the increasing plot size, which was the main reason for the model's accuracy improving. In applying airborne LiDAR to a large-scale subtropical planted forest inventory, the plot size should be at least 600 m2 for all forest types. [ABSTRACT FROM AUTHOR]

Intuitively, one would expect a more skillful forecast if predicting weather averaged over one week instead of the weather averaged over one day, and similarly for different spatial averaging areas. However, there are few systematic studies of averaging and forecast skill with modern forecasts, and it is therefore not clear how much improvement in forecast performance is produced via averaging. Here we present a direct investigation of averaging effects, based on data from operational numerical weather forecasts. Data is analyzed for precipitation and surface temperature, for lead times of roughly 1 to 7 days, and for time- and space-averaging diameters of 1 to 7 days and 100 to 4500 km, respectively. For different geographic locations, the effects of time- or space-averaging can be different, and while no clear geographical pattern is seen for precipitation, a clear spatial pattern is seen for temperature. For temperature, in general, time averaging is most effective near coastlines, also effective over land, and least effective over oceans. Based on all locations globally, time averaging was less effective than one might expect. To help understand why time averaging may sometimes be minimally effective, a stochastic model is analyzed as a synthetic weather time series, and analytical formulas are presented for the decorrelation time. In effect, while time averaging creates a time series that is visually smoother, it does not necessarily cause a substantial increase in the predictability of the time series. [ABSTRACT FROM AUTHOR]

• The spatial averaging of speckle pattern serves as an approach for measuring the spatial coherence of optical field. • Accelerate and streamline the measurement of spatial coherence in partially coherent light. • Improve the signal-to-noise ratio of spatial coherence pattern. • The experimental results confirm the feasibility and accuracy of the proposed technique. We employ spatial averaging to directly evaluate the modulus of two-dimensional spatial coherence of partially coherent field using speckle patterns. This approach offers several advantages over the temporal averaging method, including reduced workload for recording speckle patterns, enhanced precision and briefness in calculation, and improved resilience against the disturbance of background noise. We develop a comprehensive theoretical analysis to support our proposed method, which is then validated by simulation results and experimental tests involving partially coherent sources. The excellent agreement between theoretical and experimental results confirms the feasibility and accuracy of the proposed technique. [ABSTRACT FROM AUTHOR]

We obtain a kinetic description of spatially averaged dynamics of particle systems. Spatial averaging is one of the three types of averaging relevant within the Irwing–Kirkwood procedure (IKP), a general method for deriving macroscopic equations from molecular models. The other two types, ensemble averaging and time averaging, have been extensively studied, while spatial averaging is relatively less understood. We show that spatially averaged density, linear momentum and kinetic energy can be obtained from a single generating function. A kinetic equation for the generating function is obtained. The deconvolution closure used in the derivation becomes more accurate with increasing density. This yields a kinetic description suitable for fluids and amorphous solids. In addition, we consider extensions of the theory which include time averaging and coarsening in the velocity space. Since averaging is essentially a low-pass filter which damps high frequency oscillations, adding time- and velocity-variable averaging allows us to filter out all oscillations below a specified threshold. Unlike traditional kinetic theory, the proposed equation applies to single realizations of atomistic dynamics. [ABSTRACT FROM AUTHOR]

This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2–10 MHz; ${F}$ /#: 1–3) and measured with five hydrophones (sensitive element diameters ${d}_{g}$ : 85–1000 $\mu \text{m}$), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp($-\alpha {x}$), where ${x} = {d}_{g}$ /($\lambda _{{1}}{F}$ /#) and $\lambda _{{1}}$ is the fundamental wavelength, were used to model focal pressure ratios ${p}'/{p}$ (where ${p}'$ is the measured value subjected to spatial averaging and ${p}$ is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced $\alpha $ (followed by root mean squared difference between data and fit) from 0.29–0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29–0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM’/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced ${C}$ from 9% (4%) to −0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations. [ABSTRACT FROM AUTHOR]

