Spatial Averaging Research Articles

Gaussian fluctuations of spatial averages of a system of stochastic heat equations

. We consider a system of d non-linear stochastic heat equations driven by an m-dimensional space-time white noise on R + × R . In this article, we study the asymptotic behavior of spatial averages over large intervals [ − R , R ] . We establish a rate of convergence to a multivariate normal distribution in the Wasserstein distance and a functional central limit theorem.

Photoelectron momentum distribution in structured strong fields

Abstract In this study, a reaction microscope is used to explore the behavior of electrons in shaped beams under strong field conditions. Photoelectron momentum spectra indicate that the inclusion of orbital angular momentum (OAM) of light does not significantly impact the available electron angular momentum states. However, the distinctive donut shape of the beam plays a crucial role in determining the observed Photoelectron Angular Distributions (PADs). TDSE simulations, incorporating focal volume averaging indicates that the geometric properties of the focal region of the OAM and the Gaussian beams affect the photoelectron spectra differently. By averaging the spectra across different intensity regions, we have provided a qualitative explanation for the variations in photoelectron spectra resulting from the shapes of the individual beams. This result shows that the transfer of OAM in ultrashort light pulses cannot be detected in gas ensembles due to the ionization being overwhelmed by atoms in the most intense region with minimal spatial phase variation within the laser field. We demonstrate that the differences in the momentum spectra arising from shaped beams can be qualitatively explained using models that incorporate the spatial averaging of the beam, rather than focusing on the OAM content.

Enhancement of the Elastocaloric Performance of Natural Rubber by Forced Air Convection.

We study the enhancement of the elastocaloric effect in natural rubber by using forced air convection to favour heat extraction during the elongation stage of a stretching-unstretching cycle. Elastocaloric performance is quantified by means of the adiabatic undercooling that occurs after fast removal of the stress, measured by infrared thermography. To ensure accuracy, spatial averaging on thermal maps of the sample surface is performed since undercooled samples display heterogeneities caused by various factors. The influence of the stretching velocity and the air velocity is analysed. The findings indicate that there is an optimal air velocity that maximises adiabatic undercooling, with stretching velocities needing to be high enough to enhance cooling power. Our experiments allowed the characterisation of the dependence of the Newton heat transfer coefficient on the air convection velocity, which revealed an enhancement up to 600% for air velocities around 4 m/s.

New scheme of cooperative compressed spectrum sensing

Abstract This study addresses key challenges in sparse signal recovery and compressed spectrum sensing (CSS), focusing on low signal-to-noise ratios (SNR), and the computational complexity of cooperative systems. Motivated by the need for faster and more accurate recovery techniques, we first investigate and generalize the Reduced-Set Matching Pursuit (RMP) algorithm, which overcomes the speed and accuracy limitations of conventional greedy algorithms. Secondly, we propose a novel spatial averaging technique that enhances detection performance by exploiting data from multiple users to counteract low SNR. Lastly, we integrate cooperation into CSS, further improving the detection capabilities during the recovery process. Compared to existing techniques like Joint Sparse Recovery (JSR) and CoSaMP, which face computational and accuracy constraints in real-time applications, the RMP algorithm, combined with the Virtual method (data transformation) and AND fusion rule, delivers superior performance than JSR methods. Moreover, spatial averaging significantly increases the probability of cooperative detection Q d , with SNR increasing linearly by a factor of L − 1 per channel. The results are validated through the implementation of SDR. These findings demonstrate the potential of RMP and cooperation to overcome current limitations in CSS, advancing the state-of-the-art in spectrum sensing for collaborative networks.

