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Journal articles on the topic 'Spatial moments'

Author: Grafiati

Published: 19 October 2022

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1

Raupach, Timothy H., and Alexis Berne. "Invariance of the Double-Moment Normalized Raindrop Size Distribution through 3D Spatial Displacement in Stratiform Rain." Journal of Applied Meteorology and Climatology 56, no. 6 (June 2017): 1663–80. http://dx.doi.org/10.1175/jamc-d-16-0316.1.

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AbstractDouble-moment normalization of the drop size distribution (DSD) summarizes the DSD in a compact way, using two of its statistical moments and a “generic” double-moment normalized DSD function. Results are presented of an investigation into the invariance of the double-moment normalized DSD through horizontal and vertical displacement in space, using data from disdrometers, vertically pointing K-band Micro Rain Radars, and an X-band polarimetric weather radar. The invariance of the double-moment normalized DSD is tested over a vertical range of up to 1.8 km and a horizontal range of up to approximately 100 km. The results suggest that for practical use, with well-chosen input moments, the double-moment normalized DSD can be assumed invariant in space in stratiform rain. The choice of moments used to characterize the DSD affects the amount of DSD variability captured by the normalization. It is shown that in stratiform rain, it is possible to capture more than 85% of the variability in DSD moments zero to seven using the technique. Most DSD variability in stratiform rain can thus be explained through the variability of two of its statistical moments. The results suggest similar behavior exists in transition and convective rain, but the limited data samples available do not allow for robust conclusions for these rain types. The results have implications for practical uses of double-moment DSD normalization, including the study of DSD variability and microphysics, DSD-retrieval algorithms, and DSD models used in rainfall retrieval.

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2

Hoballah, M., M. B. Barbaro, R. Kunne, M. Lassaut, D. Marchand, G. Quéméner, E. Voutier, and J. van de Wiele. "Connecting spatial moments and momentum densities." Physics Letters B 808 (September 2020): 135669. http://dx.doi.org/10.1016/j.physletb.2020.135669.

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3

Lan, Kevin, and James W. Jorgenson. "Spatial and temporal progressions of spatial statistical moments in linear chromatography." Journal of Chromatography A 905, no. 1-2 (January 2001): 47–57. http://dx.doi.org/10.1016/s0021-9673(00)00988-2.

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4

Ossant, Frédéric, Frédéric Patat, Matthias Lebertre, Marie-Laure Teriierooiterai, and Léandre Pourcelot. "Effective Density Estimators Based on the K Distribution: Interest of Low and Fractional Order Moments." Ultrasonic Imaging 20, no. 4 (October 1998): 243–59. http://dx.doi.org/10.1177/016173469802000402.

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The K distribution is an efficient model to the nonRayleigh statistics of the envelope of backscattered signals in random media. This modeling leads to estimate a parameter of effective density by means of the calculation of statistical moments of the envelope signal. In this study, we propose a mathematical analysis of an effective density estimator previously used and based on superior order moments. In order to improve the effective density estimate, we propose several estimators based on low and fractional order moments. The performances of these estimators are evaluated both with simulated signals and in an experimental context with synthetic foams. Estimators based on low and fractional moments appear to be more robust than superior moment-based estimator and an improvement of the spatial resolution of the estimate can be obtained. Results also confirm the capability of the effective density parameter to characterize the spatial distribution of scattering structures.

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5

Medeiros, Walter E., and João B. C. Silva. "Simultaneous estimation of total magnetization direction and 3-D spatial orientation." GEOPHYSICS 60, no. 5 (September 1995): 1365–77. http://dx.doi.org/10.1190/1.1443872.