This article reports spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. Readers who are uninterested in hydrophone theory may proceed directly to for an easy method to estimate spatial-averaging correction factors. Hydrophones were modeled as angular spectrum filters. Simulations modeled nine circular transducers (1–10 MHz; F/1.4–F/3.2) driven at six power levels and measured with eight hydrophones (432 beam/hydrophone combinations). For example, the model predicts that if a 200- $\mu \text{m}$ membrane hydrophone measures a moderately nonlinear 5-MHz beam from an F/1 transducer, spatial-averaging correction factors are 33% (peak compressional pressure or ${p}_{c}$), 18% (peak rarefactional pressure or ${p}_{r}$), and 18% (full width half maximum or FWHM). Theoretical and experimental estimates of spatial-averaging correction factors to were in good agreement (within 5%) for linear and moderately nonlinear signals. Criteria for maximum appropriate hydrophone sensitive element size as functions of experimental parameters were derived. Unlike the oft-cited International Electrotechnical Commission (IEC) criterion, the new criteria were derived for focusing rather than planar transducers and can accommodate nonlinear signals in addition to linear signals. Responsible reporting of hydrophone-based pressure and beamwidth measurements should always acknowledge spatial-averaging considerations. [ABSTRACT FROM AUTHOR]

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by Sell and Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn--Hilliard equations, including fractional and sixth order Cahn--Hilliard equations, and several classes of modified Navier--Stokes equations, including the Leray-a regularization, hyperviscous regularization, and their combinations. All of the results are obtained in three-dimensional case with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

This paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

ICNIRP and IEEE publish standards/guidelines for exposures to low-frequency electromagnetic fields and their associated in situ electric fields. Two methods are prescribed for spatially averaging the in situ electric field to evaluate compliance: averaging (1) over a 2 mm × 2 mm × 2 mm volume (ICNIRP) and (2) along a 5 mm linear segment of neural tissue (IEEE). However, detailed calculation procedures for these two schemes are not provided, particularly when the averaging volume/line straddles a tissue/air or tissue/tissue interface. This study proposes detailed schemes for implementing the volume- and line-averaging in such cases, applying them to both a spherical model of layered tissues and a human anatomical model. To extend the applicability of the proposed averaging schemes to the voxels at the tissue boundaries, a parameter, pmax, is introduced and defined as the maximum permissible percentage of air/other tissues in the averaging volume/line. For most inner-tissue voxels results show good agreement between the two averaging schemes, in general. Excluding skin, the relative differences between the two averaging schemes were less than 9% for the 99th percentile in situ electric field, and these differences decrease as pmax increases. Results indicate that around 20-30% inclusion of air or other tissues for volume averaging of internal tissues provides stable percentile values; less stability is observed across pmax for linear averaging. Invoking the suggestion of ICNIRP (2010) that the averaging cube for skin “may extend to subcutaneous tissue,” ≥10% inclusion of air results in stable averaged induced electric fields.

This article reports underestimation of mechanical index (MI) and nonscanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after ten weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly focused beams and nonlinear, nonscanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner/transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015 to 2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse filter suggests that maximally achievable values for MI, TIB, thermal dose (${t} _{{43}}$), and spatial-peak-temporal-average intensity (${I} _{\text {spta}}$) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI ${t} _{{43}}$), 43% ± 39% (ARFI ${I} _{\text {spta}}$), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler ${t} _{{43}}$), and 33% ± 27% (pulsed Doppler ${I} _{\text {spta}}$). These values correspond to frequencies of 3.2 ± 1.3 (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves the accuracy of estimates of MI, TIB, ${t} _{{43}}$ , and ${I} _{\text {spta}}$ for ARFI and pulsed Doppler signals. [ABSTRACT FROM AUTHOR]

This article reports the experimental validation of a method for correcting underestimates of peak compressional pressure (${p}_{c}{)}$ , peak rarefactional pressure (${p}_{r}{)}$ , and pulse intensity integral (pii) due to hydrophone spatial averaging effects that occur during output measurement of clinical linear and phased arrays. Pressure parameters (${p}_{c}$ , ${p}_{r}$ , and pii), which are used to compute acoustic exposure safety indexes, such as mechanical index (MI) and thermal index (TI), are often not corrected for spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. In a companion article (Part I), a novel, analytic, inverse-filter method was derived to correct for spatial averaging for linear or nonlinear pressure waves from linear and phased arrays. In the present article (Part II), the inverse filter is validated on measurements of acoustic radiation force impulse (ARFI) and pulsed Doppler waveforms. Empirical formulas are provided to enable researchers to predict and correct hydrophone spatial averaging errors for membrane-hydrophone-based acoustic output measurements. For example, for a 400- $\mu \text{m}$ membrane hydrophone, inverse filtering reduced errors (means ± standard errors for 15 linear array/hydrophone pairs) from about 34% (${p}_{c}{)}$ , 22% (${p}_{r}{)}$ , and 45% (pii) down to within 5% for all three parameters. Inverse filtering for spatial averaging effects significantly improves the accuracy of estimates of acoustic pressure parameters for ARFI and pulsed Doppler signals. [ABSTRACT FROM AUTHOR]

