Spatial Averaging Approach Research Articles

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.

An Advanced Data Processing Algorithm for Extraction of Polarimetric Radar Signatures of Moving Automotive Vehicles Using the H/A/α Decomposition Technique

A dedicated signal and data processing chain is proposed for a fully polarimetric Doppler surveillance S-band radar to extract the polarimetric signatures of moving targets. To extract the target’s polarimetric features, detection, clustering, and tracking steps are realized for a multi-target environment in the range-Doppler domain. A dedicated data fusion method for all four polarimetric radar channel signals is implemented to take full advantage of the additional polarimetric information and improve the detection performance. While tracking each particular target, polarization information is collected and used to describe their polarization scattering characteristics. Using the polarimetric H/A/α decomposition technique, the polarimetric features of moving automotive targets are extracted and investigated. The developed processing chain has been applied to the signals scattered from vehicles moving in a highway. By employing both time averaging and spatial averaging of the statistical coherency matrix, the polarimetric signatures of both moving vehicles and static clutter have been presented in the two-dimensional H/α plane. It has been found that the spatial averaging approach results in polarimetric signatures of moving vehicles that give the opportunity to directly and without consideration of the motion of the targets compare the polarization features of moving targets and static clutter. Therefore, this method can be used to improve the performance of target detection or target classification.

The Impact of Length-Scale Variation When Diagnosing the Standard Deviations of Background Error in a 4D-Var System and Filtering Method Investigation

The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.

Undrained bearing capacity of spatially random soil for rectangular footings

In this study, a new approach for the evaluation of the 3-D random bearing capacity in rectangular footings is described. The soil strength spatial variability is modelled by random fields. Those fields are discretized via Vanmarcke’s spatial averaging approach to single random variables, which correspond to particular slip surfaces or volumes (energy dissipation regions). A series of numerical analyses is performed for a variety of foundation shapes and isotropic and anisotropic correlation structures for soil strength parameters. The results show that the consideration of three-dimensional cases for relatively long foundations offers significantly lower bearing capacity coefficients of variation. Thus, its impact on reliability assessments is crucial. The worst case correlation length for the bearing capacity mean values is observed and discussed.

Quantitative analysis of spatial averaging effect on chemical shift imaging SNR and noise coherence with k-space sampling schemes

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.

Random bearing capacity evaluation of shallow foundations for asymmetrical failure mechanisms with spatial averaging and inclusion of soil self-weight

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.

Proteome-wide mapping of immune features onto Plasmodium protein three-dimensional structures

Humoral immune responses against the malaria parasite are an important component of a protective immune response. Antibodies are often directed towards conformational epitopes, and the native structure of the antigenic region is usually critical for antibody recognition. We examined the structural features of various Plasmodium antigens that may impact on epitope location, by performing a comprehensive analysis of known and modelled structures from P. falciparum. Examining the location of known polymorphisms over all available structures, we observed a strong propensity for polymorphic residues to be exposed on the surface and to occur in particular secondary structure segments such as hydrogen-bonded turns. We also utilised established prediction algorithms for B-cell epitopes and MHC class II binding peptides, examining predicted epitopes in relation to known polymorphic sites within structured regions. Finally, we used the available structures to examine polymorphic hotspots and Tajima’s D values using a spatial averaging approach. We identified a region of PfAMA1 involving both domains II and III under a high degree of balancing selection relative to the rest of the protein. In summary, we developed general methods for examining how sequence-based features relate to one another in three-dimensional space and applied these methods to key P. falciparum antigens.

Moderate Imaging Resolution Spectroradiometer (MODIS) Aerosol Optical Depth Retrieval for Aerosol Radiative Forcing

The present study uses the Aerosol Optical Depth (AOD) retrieved from Moderate Imaging Resolution Spectroradiometer (MODIS) data for the period from January 2011 until December 2015 over an urban area in Kuching, Sarawak. The results show the minimum AOD value retrieved from MODIS is -0.06 and the maximum value is 6.0. High aerosol loading with high AOD value observed during dry seasons and low AOD monitored during wet seasons. Multi plane regression technique used to retrieve AOD from MODIS (AODMODIS) and different statistics parameter is proposed by using relative absolute error for accuracy assessment in spatial and temporal averaging approach. The AODMODIS then compared with AOD derived from Aerosol Robotic Network (AERONET) Sunphotometer (AODAERONET) and the results shows high correlation coefficient (R2) for AODMODIS and AODAERONET with 0.93. AODMODIS used as an input parameters into Santa Barbara Discrete Ordinate Radiative Transfer (SBDART) model to estimate urban radiative forcing at Kuching. The observed hourly averaged for urban radiative forcing is -0.12 Wm−2 for top of atmosphere (TOA), -2.13 Wm−2 at the surface and 2.00 Wm−2 in the atmosphere. There is a moderate relationship observed between urban radiative forcing calculated using SBDART and AERONET which are 0.75 at the surface, 0.65 at TOA and 0.56 in atmosphere. Overall, variation in AOD tends to cause large bias in the estimated urban radiative forcing.