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Magnetic interpretations are usually carried out either by assuming induced magnetization and estimating the model geometry, or by presuming a known source spatial orientation to estimate the total magnetization. We present a 3-D magnetic interpretation method that estimates simultaneously the total magnetization direction and the spatial orientation of the source. It is based on the approximation of the anomaly by the series derived from expanding the magnetic potential into multipoles and retaining source moments up to second order. The moments and linear combinations of moments appearing in the series are then inverted from the magnetic anomaly. The total magnetization is assumed constant in direction but not in magnitude. It is also presumed implicitly that the anomalous distribution of magnetization intensity has nonzero values in a finite‐volume region, is far from the observation points, and presents three othogonal planes of symmetry intersecting at the center of the dipole moment. The method is essentially linear and requires no a priori explicit assumption of a fixed geometry for the sources. The method is particularly suited to interpret compact, isolated or disjoint, but spatially correlated sources. If the source satisfies all assumptions presumed by the method, it is possible to obtain accurate, stable estimates of the total dipole moment vector, the position of the center of dipole moment, and the directions of all three principal axes of symmetry. If the source is not far from the observation plane and/or if the total magnetization direction is not constant, it is still possible to obtain accurate and stable estimates of the direction of the mean total magnetization and the projection, on the observation plane, of the center of dipole moment. The method is applied to magnetic data from the Gulf of Guinea Seamount. The estimated magnetic palaeopole is at 50°48′S and 74°54′E which is in good agreement with estimates published by other authors.

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6

Baddeley, Adrian, and Gopal Nair. "Approximating the moments of a spatial point process." Stat 1, no. 1 (September 12, 2012): 18–30. http://dx.doi.org/10.1002/sta4.5.

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7

SHEN, JUN, WEI SHEN, and DANFEI SHEN. "ON GEOMETRIC AND ORTHOGONAL MOMENTS." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 07 (November 2000): 875–94. http://dx.doi.org/10.1142/s0218001400000581.

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Moments are widely used in pattern recognition, image processing, computer vision and multiresolution analysis. To clarify and to guide the use of different types of moments, we present in this paper a study on the different moments and compare their behavior. After an introduction to geometric, Legendre, Hermite and Gaussian–Hermite moments and their calculation, we analyze at first their behavior in spatial domain. Our analysis shows orthogonal moment base functions of different orders having different number of zero-crossings and very different shapes, therefore they can better separate image features based on different modes, which is very interesting for pattern analysis and shape classification. Moreover, Gaussian–Hermite moment base functions are much more smoothed, they are thus less sensitive to noise and avoid the artifacts introduced by window function discontinuity. We then analyze the spectral behavior of moments in frequency domain. Theoretical and numerical analyses show that orthogonal Legendre and Gaussian–Hermite moments of different orders separate different frequency bands more effectively. It is also shown that Gaussian–Hermite moments present an approach to construct orthogonal features from the results of wavelet analysis. The orthogonality equivalence theorem is also presented. Our analysis is confirmed by numerical results, which are then reported.

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8

Wang, Xinran, Hailin Ren, Anil Kumar, and Pinhas Ben-Tzvi. "Design and Analysis of a Variable Inertia Spatial Robotic Tail for Dynamic Stabilization." Biomimetics 5, no. 4 (October 25, 2020): 55. http://dx.doi.org/10.3390/biomimetics5040055.

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This paper presents the design of a four degree-of-freedom (DoF) spatial tail and demonstrates the dynamic stabilization of a bipedal robotic platform through a hardware-in-loop simulation. The proposed tail design features three active revolute joints with an active prismatic joint, the latter of which provides a variable moment of inertia. Real-time experimental results validate the derived mathematical model when compared to simulated reactive moment results, both obtained while executing a pre-determined trajectory. A 4-DoF tail prototype was constructed and the tail dynamics, in terms of reactive force and moments, were validated using a 6-axis load cell. The paper also presents a case study where a zero moment point (ZMP) placement-based trajectory planner, along with a model-based controller, was developed in order for the tail to stabilize a simulated unstable biped robot. The case study also demonstrates the capability of the motion planner and controller in reducing the system’s kinetic energy during periods of instability by maintaining ZMP within the support polygon of the host biped robot. Both experimental and simulation results show an improvement in the tail-generated reactive moments for robot stabilization through the inclusion of prismatic motion while executing complex trajectories.