This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer ${F}$ number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophone pairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure (${p}_{c}$), peak rarefactional pressure (${p}_{r}$), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, ${F}$ /2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500- $\mu \text{m}$ membrane hydrophone, then spatial averaging errors are approximately 16% (${p}_{c}$), 12% (${p}_{r}$), and 24% (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays. [ABSTRACT FROM AUTHOR]

In a fluidized bed system, mean trajectories of fuel particles within the bed of fluidized inert particles are governed by the associated drag forces and characterize hydrodynamic, chemical and thermal processes taken place in the system. A large particle size ratio between the bed material and the fuel particles affects the hydrodynamics of gas-solid multiphase flows via influencing the drag forces between solid phases. The present work focuses on the analysis of forces between the two solid phases with large size ratios using the Lagrangian simulations of discrete element method (DEM). The results are spatially averaged over variable control volume size for comparison to the continuum interphase momentum transfer model. Using our DEM simulation results, a correction factor of drag force is presented versus the size of averaging control volume usable in continuum models. In addition, the role of inhomogeneity of particles distribution within the averaging box is discussed. Unlabelled Image • Lagrangian simulations conducted to study the solid-solid drag force for large particle size ratios. • Spatial averaging performed over results obtained from DEM simulations and Syamlal's equation to obtain correction factor. • Correction factor depends on the averaging control volume. • Inhomogeneity effects studied by simulating non-uniform particles distribution in a control volume. [ABSTRACT FROM AUTHOR]

Evident lack of verified and comprehensive theoretical models for shadow fading, which enable analytical estimation of its statistical distribution and statistical parameters, has promoted the empirical alternatives for this task in many aspects of a wireless system lifecycle, such as e.g. coverage planning, where the imperative is to determine the optimal number of base stations, which balances the system performance and implementation efficiency. However, in addition to shadow fading, the composite received signal is simultaneously affected by deterministic path loss and multipath fading, too, so the prerequisite for accurate estimation of shadow fading from the composite received signal samples is efficient elimination of its fast temporal variations, fast spatial variations, and finally, path loss. Unfortunately, the available methods for this are often not appropriate for measurements related to shadow fading estimation. So, for example, even the commonly used drive/walk test provides neither elimination of time variations, nor accurate path loss estimation. So, in this paper, after identifying drawbacks of the existing techniques for shadow fading estimation, the appropriate procedure is proposed with concrete and unambiguous guidelines for elimination of undesirable components of the composite signal through a five-step algorithm, which is shown to provide significant advantage with respect to common drive/walk testing, in terms of shadow fading values and its statistical parameters estimation. [ABSTRACT FROM AUTHOR]

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence- flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frameindifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volumeaveraging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass. [ABSTRACT FROM AUTHOR]

Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data. [ABSTRACT FROM AUTHOR]

When canopy flows are horizontally averaged to obtain mean profiles, the averaging operation can be defined either as an intrinsic average, normalized by the variable fluid volume, or as a superficial average, normalized by the total volume including solid canopy elements. Properties of spatial averages have been explored extensively in the context of flow through plant canopies, albeit with the assumption that the solid volume fraction is negligible. Without this simplification, properties relevant for non-linear terms apply to intrinsic averages while properties of gradients apply to superficial averages. To avoid inconsistencies and inaccuracies the impact of a non-negligible solid volume fraction should be considered carefully when interpreting mean profiles, when deriving mathematical relations for averaged quantities, and when introducing modelling assumptions for such terms. On this basis, we review the definitions and properties of the method of volume averaging, as developed in the more general context of flow through porous media, and discuss its application to urban canopy flows. We illustrate the properties of intrinsic and superficial averages and their effect on mean profiles with example data from a simulation of flow over constant-height cubes. [ABSTRACT FROM AUTHOR]