Backreaction in Numerical Relativity: Averaging on Newtonian gauge-like hypersurfaces in Einstein Toolkit cosmological simulations

We introduce a spatial averaging scheme and use it to study the evolution of spatial averages in large-scale simulations of cosmological structure formation performed with the Einstein Toolkit. The averages are performed on the spatial hypersurfaces of the simulation setup which, at least initially, represent the hypersurfaces of statistical homogeneity and isotropy. We find only negligible cosmic backreaction on these hypersurfaces even on very small scales, but find significant curvature fluctuations of up to 10% in ΩR for sub-volumes with radius ∼200 Mpc and even larger fluctuations in smaller sub-volumes. In addition, we quantify fluid flow in and out of these sub-volumes. We find this to be significant, up to a 5% change in the density between redshift z=1 and z=0 of a single sphere of radius ∼200 Mpc (and larger for smaller spheres). We suggest this may be important for studies basing averages on volumes co-moving with the simulation hypersurfaces.

Electron Dissipation and Electromagnetic Work

AbstractWith the increase in technical capabilities of computer simulation in recent years, it has become feasible to quantify the degradation of fluid scale plasma and electromagnetic energies in favor of increases of internal energies. While it is understood that electromagnetic energy can be exchanged with fluid scale velocities, it is the pressure strain interaction that exchanges energy between fluid motions and internal energy. Here using simulations of both turbulence and reconnection we show that for electrons, the pressure strain and electromagnetic work are closely related and are frequently comparable when appropriate time and spatial averaging is applied. Otherwise, the instantaneous spatial averaged pressure strain and electromagnetic work are nearly equal for slowly evolving systems, like the reconnection case, while they differ significantly in rapidly evolving systems, like the turbulence case. This clarifies the relationship between these two quantities, which are each frequently used as measures of dissipation.

Simulated analysis and experimental validation of sound field distribution regularity for a large-scale non-anechoic harbor pool

The large-scale underwater space, such as large water pool or large-scale harbor pool can provide a good experimental environment for the measurement of the underwater radiated noise of vessel. However, it's not as simple as measuring the sound power of a small machine in the air, the measurement and evaluation of the low frequency mechanical noise and radiated sound power of vessel requires a specific reverberation environment in the large-scale underwater space. Therefore, in this paper, the reverberant sound field characteristics of large-scale underwater space are simulated and calculated by finite element analysis, and experimental measurements are carried out in the large-scale harbor pool. It was found the cut-off frequency of large-scale underwater space depends on the depth of the water pool, and the lower limit frequency depends on the volume of the water pool. The dock door does not reduce the spatial average sound pressure in the reverberation sound field, the floating box platform does not effect on the cut-off frequency but has an effect on the sound energy of the reverberant sound field. It is possible to select the appropriate underwater experimental environment for the measurement and evaluation of different mechanical noise sources. The sound pressure level obtained by calculating the sound source at different locations in the reverberation area is basically the same, and in a 16 × 22 hydrophone arrays, more than 160 array elements are selected, each between 0.25 m and 1 m, a stable sound pressure level can be obtained through spatial averaging. Through experimental measurement verification in the large-scale harbor pool, low-frequency sound sources are emitted from 6 different positions, three hydrophone arrays data are collected, and the measured sound pressure level error is within 1.4 dB. These conclusions are conducive to the actual measurement and evaluation of noise sources of vessel.

(Invited) Chiral Metamaterials for Polarized Photoluminescence

Metasurfaces offer compact routes to spatial and polarization control of luminescence from nearby emitters, enabling applications ranging from document security to stereoscopic displays to sensing.Most of the time, light-emitters are distributed evenly across the surface. This talk will discuss an alternate approach, where we use direct-write electron beam lithography to pattern semiconductor nanocrystals into targeted shapes and locations, creating a highly tailored metasurface. We use a combination of nanoscale fabrication, Fourier-space photoluminescence measurements, and computational methods to study the circularly polarized photoluminescence from these designer structures.We will discuss the influence of patterning on the resulting optical properties, including the effects of spatial averaging and dipole orientation. We will then show an optimization strategy to produce highly polarized light at chosen angles of outcoupling. The final part of the talk will discuss adding layers of complexity, including the chirality of the underlying pattern, and creating light-emitting solids from intrinsically chiral semiconductor nanocrystals.