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9

Zoccatelli, D., M. Borga, A. Viglione, G. B. Chirico, and G. Blöschl. "Spatial moments of catchment rainfall: rainfall spatial organisation, basin morphology, and flood response." Hydrology and Earth System Sciences 15, no. 12 (December 20, 2011): 3767–83. http://dx.doi.org/10.5194/hess-15-3767-2011.

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Abstract. This paper describes a set of spatial rainfall statistics (termed "spatial moments of catchment rainfall") quantifying the dependence existing between spatial rainfall organisation, basin morphology and runoff response. These statistics describe the spatial rainfall organisation in terms of concentration and dispersion statistics as a function of the distance measured along the flow routing coordinate. The introduction of these statistics permits derivation of a simple relationship for the quantification of catchment-scale storm velocity. The concept of the catchment-scale storm velocity takes into account the role of relative catchment orientation and morphology with respect to storm motion and kinematics. The paper illustrates the derivation of the statistics from an analytical framework recently proposed in literature and explains the conceptual meaning of the statistics by applying them to five extreme flash floods occurred in various European regions in the period 2002–2007. High resolution radar rainfall fields and a distributed hydrologic model are employed to examine how effective are these statistics in describing the degree of spatial rainfall organisation which is important for runoff modelling. This is obtained by quantifying the effects of neglecting the spatial rainfall variability on flood modelling, with a focus on runoff timing. The size of the study catchments ranges between 36 to 982 km2. The analysis reported here shows that the spatial moments of catchment rainfall can be effectively employed to isolate and describe the features of rainfall spatial organization which have significant impact on runoff simulation. These statistics provide useful information on what space-time scales rainfall has to be monitored, given certain catchment and flood characteristics, and what are the effects of space-time aggregation on flood response modeling.

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Zoccatelli, D., M. Borga, A. Viglione, G. B. Chirico, and G. Blöschl. "Spatial moments of catchment rainfall: rainfall spatial organisation, basin morphology, and flood response." Hydrology and Earth System Sciences Discussions 8, no. 3 (June 21, 2011): 5811–47. http://dx.doi.org/10.5194/hessd-8-5811-2011.

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Abstract. This paper provides a general analytical framework for assessing the dependence existing between spatial rainfall organisation, basin morphology and runoff response. The analytical framework builds upon a set of spatial rainfall statistics (termed "spatial moments of catchment rainfall") which describe the spatial rainfall organisation in terms of concentration and dispersion statistics as a function of the distance measured along the flow routing coordinate. The introduction of these statistics permits derivation of a simple relationship for the quantification of storm velocity at the catchment scale. The paper illustrates the development of the analytical framework and explains the conceptual meaning of the statistics by means of application to five extreme flash floods occurred in various European regions in the period 2002–2007. High resolution radar rainfall fields and a distributed hydrologic model are employed to examine how effective are these statistics in describing the degree of spatial rainfall organisation which is important for runoff modelling. This is obtained by quantifying the effects of neglecting the spatial rainfall variability on flood modelling, with a focus on runoff timing. The size of the study catchments ranges between 36 to 982 km2. The analysis reported here shows that the spatial moments of catchment rainfall can be effectively employed to isolate and describe the features of rainfall spatial organization which have significant impact on runoff simulation. These statistics provide essential information on what space-time scales rainfall has to be monitored, given certain catchment and flood characteristics, and what are the effects of space-time aggregation on flood response modeling.

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11

Afzalifar, Ali, Teemu Turunen-Saaresti, and Aki Grönman. "Non-realisability problem with the conventional method of moments in wet-steam flows." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 5 (October 11, 2017): 473–89. http://dx.doi.org/10.1177/0957650917735955.