This contribution proposes a framework to identify optimal borehole configurations for the design of shallow foundation systems under undrained soil conditions. To this end, the minimization of a performance measure defined in terms of the bearing capacity standard deviations is considered. The random failure mechanism method is adopted for random bearing capacity evaluation, thereby enabling explicit treatment of soil spatial variability with tractable numerical efforts. A sampling-based optimization scheme is implemented to account for the non-smooth nature of the resulting objective function. The proposed framework provides non-trivial sensitivity information of the chosen performance measure as a byproduct of the solution process. Further, the method allows assessing the effect of increasing the number of soil soundings into bearing capacity standard deviations. Three cases involving different foundation layouts are studied to illustrate the capabilities of the approach. Numerical results suggest that the herein proposed framework can be potentially adopted as a supportive tool to determine optimal soil sounding strategies for the design of a practical class of civil engineering systems. • Borehole placement for shallow foundation design under undrained soil conditions. • Stochastic framework accounts for spatial variability of undrained shear strength. • Non-trivial insight about the sensitivity of borehole locations is obtained. • Potentially useful tool to assist the formulation of site investigation programs. [ABSTRACT FROM AUTHOR]

Exposure of humans to electromagnetic fields of high frequency (above 100 kHz), i.e. radiofrequency radiation from the modern wireless systems, today inevitable is. The purpose of this paper is to highlight the importance of broadband measurements of the electric field of high frequency in order to fast and reliable assessment of human exposure. A practical method of ‘in situ’ measurement the electric field intensity which is related to the frequency range of 3 MHz to 18 GHz, is provided.

High-intensity therapeutic ultrasound (HITU) pressure is often measured using a hydrophone. HITU pressure waves typically contain multiple harmonics due to nonlinear propagation. As harmonic frequency increases, harmonic beamwidth decreases. For sufficiently high harmonic frequency, beamwidth may become comparable to the hydrophone effective sensitive element diameter, resulting in signal reduction due to spatial averaging. An analytic formula for a hydrophone spatial averaging filter for beams with Gaussian harmonic radial profiles was tested on HITU pressure signals generated by three transducers (1.45 MHz, F/1; 1.53 MHz, F/1.5; 3.91 MHz, F/1) with focal pressures up to 48 MPa. The HITU signals were measured using fiber-optic and needle hydrophones (nominal geometrical sensitive element diameters: 100 and $400~\mu \text{m}$). Harmonic radial profiles were measured with transverse scans in the focal plane using the fiber-optic hydrophone. Harmonic radial profiles were accurately approximated by Gaussian functions with root-mean-square (rms) differences between transverse scans and Gaussian fits less than 9% for frequencies up to approximately 50 MHz. The Gaussian harmonic beamwidth parameter $\sigma _{n}$ varied with harmonic number $n$ according to a power law, $\sigma _{n} = \sigma _{1}/n^{q}$ where $0.5< q < 0.6$. RMS differences between experimental and theoretical spatial averaging filters were 11% ± 1% (1.45 MHz), 8% ± 1% (1.53 MHz), and 4% ± 1% (3.91 MHz). For the two more highly focused (F/1) transducers, the effect of spatial averaging was to underestimate peak compressional pressure (pcp), peak rarefactional pressure (prp), and pulse intensity integral (pii) by (mean ± standard deviation) (pcp: 4.9% ± 0.5%, prp: 0.4% ± 0.2%, pii: 2.9% ± 1%) and (pcp: 28.3% ± 9.6%, prp: 6% ± 2.4%, pii: 24.3% ± 6.7%) for the 100- and 400- $\mu \text{m}$ -diameter hydrophones, respectively. These errors can be suppressed by the application of the inverse spatial averaging filter. [ABSTRACT FROM AUTHOR]

Modeling scalar transport by advection and diffusion in multiscale porous structures is a challenging problem, particularly in the preasymptotic regimes when non-Fickian effects are prominent. Mathematically, one of the main difficulties is to obtain macroscale models from the homogenization of conservation equations at microscale when epsilon, the ratio of characteristic lengthscales between the micro- and macroscale, is not extremely small compared to unity. Here, we propose the basis of a mathematical framework to do so. The focal idea is to decompose the spatial domain at pore-scale into a set of N subdomains to capture characteristic times associated with exchanges between these subdomains. At macroscale, the corresponding representation consists of a system of N coupled partial differential equations describing the transport of the spatially averaged scalar variable within each subdomain. Besides constructing the framework, we also compare numerically the results of our models to a complete resolution of the problem at the pore-scale, which shows great promises for capturing preasymptotic regimes, non-Fickian transport, and going toward finite-epsilon homogenization. [ABSTRACT FROM AUTHOR]