Superobbing and Thinning Scales for All-Sky Humidity Sounder Assimilation

Abstract Humidity sounder radiances are currently thinned to 110-km spacing prior to assimilation at ECMWF and used with no averaging applied. In this paper, the thinning scale and possible averaging of all-sky humidity sounder observations into “superobs” are considered. The short- and medium-range forecast impacts of changing the thinning and averaging scales of humidity sounder radiances prior to the data assimilation are investigated separately and then together. Superobbing acts as a low-pass filter and provides smoother images of departures, decreasing the effective sensor noise and thus the standard deviation of background departures, marginally for 183-GHz channels (5%–15%) and significantly for 118-GHz channels (5%–55%). Observations are thus more representative of the model effective resolution, with a better utilization of total information content than thinning native-resolution radiances, as less information is discarded. Whether changed in isolation or combination, the additions of data via superobbing and finer thinning are both shown to markedly improve background fits to independent observations, indicative of better short-range forecasts of humidity and improved winds via the 4D-Var tracer effect. Wind forecasts in the Southern Hemisphere are slightly improved in the medium range. A final configuration is tested at the resolution of the current operational model, with humidity sounder radiances averaged into 50-km superobs with 70-km spacing. This provides about 140% more radiances for assimilation and more finely detailed maps to analyze mesoscale features. The forecast impact of this change is larger in testing with higher model and data assimilation resolutions, showing the scale dependence of such decisions and the expected performance in an operational configuration. Significance Statement This paper investigates thinning and averaging scales for humidity-sounding microwave observations in the ECMWF data assimilation system. The introduction of spatial averaging shows a positive impact, as does the assimilation of observations with finer spacing. These changes permit more total information on humidity into the system, and both are beneficial for short-range forecasts of humidity and winds in the mid- to upper troposphere. The results highlight the interplay between spatial scales of observations and those of the analysis system, with possibilities for improved utilization in this particular case. This is expected to remain a key consideration in assimilation systems going forward, given the continued increases in the resolution of assimilation systems and forecast models.

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.Graphical abstract

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

A new global daily sea‐surface temperature analysis system at Environment and Climate Change Canada

AbstractA new global daily sea‐surface temperature (SST) analysis system has been developed at Environment and Climate Change Canada (ECCC). All components of the new SST analysis system are implemented within the Modular and Integrated Data Assimilation System (MIDAS) software. MIDAS is already used for the data assimilation component of the main operational numerical weather prediction (NWP) systems at ECCC. The new SST analysis system, integrated together with the global sea‐ice analysis, will be part of the combined ocean surface analysis used for all operational prediction systems at ECCC. The data assimilation method used to compute the new SST analyses is two‐dimensional variational method with a diffusion operator for representing the horizontal background‐error correlations. A new algorithm for satellite data bias estimation has also been developed employing gridded bias estimates computed from a spatial averaging of the differences between collocated satellite and in‐situ data. New algorithms for quality control and thinning of satellite data have also been implemented, making each type of observational dataset more evenly distributed over the globe. The performance of the new SST system is examined relative to the current operational SST system by using independent data. The impact of using the new SST analysis within NWP and ocean prediction systems is also evaluated. When compared with the operational system currently in use, the experiments employing the new SST analysis system produce a nearly neutral impact on the NWP and ocean prediction systems. This validation of the new system is an important first step towards the ability to use MIDAS to perform ensemble‐based three‐dimensional ocean and coupled ocean‐ice–atmosphere data assimilation.

Incorporation of RCM-simulated spatial details into climate change projections derived from global climate models

Regional climate models (RCMs) exhibit greater potential than global models (GCMs) in capturing geographical details of climate change arising from orography and land–water distribution, but dynamical downscalings are only available for a limited number of GCMs. The full GCM ensembles are much more representative. Furthermore, the current EURO-CORDEX RCM runs most likely underestimate future warming. Thus, neither GCMs nor RCMs as such constitute an ideal tool for preparing reliable spatially detailed climate projections. This study introduces an easy-to-use GCM-RCM hybrid method that takes advantage of the best properties of both model categories. The large-scale response is adopted from GCM simulations, but the pattern is enriched with RCM-simulated details. For temperature projections, the procedure resembles the conventional pattern-scaling technique. However, the spatial averages of temperature change used for scaling are calculated over an area surrounding each grid point, either by giving an equal weight to the entire area or by taking into account the land–sea distribution. For precipitation, a linearised version of the method has been formulated. The method is demonstrated by integrating spatial details from 12 EURO-CORDEX RCM simulations with the CMIP6 multi-GCM mean projection. The resulting temperature responses include RCM-generated spatial details of up to ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document} 1 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document}C while effectively correcting the general tendency of RCMs to underestimate warming in Europe. For precipitation, geographical details originating from the different CORDEX runs tend to diverge, resulting in a low signal-to-noise ratio. This probably reflects the substantial impact of internal variability on small-scale changes in precipitation.