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The method of moments offers an efficient way to preserve the essence of particle size distribution, which is required in many engineering problems such as modelling wet-steam flows. However, in the context of the finite volume method, high-order transport algorithms are not guaranteed to preserve the moment space, resulting in so-called ‘non-realisable’ moment sets. Non-realisability poses a serious obstacle to the quadrature-based moment methods, since no size distribution can be identified for a non-realisable moment set and the moment-transport equations cannot be closed. On the other hand, in the case of conventional method of moments, closures to the moment-transport equations are directly calculated from the moments themselves; as such, non-realisability may not be a problem. This article describes an investigation of the effects of the non-realisability problem on the flow conditions and moment distributions obtained by the conventional method of moments through several one-dimensional test cases involving systems that exhibited similar characteristics to low-pressure wet-steam flows. The predictions of pressures and mean droplet sizes were not considerably disturbed due to non-realisability in any of the test cases. However, in one case that was characterised by strong temporal and spatial gradients, non-realisability did undermine the accuracy of the predictions of measures for the underlying size distributions, including the standard deviation and skewness.

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12

Srivastava, Rajesh, Pramod K. Sharma, and Mark L. Brusseau. "Spatial Moments for Reactive Transport in Heterogeneous Porous Media." Journal of Hydrologic Engineering 7, no. 4 (July 2002): 336–41. http://dx.doi.org/10.1061/(asce)1084-0699(2002)7:4(336).

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13

Newman, Peter. "Strategic Spatial Planning: Collective Action and Moments of Opportunity." European Planning Studies 16, no. 10 (November 2008): 1371–83. http://dx.doi.org/10.1080/09654310802420078.

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14

Densmore, Jeffery D. "Spatial Moments of Continuous Transport Problems Computed on Grids." Transport Theory and Statistical Physics 41, no. 5-6 (October 2012): 389–405. http://dx.doi.org/10.1080/00411450.2012.671223.

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15

Hobler, G., E. Langer, and S. Selberherr. "Two-dimensional modeling of ion implantation with spatial moments." Solid-State Electronics 30, no. 4 (April 1987): 445–55. http://dx.doi.org/10.1016/0038-1101(87)90175-4.

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16

Chakrawal, Arjun, Anke M. Herrmann, John Koestel, Jerker Jarsjö, Naoise Nunan, Thomas Kätterer, and Stefano Manzoni. "Dynamic upscaling of decomposition kinetics for carbon cycling models." Geoscientific Model Development 13, no. 3 (March 23, 2020): 1399–429. http://dx.doi.org/10.5194/gmd-13-1399-2020.

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Abstract. The distribution of organic substrates and microorganisms in soils is spatially heterogeneous at the microscale. Most soil carbon cycling models do not account for this microscale heterogeneity, which may affect predictions of carbon (C) fluxes and stocks. In this study, we hypothesize that the mean respiration rate R‾ at the soil core scale (i) is affected by the microscale spatial heterogeneity of substrate and microorganisms and (ii) depends upon the degree of this heterogeneity. To theoretically assess the effect of spatial heterogeneities on R‾, we contrast heterogeneous conditions with isolated patches of substrate and microorganisms versus spatially homogeneous conditions equivalent to those assumed in most soil C models. Moreover, we distinguish between biophysical heterogeneity, defined as the nonuniform spatial distribution of substrate and microorganisms, and full heterogeneity, defined as the nonuniform spatial distribution of substrate quality (or accessibility) in addition to biophysical heterogeneity. Four common formulations for decomposition kinetics (linear, multiplicative, Michaelis–Menten, and inverse Michaelis–Menten) are considered in a coupled substrate–microbial biomass model valid at the microscale. We start with a 2-D domain characterized by a heterogeneous substrate distribution and numerically simulate organic matter dynamics in each cell in the domain. To interpret the mean behavior of this spatially explicit system, we propose an analytical scale transition approach in which microscale heterogeneities affect R‾ through the second-order spatial moments (spatial variances and covariances). The model assuming homogeneous conditions was not able to capture the mean behavior of the heterogeneous system because the second-order moments cause R‾ to be higher or lower than in the homogeneous system, depending on the sign of these moments. This effect of spatial heterogeneities appears in the upscaled nonlinear decomposition formulations, whereas the upscaled linear decomposition model deviates from homogeneous conditions only when substrate quality is heterogeneous. Thus, this study highlights the inadequacy of applying at the macroscale the same decomposition formulations valid at the microscale and proposes a scale transition approach as a way forward to capture microscale dynamics in core-scale models.