Spatial averaging of multiple voxels from high-resolution chemical shift imaging (hrCSI) is a common strategy for in vivo metabolic studies to achieve a better signal-to-noise ratio (SNR) for a region-of-interest. However, the mechanism about how the spatial averaging approach influences the respective spectral signal and noise and its relevance to the k-space sampling schemes remains unclear. Using three-dimension 17O CSI technique with the weighted k-space sampling method of Fourier series window, we performed quantitative SNR comparisons between a single low-resolution CSI (lrCSI) voxel (being 27 times larger than the hrCSI voxel size) and the spatially averaged hrCSI voxels with matched sampling volume and location. We demonstrated that the averaged hrCSI voxel spectrum had a large SNR loss (> 4 times) compared to the lrCSI voxel, which was resulted from unmatched increases in signal (~1.9 fold) and noise (~9.3 fold). The signal increase was caused by the spatial overlapping between the adjacent hrCSI voxels. The substantial noise increase was mainly attributed to the strong noise coherence among hrCSI voxels acquired with the weighted k-space sampling. This study presents a quantitative relation between the k-space sampling schemes to an apparent SNR penalty of the spatial averaging approach. The information could be useful for designing CSI acquisition method and determination of optimal spatial resolution for in vivo metabolic imaging studies. [ABSTRACT FROM AUTHOR]

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent “effective” sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction). [ABSTRACT FROM AUTHOR]

Acoustic pressure can be measured with a hydrophone. Hydrophone measurements can underestimate incident acoustic pressure due to spatial averaging effects across the hydrophone sensitive element. The spatial averaging filter for a nonlinear focused beam is a low-pass filter that decreases monotonically from 1 to 0 as frequency increases from 0 to infinity. Experiments were performed to test an analytic model for the spatial averaging filter. Nonlinear pressure tone bursts were generated by three source transducers with driving frequencies ranging from 2.5 to 6 MHz, diameters ranging from 19 to 64 mm, and focal lengths ranging from 38 to 89 mm. The nonlinear pressure fields were measured using four needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and $1000~\mu \text{m}$. The average root-mean-square difference between theoretical and experimental spatial averaging filters was 5.8% ± 2.6%. [ABSTRACT FROM AUTHOR]

Determining high frequency electromagnetic field levels in urban areas represents a very complex task, having in mind the exponential growth of the number of sources embodied in public cellular telephony systems in the past twenty years. The main goal of this paper is a representation of a practical solution in the evaluation of measurement uncertainty for in-situ measurements in the case of spatial averaging. An example of the estimation of the uncertainty for electric field strength broadband measurements in the frequency range from 3 MHz to 18 GHz is presented.

Rockfall inventories are essential to quantify a rockfall activity and characterize the hazard. Terrestrial laser scanning and advancements in processing algorithms have resulted in three-dimensional (3D) semi-automatic extraction of rockfall events, permitting detailed observations of evolving rock masses. Currently, multiscale model-to-model cloud comparison (M3C2) is the most widely used distance computation method used in the geosciences to evaluate 3D changing features, considering the time-sequential spatial information contained in point clouds. M3C2 operates by computing distances using points that are captured within a projected search cylinder, which is locally oriented. In this work, we evaluated the effect of M3C2 projection diameter on the extraction of 3D rockfalls and the resulting implications on rockfall volume and shape. Six rockfall inventories were developed for a highly active rock slope, each utilizing a different projection diameter which ranged from two to ten times the point spacing. The results indicate that the greatest amount of change is extracted using an M3C2 projection diameter equal to, or slightly larger than, the point spacing, depending on the variation in point spacing. When the M3C2 projection diameter becomes larger than the changing area on the rock slope, the change cannot be identified and extracted. Inventory summaries and illustrations depict the influence of spatial averaging on the semi-automated rockfall extraction, and suggestions are made for selecting the optimal projection diameter. Recommendations are made to improve the methods used to semi-automatically extract rockfall from sequential point clouds.