Impact of natural urban terrain on the pedestrian wind environment in neighborhoods: A CFD study with both wind and buoyancy-driven scenarios

The impact of topography on airflow has been studied at different scales, however the influence of urban natural terrain on local wind conditions is unclear. In this study, the impact of natural urban terrain on mean wind speed at the pedestrian level is investigated. A numerical study is conducted using a Large Eddy Simulation (LES) model for a high-density residential neighbourhood in Singapore with the natural terrain and a flat surface. The following two wind variations are examined (1) low wind speed and high temperature conditions for which the atmospheric boundary layer exhibits unstable thermal stratification; (2) annually averaged wind conditions with neutral thermal stratification. The results show that the overall impact of natural urban terrain on pedestrian wind speed is pronounced when the wind environment exhibits unstable thermal stratification i.e. buoyancy driven flows, compared with wind driven flows. For both cases, the results indicate a localized effect based on building density and proximity to steep terrain with spatial averages as high as approximately 0.8 m/s. In areas characterized by low density, fewer surrounding buildings, or open spaces, it is advisable to model the topography when it is shallow or steeply sloping. For medium density built areas, natural urban terrain modelling is also recommended. However, it is observed that in a high-density region, pedestrian wind flow is more strongly affected by the surrounding buildings than the terrain. These results are potentially important to balance computational cost and accuracy in urban wind simulations in urban areas with various densities and microclimate scenarios.

Statistical insights of polarization speckle via von Mises–Fisher distribution on the Poincaré sphere

Polarization speckles generated via random scattering of light are ubiquitous in natural and engineered systems. They not only manifest intensity fluctuations but also reveal a spatially fluctuating, random polarization distribution. The precise morphology of the polarization speckle pattern serves as a deterministic signature of the light’s state of polarization fluctuation within a scattering medium. Given the inherent randomness of polarization speckle patterns, a statistical approach emerges as the most pragmatic method for their analysis. Stokes parameters, implemented as temporal or spatial averages, are utilized for this purpose. However, within a polarization speckle field featuring a specific spatial average of Stokes parameters, the polarization state exhibits spatial variations across the speckle pattern. These random polarization fluctuations can be effectively modeled using a particular probability density function (PDF), visually represented on the Poincaré sphere. In this work, von Mises–Fisher (vMF) distribution on the Poincaré sphere is extended and applied to demonstrate a statistical insight of polarization speckle fields. A complete theoretical basis is established to investigate the spatial fluctuation of the state of polarization in the polarization speckle using vMF distribution on the Poincaré sphere, including the spatial mean direction, and spatial concentration parameter. Behavior of the marginal vMF distribution on the axes of the Poincaré sphere and its association with the probability density function of the normalized at-the-point Stokes parameters for three different polarization speckles are examined by experiment and simulation. The experimental results are in good agreement with the simulation results and confirm the usefulness of the established theoretical framework for the analysis of the polarization speckles. Characterization of spatial polarization fluctuation offers significant applications, such as in polarimetric analysis and optical sensing, and the same analogy can be used in quantum optics.

Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments.

The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law's applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.