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17

Cavanaugh, Nicholas R., and Samuel S. P. Shen. "The Effects of Gridding Algorithms on the Statistical Moments and Their Trends of Daily Surface Air Temperature*." Journal of Climate 28, no. 23 (December 1, 2015): 9188–205. http://dx.doi.org/10.1175/jcli-d-14-00668.1.

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Abstract This paper explores the effects from averaging weather station data onto a grid on the first four statistical moments of daily minimum and maximum surface air temperature (SAT) anomalies over the entire globe. The Global Historical Climatology Network–Daily (GHCND) and the Met Office Hadley Centre GHCND (HadGHCND) datasets from 1950 to 2010 are examined. The GHCND station data exhibit large spatial patterns for each moment and statistically significant moment trends from 1950 to 2010, indicating that SAT probability density functions are non-Gaussian and have undergone characteristic changes in shape due to decadal variability and/or climate change. Comparisons with station data show that gridded averages always underestimate observed variability, particularly in the extremes, and have altered moment trends that are in some cases opposite in sign over large geographic areas. A statistical closure approach based on the quasi-normal approximation is taken to explore SAT’s higher-order moments and point correlation structure. This study focuses specifically on relating variability calculated from station data to that from gridded data through the moment equations for weighted sums of random variables. The higher-order and nonlinear spatial correlations up to the fourth order demonstrate that higher-order moments at grid scale can be determined approximately by functions of station pair correlations that tend to follow the usual Kolmogorov scaling relation. These results can aid in the development of constraints to reduce uncertainties in climate models and have implications for studies of atmospheric variability, extremes, and climate change using gridded observations.

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18

Khasanov, Oleg, Tatiana Smirnova, Olga Fedotova, Grigory Rusetsky, Vladimir Gayvoronsky, and Sergey Pokutnyi. "Time resolved femtosecond spectroscopy of nanocomposites." EPJ Web of Conferences 190 (2018): 03004. http://dx.doi.org/10.1051/epjconf/201819003004.

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Characterization methods of nanocomposites consisted of semiconductor metal-oxide quantum dots (QD) incorporated into a dielectric matrix have been elaborated on the base of time resolved four-wave mixing and photon echo. Large permanent dipole moment, inherent to QDs under study, local field effect, the QD spatial dispersion and distribution function of the transition dipole moments in QDs are taken into account. New responses at multiple frequencies in directions differed from spatial synchronism conditions of well-known signals have been predicted.

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19

Cavanaugh, Nicholas R., and Samuel S. P. Shen. "Northern Hemisphere Climatology and Trends of Statistical Moments Documented from GHCN-Daily Surface Air Temperature Station Data from 1950 to 2010." Journal of Climate 27, no. 14 (July 10, 2014): 5396–410. http://dx.doi.org/10.1175/jcli-d-13-00470.1.

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Abstract The first four statistical moments and their trends are calculated for the average daily surface air temperature (SAT) from 1950 to 2010 using the Global Historical Climatology Network–Daily station data for each season relative to the 1961–90 climatology over the Northern Hemisphere. Temporal variation of daily SAT probability distributions are represented as generalized linear regression coefficients on the mean, standard deviation, skewness, and kurtosis calculated for each 10-yr moving time window from 1950–59 to 2001–10. The climatology and trends of these statistical moments suggest that daily SAT probability distributions are non-Gaussian and are changing in time. The climatology of the first four statistical moments has distinct spatial patterns with large coherent structure for mean and standard deviation and relatively smaller and more regionalized patterns for skewness and kurtosis. The linear temporal trends from 1950 to 2010 of the first four moments also have coherent spatial patterns. The linear temporal trends in the characterizing statistical moments are statistically significant at most locations and have differing spatial patterns for different moments. The regionalized variations specific to higher moments may be related to the climate dynamics that contribute to extremes. The nonzero skewness and kurtosis makes this detailed documentation on the higher statistical moments useful for quantifying climate changes and assessing climate model uncertainties.