In this study, multi-block failure mechanisms in conjunction with Vanmarcke’s spatial averaging approach are used to evaluate random bearing capacity. This new approach examines the impact of the asymmetrical mechanism in spatially variable soil and the effect of anisotropy. The soil strength parameters were modelled by random fields that were discretized by spatial averaging along slip surfaces. Reliability indices were evaluated for symmetrical and asymmetrical cases. The results show that for higher values of horizontal fluctuation scales, the difference between symmetrical and asymmetrical approaches becomes negligible; however, for smaller values, it can be significant. [ABSTRACT FROM AUTHOR]

The error in the local mean magnitude of the electric field (E-field), due to the numerical anisotropy, obtained by the finite-difference time-domain (FDTD) method is investigated in this paper. The spatial averaging is applied over a cube. In order to quantify the error, the numerical results are compared with theoretical and measured ones. The comparison between the FDTD method and theory is conducted for two empty rooms with perfect electric conductor walls at 3 and 5 GHz. It is found that averaging over a cube with side length of 3.3 wavelengths ($\lambda _{0}$) ensures a good matching between the local mean magnitude of the FDTD and theoretical E-field—maximum error below 23%, 95th percentile of the error below 6%, and correlation above 0.83. Measurements over a cube at 3 GHz in empty and office environments are performed. The difference between the averaged numerical and measured magnitude of the E-field decreases with increasing the averaging stencil. For empty room, the maximum error in the local mean FDTD results is 46% and for office scenario is 49% if the cube side length is 0.5 $\lambda _{0}$. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations have been used for decades to investigate continuum mechanics failure to give the correct distribution of stress near discontinuities, such as holes and crack tips. In this paper, stress distribution around elliptical holes in a sheet material has been examined in an atomistic and a continuum model. Atomistic interactions are described by the Tersoff potential tuned for carbon. Calculations were conducted for the problem of stress distribution around the elliptic hole in a 2D graphene sheet subjected to the gradually increasing uniaxial tension load. The atomistic stress is calculated as spatial average utilizing Hardy's formulation. The results have been compared with the Kirsch solution for stress concentration at the edge of the circular hole. A quantitative measure for switching from atomistic to continuum model and vice versa has been proposed. Routes toward the effective data-driven coupling of macro- and micromechanical models where continuum mechanics approach fails are pointed out. [ABSTRACT FROM AUTHOR]

This paper compares three classes and six methods for evaluation of display sparkle, it provides experimental data and theoretical background for comparison of the procedures, the results and their reproducibility, the sensitivity of the approaches, and their advantages and drawbacks, in order to establish a solid basis for the ongoing standardization process. [ABSTRACT FROM AUTHOR]

This paper presents the gradient structure of a turbulent partially premixed dimethyl ether (DME)/air jet flame operating at a jet Reynolds number of 29,300. Temperature and mixture fraction profiles from Raman/Rayleigh/CO-LIF line measurements are used to determine one-dimensional scalar dissipation rates at six axial locations. A major focus of the current work is to assess the effects of experimental artifacts, including spatial resolution, noise, and dimensionality, on the accuracy of the derived scalar dissipation rate. Two-dimensional probability density functions (PDFs) of the mixture fraction gradients are used to determine possible clipping effects due to insufficient spatial resolution. This resolution limit is compared to values determined from one-dimensional dissipation spectra and scaling laws. Spatial resolution also is investigated using laminar flame calculations in conjunction with optical-blur filters representing the experimental setup. The impact of noise is treated by error propagation methods. Monte Carlo simulations and experimental data from laminar flames are used to verify and validate the models used to predict noise propagation for the measurements of the absolute gradients, squared gradients, and scalar dissipation rates. Gradient and scalar dissipation rate detection limits and contribution from apparent dissipation (due to noise effects) are presented as functions of measurement signal-to-noise ratios. A noised lognormal function is introduced to investigate the impact of noise on derived PDFs and corresponding statistical moments of the measured scalar gradients and the scalar dissipation rate within the turbulent flame. Results from the turbulent flame measurements are presented in the form of scatter plots and conditional statistics to examine turbulence-chemistry interaction and develop a database for model assessment. Specifically, the results are compared to laminar flame calculations over a broad range of strain rates with multi-component and unity Lewis number transport assumptions. This comparison is used to assess the relevance of differential diffusion effects on scalar dissipation rates in the turbulent flame. [ABSTRACT FROM AUTHOR]