Time‐And‐Space Averaging Applied to Intermittent Multiphase Flow Experiments

AbstractVarious researchers have studied fluctuations in pore‐scale phase occupancy during multiphase flow in porous media using synchrotron‐based X‐ray microcomputed tomography (micro‐CT). However, the impact of these fluctuations on the concept of a representative volume is not yet fully understood. In this study, we performed spatial and temporal averaging of multiphase flow experiments visualized with synchrotron‐based micro‐CT, focusing on oil saturation as the key parameter to determine a representative time‐and‐space average. Our findings revealed that a saturation value representative of both time and space was achieved during fractional flow experiments in drainage mode with fractional flows of 0.8, 0.5, and 0.3. Furthermore, we computed a range of relative permeabilities on the basis of whether momentaneous saturation or time‐and‐space averaged saturation was utilized for direct simulation. Our results highlighted the importance of time‐and‐space averaging in determining a representative relative permeability and indicated that the temporal and spatial scales covered in a typical micro‐CT flow experiment were sufficient to obtain a representative saturation value for sandstone rock under intermittent flow conditions.

Trends in mass utilization of a magnetically shielded Hall thruster operating on xenon and krypton

The trends in mass utilization with increasing discharge voltage and current are investigated for a magnetically shielded Hall thruster operating on xenon and krypton. A 9 kW class shielded thruster is operated with discharge voltages from 300 to 600 V and discharge currents from 15 to 30 A on xenon and krypton. Experimental measurements of discharge current, thrust, anode efficiency, and ion velocity as a function of axial position are used to calibrate a multi-fluid 2D Hall thruster code at all operating conditions. The results of these calibrated simulations are employed to interrogate the plasma properties inside the thruster channel. A simplified 0D model for mass utilization evaluated on spatial averages of the simulated plasma parameters is employed to interpret the response of this efficiency mode with power for each propellant. It is found that with both higher voltage and current, mass utilization increases for both gases and their relative gap in this efficiency decreases. This can be attributed to the higher plasma densities and ionization rate coefficients at high voltage, and solely to higher plasma densities at high current. The driving factors for the increase in mass utilization are examined in the context of its nonlinear response to internal plasma properties. The behavior of mass utilization is also discussed in context of the gap in overall efficiency between the propellants. Finally, the implications of these results for improving the performance of high power Hall thrusters operating on krypton are examined.

Experimental measurement of local noise power spectrum (NPS) in photon counting detector-CT (PCD-CT) using a single data acquisition.

Accurate noise power spectra (NPS) measurement in clinical X-ray CT exams is challenging due to the need for repeated scans, which expose patients to high radiation risks. A reliable method for single CT acquisition NPS estimation is thus highly desirable. To develop a method for estimating local NPS from a single photon counting detector-CT (PCD-CT)acquisition. A novel nearly statistical bias-free estimator was constructed from the raw counts data of PCD-CT scan to estimate the variance of sinogram projection data. An analytical algorithm is employed to reconstruct point-wise covariance between any two image pixel/voxel locations and . A Fourier transform is applied to obtain the desired point-wise NPS for any chosen location . The method was validated using experimental data acquired from a benchtop PCD-CT system with various physical phantoms, and the results were compared with the conventional local NPS measurement method using repeated scans and statistical ensembleaveraging. The experimental results demonstrate that (1) the proposed method can achieve pointwise/local NPS measurement for a region of interest (ROI) located at any chosen position, accurately characterizing the NPS with spatial structures resulting from image content heterogeneity; (2) the local NPS measured using the proposed method show a higher precision in the measured NPS compared to the conventional measurement method; (3) spatial averaging of the local NPS yields the conventional NPS for a given localROI. A new method was developed to enable local NPS from a single PCD-CTacquisition.

Remarks on overestimating the effects of inhomogeneities on the Hubble constant

The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopting the adhesion model in Newtonian cosmology as the model of structure formation, we investigate whether or not the effects of inhomogeneities can be sufficiently large to affect the current observations of the Hubble constant. We show that inappropriate treatment of the effects of inhomogeneities can cause a large deviation of the measured value of the Hubble constant from the background value, whose magnitude is comparable with the Hubble tension. Our main message is the importance of adopting an appropriate model of structure formation to investigate the effects of inhomogeneities. We also add discussion on the spatial averaging approach used to estimate the measured Hubble constant in the inhomogeneous universe.