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20

MERRYFIELD, WILLIAM J., and GREG HOLLOWAY. "Predictability of quasi-geostrophic turbulence." Journal of Fluid Mechanics 465 (August 25, 2002): 191–212. http://dx.doi.org/10.1017/s0022112002001039.

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A method is developed for statistical prediction of turbulent geophysical flows that is more efficient than ensemble integrations. We consider the evolution of low-order moments for inviscid quasi-geostrophic turbulence. Guided by statistical mechanics, equations are developed for predicting the mean and the variance about the mean as functions of position and time. These equations are consistent with the exact moment equations and contain irreversible (entropy producing) fluxes that must be specified in terms of known moments. Using simple choices for these dependences, the resulting scheme, involving just two spatial fields, typically outperforms 100-realization ensembles.

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21

Belmont, M. R. "Correlation Moment Analysis and the Time Dependence of Coherence in Systems Described by Nonlinear Partial Differential Equations." Journal of Applied Mechanics 73, no. 2 (May 31, 2005): 197–205. http://dx.doi.org/10.1115/1.2065687.

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The work presented introduces correlation moment analysis. This technique can be employed to explore the growth of determinism from stochastic initial conditions in physical systems described by non-linear partial differential equations (PDEs) and is also applicable to wholly deterministic situations. Correlation moment analysis allows the analytic determination of the time dependence of the spatial moments of the solutions of certain types of non-linear partial differential equations. These moments provide measures of the growth of processes defined by the PDE, furthermore the results are obtained without requiring explicit solution of the PDE. The development is presented via case studies of the linear diffusion equation and the non-linear Kortweg de-Vries equation which indicate strategies for exploiting the various properties of correlation moments developed in the text. In addition, a variety of results have been developed which show how various classes of terms in PDEs affect the structure of a sequence of correlation moment equations. This allows results to be obtained about the behavior of the PDE solution, in particular how the presence of certain types of terms affects integral measures of the solution. It is also demonstrated that correlation moments provide a very simple, natural approach to determining certain subsets of conserved quantities associated with the PDEs.

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22

Laidig, Keith E. "General expression for the spatial partitioning of the moments and multipole moments of molecular charge distributions." Journal of Physical Chemistry 97, no. 49 (December 1993): 12760–67. http://dx.doi.org/10.1021/j100151a022.

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23

Jenish, Nazgul. "SPATIAL SEMIPARAMETRIC MODEL WITH ENDOGENOUS REGRESSORS." Econometric Theory 32, no. 3 (December 18, 2014): 714–39. http://dx.doi.org/10.1017/s0266466614000905.

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This paper proposes a semiparametric generalized method of moments estimator (GMM) estimator for a partially parametric spatial model with endogenous spatially dependent regressors. The finite-dimensional estimator is shown to be consistent and root-n asymptotically normal under some reasonable conditions. A spatial heteroscedasticity and autocorrelation consistent covariance estimator is constructed for the GMM estimator. The leading application is nonlinear spatial autoregressions, which arise in a wide range of strategic interaction models. To derive the asymptotic properties of the estimator, the paper also establishes a stochastic equicontinuity criterion and functional central limit theorem for near-epoch dependent random fields.

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24

Persinger, Michael A. "Relating Casimir to Magnetic Energies Results in Spatial Dimensions that Define Biology Systems." International Letters of Chemistry, Physics and Astronomy 39 (October 2014): 160–65. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.39.160.