Imaging photoplethysmography (iPPG) is a non-contact measuring technology for several physiological parameters reflecting personal health status without a special sensor. However, the pulse signal obtained using the iPPG usually is contaminated by various noises, and the intensity of the interesting pulse signal is relatively weak compared to the noises, emphasizing the necessity of obtaining high-quality pulse signals to measure physiological parameters correctly. Various regions of the face harbor distinct pulse information. We propose a spatial averaging method based on adaptive weights, which can obtain high-quality pulse signals by applying different weights to facial sub-regions of interest (sub-ROIs; sROIs). First, the facial ROI is divided into seven sROIs and the coarse heart rate (HR) is calculated from them. Next, the signal-to-noise ratio (SNR) of the raw signal obtained from each sROI is calculated using the coarse HR, and then a high-quality pulse signal is obtained by assigning positive or negative weights to each sROI based on the SNRs. We compare our method with others through the quality analysis of the obtained pulse signals using the self-collected database and the public database PURE. The comparison results show that the proposed method can provide a better pulse signal compared to other methods under various resolutions and states. This proposed method can obtain the pulse signal with better quality, which is helpful to accurately measure physiological parameters, such as HR and HR variability. [ABSTRACT FROM AUTHOR]

Accurate average flow velocity determination is essential for flow measurement in many industries, including automotive, chemical, and oil and gas. The ultrasonic transit-time method is common for average flow velocity measurement, but current limitations restrict measurement accuracy, including fluid dynamic effects from unavoidable phenomena such as turbulence, swirls or vortices, and systematic flow meter errors in calibration or configuration. A new spatial averaging method is proposed, based on flexural ultrasonic array transducer technology, to improve measurement accuracy and reduce the uncertainty of the measurement results. A novel two-dimensional flexural ultrasonic array transducer is developed to validate this measurement method, comprising eight individual elements, each forming distinct paths to a single ultrasonic transducer. These paths are distributed in two chordal planes, symmetric and adjacent to a diametral plane. It is demonstrated that the root-mean-square deviation of the average flow velocity, computed using the spatial averaging method with the array transducer is 2.94%, which is lower compared to that of the individual paths ranging from 3.65% to 8.87% with an average of 6.90%. This is advantageous for improving the accuracy and reducing the uncertainty of classical single-path ultrasonic flow meters, and also for conventional multi-path ultrasonic flow meters through the measurement via each flow plane with reduced uncertainty. This research will drive new developments in ultrasonic flow measurement in a wide range of industrial applications.

Reliable acoustic characterization is fundamental for patient safety and clinical efficacy during high-intensity therapeutic ultrasound (HITU) treatment. Technical challenges, such as measurement variation and signal analysis, still exist for HITU exposimetry using ultrasound hydrophones. In this work, four hydrophones were compared for pressure measurement: a robust needle hydrophone, a small polyvinylidene fluoride capsule hydrophone and two fiberoptic hydrophones. The focal waveform and beam distribution of a single-element HITU transducer (1.05 MHz and 3.3 MHz) were evaluated. Complex deconvolution between the hydrophone voltage signal and frequency-dependent complex sensitivity was performed to obtain pressure waveforms. Compressional pressure (p+), rarefactional pressure (p-) and focal beam distribution were compared up to 10.6/-6.0 MPa (p+/p-) (1.05 MHz) and 20.65/-7.20 MPa (3.3 MHz). The effects of spatial averaging, local non-linear distortion, complex deconvolution and hydrophone damage thresholds were investigated. This study showed a variation of no better than 10%-15% among hydrophones during HITU pressure characterization. [ABSTRACT FROM AUTHOR]

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design. [ABSTRACT FROM PUBLISHER]

The familiar diffusion equation, ∂g/∂t = DΔg, is studied by using the spatially averaged quantities. A non-local relation, so-called the self-measurability condition, fulfilled by this equation is obtained. We define a broad class of diffusion equations defined by some "diffusion inequality", ∂g/∂t · Δg ≥ 0, and show that it is equivalent to the self-measurability condition. It allows formulating the diffusion inequality in a non-local form. That represents an essential generalization of the diffusion problem in the case when the field g(x, t) is not smooth. We derive a general differential equation for averaged quantities coming from the self-measurability condition.