Modelling Slope Failure Using a Quasi-static MPM with a Non-local Strain Softening Approach

The Material Point Method (MPM), which can be thought of as a mesh-free technique, has been shown to be very efficient in avoiding the mesh distortion problem in large deformation analyses. However, for the widely used explicit dynamic MPM formulation, the time step must inevitably be very small in order to guarantee convergence, especially in the case of quasi-static problems. In this paper, an incremental updated Lagrangian quasi-static MPM formulation is developed, which requires less computation effort by using much larger time steps. Issues pertaining to the implementation of the present MPM formulation are discussed. Strain softening, which may potentially lead to localisation phenomena, is also considered in the constitutive model. Scale effects and mesh size dependency in the solution are accounted for by applying a spatial averaging approach to the strains using a weighting function defined by an internal length scale characterising the non-local deformation. A progressive failure of a slope is simulated in order to demonstrate the efficiency and good performance of the proposed formulation.

Macroscale Vs. Microscale Simulation of Porous Battery Electrodes

Typical porous composite electrodes are enormously complicated, disordered arrangements of active material, binder, conductive material, and pore space. In spite of this complexity, battery simulations based on the porous electrode model pioneered by John Newman have provided a wealth of insight into battery operation at low computational cost. This is made possible by the use of spatial averaging to produce vastly simplified spatial domains on which averaged governing equations can be rapidly solved. With these simplifications, the porous electrode model can provide information about the average spatial variation of quantities such as lithium ion concentration and electrochemical potential.However, results from simulations based on the porous electrode model are known to diverge from experimental results under relatively demanding operating conditions (see, for instance, [1]) that can arise during typical electric vehicle use. This might be the consequence of the spatial averaging approach of the porous electrode method, as electrode microstructure might have a significant influence on transport processes and cell performance. In order to explore this possibility, we have performed traditional porous electrode model simulations and corresponding electrochemical simulations based on the microscale electrode structure.Nickel manganese cobalt oxide (NMC) electrodes were fabricated and incorporated into half-cells, from which discharge curves were obtained. Electrode parameters were used to construct simulations based on the porous electrode model, and an optimization scheme was used to minimize discrepancies between simulation and experimental results.Samples of the same uncycled NMC electrode material were then imaged at the X-ray microtomography beamline of the Advanced Light Source (ALS). Three-dimensional reconstructions were transformed into spatial domains, on which direct numerical simulations were performed to obtain discharge curves. These simulations preserved spatial detail but involved much higher computational costs than those based on the porous electrode model.We will present results from these microscale and macroscale simulations, exploring reasons for discrepancies between the two models and discussing present shortcomings with respect to experimental results.[1] M. Doyle, J. Newman, A. S. Gozdz, C. N. Schmutz, and J.-M. Tarascon, J. Electrochem. Soc. 1996, vol. 143, issue 6, pp. 1890-1903

A simplified approach for modeling spatial variability of undrained shear strength in out-plane failure mode of earth embankment

This paper presents a probabilistic study of the out-plane failure mode of long embankments by first-order reliability method (FORM) and limit equilibrium method (LEM). The uncertainty and longitudinal spatial variability of soils that are deemed the most important factors producing the 3-D failure modes are considered in the probabilistic analysis. The longitudinal (out-plane) spatial variation of undrained shear strength is modeled by both spatial-averaging approach and spatial-autocorrelation approach. Comparisons are made between the two methods. For a long earth embankment, the local 3-D failure with a probabilistic critical width is investigated.

Dual Phase-shifting Moiré Projection with Tunable High Contrast Fringes for Three-Dimensional Microscopic Surface Profilometry

A new dual phase-shifting moiré projection method is proposed for microscopic three-dimensional surface profilometry. One of the most difficult technological challenges encountered in employing moiré triangulation projection for automatic optical inspection (AOI) is to detect high contrast projected fringes from an object's surface having vast variation of surface reflectance. Surface reflectance from different surface regions could vary significantly due to diverse surface characteristics, such as texture and roughness, in which returning light may be arbitrary combination of specular reflection, diffusion and scattering. Undesired measurement results are common when deformed moiré fringes cannot be satisfactorily detected by an imaging detector. To resolve this, the proposed method generates a moiré fringe formed by employing a combination of the deformed fringe detected from the object's surface and a virtual sinusoidal grating self-generated by the computer. A spatial averaging approach is applied to phase-shifted moiré interferograms formed between one deformed fringe and virtual fringes having an equal shifted phase, such as π/2. High-contrast phase-shifted interferograms can be generated for more accurate 3-D surface reconstruction via phase wrapping and unwrapping. One great advantage of the method is its tunable control over the moiré fringe period for reaching more measurable step heights without encountering phase ambiguity problem. From the experimental analysis using standard targets and industrial PCB, it is verified that the method can significantly improve measurement accuracy with a measuring standard deviation less than 0.14% of the overall measuring depth range when measuring a low reflected industrial object surface.