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The volume-independence that occurs when Casimir and magnetic energies were equated wasemployed to solve for optimal spatial separations. For the magnetic moments of a proton and anelectron in the presence of a magnetic field strength that produced the energy associated with theneutral hydrogen line, the distances were 1 nm and 24 nm or the width of an ion channel in a plasmacell membrane and the average synaptic width, respectively. The small discrepancies in orbit-spinmagnetic moments of the electron with the magnetic moment of the proton emerged as relevant.Calculation of the radius in the bound (circular) system associated with the required magnetic fieldstrength for the ~3.41·10-27 A·m2 discrepancy solved as the Compton wavelength of the electron.Applications of the approach allowed quantitative convergence between universal photon densitieswithin 1 nm widths as well as integration of the energy from acceleration for estimated upper limits ofresting photon masses with Planck’s constant. The results suggest that the physical and chemicalproperties that define biological systems, particularly the brain, reflect astronomical principles.

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Filippone, W. L. "Analytic Solution of the Spencer-Lewis Angular-Spatial Moments Equations." Nuclear Science and Engineering 92, no. 3 (March 1986): 421–39. http://dx.doi.org/10.13182/nse86-a17530.

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Druska, Viliam, and William C. Horrace. "Generalized Moments Estimation for Spatial Panel Data: Indonesian Rice Farming." American Journal of Agricultural Economics 86, no. 1 (February 2004): 185–98. http://dx.doi.org/10.1111/j.0092-5853.2004.00571.x.

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Anekawati, Anik, Bambang Widjanarko Otok, Purhadi, and Sutikno. "GENERALIZED METHOD OF MOMENTS APPROACH TO SPATIAL STRUCTURAL EQUATION MODELING." Far East Journal of Mathematical Sciences (FJMS) 103, no. 6 (March 20, 2018): 1057–76. http://dx.doi.org/10.17654/ms103061057.

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Cunningham, Jeffrey A., Mark N. Goltz, and Paul V. Roberts. "Simplified Expressions for Spatial Moments of Ground-Water Contaminant Plumes." Journal of Hydrologic Engineering 4, no. 4 (October 1999): 377–80. http://dx.doi.org/10.1061/(asce)1084-0699(1999)4:4(377).

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Rajaram, Harihar, and Lynn W. Gelhar. "Three-dimensional spatial moments analysis of the Borden Tracer Test." Water Resources Research 27, no. 6 (June 1991): 1239–51. http://dx.doi.org/10.1029/91wr00326.

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30

Farrell, D. A., A. D. Woodbury, and E. A. Sudicky. "The 1978 Borden tracer experiment: Analysis of the spatial moments." Water Resources Research 30, no. 11 (November 1994): 3213–23. http://dx.doi.org/10.1029/94wr00622.

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31

McCormick, Norman J. "Angular and spatial moments for half-space albedo transport problems." Annals of Nuclear Energy 86 (December 2015): 72–79. http://dx.doi.org/10.1016/j.anucene.2014.12.021.

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32

Severino, Gerardo, Vladimir Cvetkovic, and Antonio Coppola. "Spatial moments for colloid-enhanced radionuclide transport in heterogeneous aquifers." Advances in Water Resources 30, no. 1 (January 2007): 101–12. http://dx.doi.org/10.1016/j.advwatres.2006.03.001.

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Elhorst, J. Paul, Pim Heijnen, Anna Samarina, and Jan P. A. M. Jacobs. "Transitions at Different Moments in Time: A Spatial Probit Approach." Journal of Applied Econometrics 32, no. 2 (February 16, 2016): 422–39. http://dx.doi.org/10.1002/jae.2505.

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34

KAISER, A. B., and A. M. OLEŚ. "ELECTRONIC SPIN STATES IN CHROMIUM." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 634–37. http://dx.doi.org/10.1142/s0217979293001335.