The purpose of this work was to improve the existing models that allow spatial averaging effects of piezoelectric hydrophones to be accounted for. The model derived in the present study is valid for a planar source and was verified using transducers operating at 5 and 20 MHz. It is based on Fresnel approximation and enables corrections for both on-axis and off-axis measurements. A single-integral approximate formula for the axial acoustic pressure was derived, and the validity of the Fresnel approximation in the near field of the planar transducer was examined. The numerical results obtained using 5 and 20 MHz planar transmitters with an effective diameter of 12.7 mm showed that the derived model could account for spatial averaging effects to within 0.2% with Beissner’s exact integral (Beissner, 1981), for k ( a + b ) 2 ≫ π (where k is the circular wavenumber, and a and b are the effective radii of the transmitter and hydrophone, respectively). The field distributions along the acoustic axis and the beam directivity patterns are also included in the model. The spatial averaging effects of the hydrophone were generally observed to cause underestimation of the absolute pressure amplitudes of the acoustic beam, and overestimation of the cross-sectional size of the beam directivity pattern. However, the cross-sectional size of the directivity pattern was also found to be underestimated in the “far zone” (beyond Y 0 = a 2 / λ ) of the transmitter. The results of this study indicate that the spatial averaging effect on the beam directivity pattern is negligible for π ( γ 2 + 4 γ ) s ≪ 1 (where γ = b / a , and s is the normalized distance to the planar transducer). [ABSTRACT FROM AUTHOR]

In the global effect, saccades are displaced towards a distractor if the latter is near to the target, an effect thought to reflect spatial averaging in neurons of the superior colliculus. The temporal dynamics of the global effect have not been well studied, however. We had twelve subjects perform horizontal saccades to a target in trials in which there were either no distractor or a distractor stimulus located 20° above or below the target. The distractor appeared either simultaneously with the target or preceded it by an interval of between 100 and 800 ms, and was either flashed for only 100 ms or remained visible until the subject responded with a saccade. Both flashed and persistent distractors reduced saccadic latency if they preceded target onset, indicating that subjects could use this cue to prepare saccades in advance. Saccadic endpoint was displaced towards a flashed distractor only if it was simultaneous with the target. However, persistent distractors produced a global effect for both simultaneous presentation and distractor-target intervals of 100 ms, but not for longer intervals. We conclude that the global effect requires of the distractor both a recent onset and persistence of the distractor, and that distractor-related activity decays rapidly within 300 ms. [ABSTRACT FROM AUTHOR]

This paper describes Orientation Analysis Tools (OATools), a new add-in, which has been developed for ArcGIS software (ESRI) to allow the spatial analysis of structural data. These tools bring a complex approach to structural data analysis that highlights the spatial aspect of oriented data. In this paper we introduce the functionality of this add-in, which allows users to plot selected data in azimuthal projection, calculate and plot fold axes, construct density distribution diagrams and rose histograms, and create maps of spatial averages and fold axes. There is a link between projections and maps; therefore, it is possible to select point data in the projection and see their location on the map, and vice versa. Practical use of these tools is demonstrated in a case study of the Svratka and Polička crystalline units (Eastern margin of the Bohemian Massif, Czech Republic), where a large dataset was collected. Using OATools the structural conditions were explored. Major changes in foliation dip directions were detected and the axial surfaces of the folds were determined. We also demonstrate the benefit of applying these tools, together with the potential of GIS with respect to spatial data queries, storage, and visualization. [ABSTRACT FROM AUTHOR]

This paper presents spatially averaged Navier–Stokes equations for modelling macro-scale flow in devices with periodic solid structures such as fin and tube arrays. The properties of steady and unsteady periodically developed flow are investigated to assess different strategies for determining the closure terms in the macro-scale flow equations. It is shown that the spatial averaging technique requires an appropriate weighting function to ensure that the closure terms are spatially constant for periodically developed flow. Moreover, through an appropriate choice of the weighting function, the closure terms can be obtained by solving a local closure problem on a unit cell of the periodic structures. The theoretical framework of this paper is applied as multi-scale modelling technique for flow through a cylindrical tube array. This case study illustrates the advantages of the weighted spatial averaging technique over the volume averaging technique. [ABSTRACT FROM AUTHOR]

The issue of spatial averaging effect arises in CARS temperature measurements when the probe volume contains temperature gradients, a situation frequently encountered in turbulent reacting flows where flow patterns are irregular and temperature gradients are typically steep. In present work, a new dual-temperature fitting model is developed to deal with the spatial averaging effect and then applied to evaluate the measured pure rotational CARS spectra performed on a premixed flame of a Wolfhard–Parker slot burner. Comparing with the traditional single-temperature fitting model, an improved spectral fitting and therefore, temperature and concentration evaluation by using the dual-temperature fitting model, is demonstrated. Finally, the feasibility of the dual-temperature model is shown in turbulent spray flame. [ABSTRACT FROM AUTHOR]