A Unified Interpretation of Stress in Molecular Systems

The microscopic definition for the Cauchy stress tensor has been examined in the past from many different perspectives. This has led to different expressions for the stress tensor and consequently the "correct" definition has been a subject of debate and controversy. In this work, a unified framework is set up in which all existing definitions can be derived, thus establishing the connections between them. The framework is based on the non-equilibrium statistical mechanics procedure introduced by Irving, Kirkwood and Noll, followed by spatial averaging. The Irving--Kirkwood--Noll procedure is extended to multi-body potentials with continuously differentiable extensions and generalized to non-straight bonds, which may be important for particles with internal structure. Connections between this approach and the direct spatial averaging approach of Murdoch and Hardy are discussed and the Murdoch--Hardy procedure is systematized. Possible sources of non-uniqueness of the stress tensor, resulting separately from both procedures, are identified and addressed. Numerical experiments using molecular dynamics and lattice statics are conducted to examine the behavior of the resulting stress definitions including their convergence with the spatial averaging domain size and their symmetry properties.

Catchment-scale non-linear groundwater-surface water interactions in densely drained lowland catchments

Abstract. Freely discharging lowland catchments are characterized by a strongly seasonal contracting and expanding system of discharging streams and ditches. Due to this rapidly changing active channel network, discharge and solute transport cannot be modeled by a single characteristic travel path, travel time distribution, unit hydrograph, or linear reservoir. We propose a systematic spatial averaging approach to derive catchment-scale storage and discharge from point-scale water balances. The effects of spatial heterogeneity in soil properties, vegetation, and drainage network are lumped and described by a relation between groundwater storage and the spatial probability distribution of groundwater depths with measurable parameters. The model describes how, in lowland catchments, the catchment-scale flux from groundwater to surface water via various flow routes is affected by a changing active channel network, the unsaturated zone and surface ponding. We used observations of groundwater levels and catchment discharge of a 6.6 km2 Dutch watershed in combination with a high-resolution spatially distributed hydrological model to test the model approach. Good results were obtained when modeling hourly discharges for a period of eight years. The validity of the underlying assumptions still needs to be tested under different conditions and for catchments of various sizes. Nevertheless, at this stage the model can already improve monitoring efficiency of groundwater-surface water interactions.

A spatial averaging approach to rare-event sampling

We describe a method for treating the sparse or rare-event sampling problem. Our approach is based on the introduction of a family of modified importance functions, functions that are related to but easier to sample than the original statistical distribution. We quantify the performance of the approach for a series of example problems using an asymptotic convergence analysis based on transition matrix methods.

Spatial averaging infiltration model for layered soil

To quantify the influences of soil heterogeneity on infiltration, a spatial averaging infiltration model for layered soil (SAI model) is developed by coupling the spatial averaging approach proposed by Chen et al. and the Generalized Green-Ampt model proposed by Jia et al. In the SAI model, the spatial heterogeneity along the horizontal direction is described by a probability distribution function, while that along the vertical direction is represented by the layered soils. The SAI model is tested on a typical soil using Monte Carlo simulations as the base model. The results show that the SAI model can directly incorporate the influence of spatial heterogeneity on infiltration on the macro scale. It is also found that the homogeneous assumption of soil hydraulic conductivity along the horizontal direction will overestimate the infiltration rate, while that along the vertical direction will underestimate the infiltration rate significantly during rainstorm periods. The SAI model is adopted in the spatial averaging hydrological model developed by the authors, and the results prove that it can be applied in the macro-scale hydrological and land surface process modeling in a promising way.

Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm

The quantum clock synchronization algorithm proposed by I. L. Chuang (Phys. Rev. Lett, 85, 2006(2000)) has been implemented in a three qubit nuclear magnetic resonance quantum system. The effective-pure state is prepared by the spatial averaging approach. The time difference between two separated clocks can be determined by reading out directly through the NMR spectra.

An Approximate Model for Well Productivity in Heterogeneous Porous Media

An approximate analytical model describing the productivity of vertical wells in two-dimensional, heterogeneous porous media is presented. The model represents well-driven flow in terms of an effective permeability for linear flow coupled with an effective near-well skin. This representation is different from previous descriptions, which represent the problem solely in terms of a system-dependent equivalent permeability for radial flow. Extensive comparisons between the model predictions and numerical calculations for single wells and two-well systems in log-normally distributed permeability fields are presented. These results demonstrate the high degree of accuracy of the approximate model over an extensive parameter range. For the problems considered, the method is shown to be more accurate than a previous spatial averaging approach. More importantly, the new method provides a basis for extending existing semianalytical solutions, applicable to homogeneous or layered systems, to more general heterogeneous systems in three dimensions.