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The electronic spin density and its spatial and temporal variation in Cr and its alloys are still not fully understood. The suggestion that Cr is an example of a spin-split metal is not supported by the evidence. Instead, it appears that three rather different types of magnetic moment are required to describe the electronic spin density in Cr: (1) static spin-density-wave moments and associated low-energy spin fluctuations that collapse at high temperatures; (2) higher-energy paramagnetic fluctuations that increase with temperature; and (3) 3d atomic moments formed due to intra-atomic exchange within 1 Å of the atomic centre showing almost no temperature dependence. We suggest further experiments to clarify this picture.

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Tang, Jie, Chungang Chen, Xueshun Shen, Feng Xiao, and Xingliang Li. "A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere." Advances in Atmospheric Sciences 38, no. 9 (July 22, 2021): 1460–73. http://dx.doi.org/10.1007/s00376-021-0393-7.

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AbstractA positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function (CSLR) scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one. Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1D CSLR solver with large Courant number. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in a real atmospheric model.

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MANOHARAN, H. "MAGNETISM AT THE SPATIAL LIMIT." International Journal of Modern Physics B 16, no. 20n22 (August 30, 2002): 3272. http://dx.doi.org/10.1142/s0217979202014140.

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In this talk I will survey our recent experimental results in the detection and manipulation of magnetism at the spatial limit. Our experiments rely on atom manipulation techniques and scanning tunneling microscopy at low temperatures to enable atomic-scale imaging and control. We have observed "quantum mirages" in focusing devices of order 10 nanometers in size, built by assembling structures out of individual atoms. We have directly imaged the spin perturbations due to isolated magnetic moments on a metal surface. The detection of this localized magnetism can then be utilized in a type of teleportation experiment, in which the spectroscopic signature of an atom is sampled and projected to a remote location by means of a surrounding sea of electrons confined in an engineered nanostructure. The quantum mirage thus cast by a single magnetic atom can be coherently refocused at a distinct point where it is detected as a phantom atom around which the electronic structure mimics that at the real atom. Once materialized, this phantom can interact with real matter in intriguing ways. We have constructed other nanoscale magnetic structures which either elucidate the coupling between isolated moments or provide a mechanism for controlling and exploiting spin coupling over long distances. We have also been developing novel communication methods based on the fundamental effects we have discovered.

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Inoue, Kazuya, Gerard J. M. Uffink, Akira Kobayashi, Naoko Matsunaga, and Tsutomu Tanaka. "Disparity of Macrodispersivity Estimated from Temporal and Spatial Moments Using Random Walk Particle Tracking in Heterogeneous Porous Formations." Journal of Rainwater Catchment Systems 15, no. 2 (2010): 21–31. http://dx.doi.org/10.7132/jrcsa.kj00006069059.

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Fattah, Abbas, and Sunil K. Agrawal. "Design and simulation of a class of spatial reactionless manipulators." Robotica 23, no. 1 (January 2005): 75–81. http://dx.doi.org/10.1017/s0263574704000670.

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For conventional designs of robots, manipulator motions result in forces and moments on the base. These forces and moments may cause undesirable translation and rotation of the base. The objective of this paper is to systematically analyze the fundamentals of reactionless robots. Based on this analysis, a design of one distinct class of spatial robot is proposed. The design is achieved through appropriate choices of geometric and inertial parameters. Due to the underlying conservation laws, the trajectory must satisfy additional constraints. We illustrate the reactionless feature of this robot through computer simulations. We are also fabricating reactionless robots to illustrate the underlying concepts.

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Kuersteiner, Guido M., and Ingmar R. Prucha. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity." Econometrica 88, no. 5 (2020): 2109–46. http://dx.doi.org/10.3982/ecta13660.

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This paper considers a class of generalized methods of moments (GMM) estimators for general dynamic panel models, allowing for weakly exogenous covariates and cross‐sectional dependence due to spatial lags, unspecified common shocks, and time‐varying interactive effects. We significantly expand the scope of the existing literature by allowing for endogenous time‐varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions. For the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In general, the asymptotic distribution of our estimators is found to be mixed normal due to random norming. However, the asymptotic distribution of our test statistics is still chi‐square.

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Koverda, Mikhail N., Eugeny N. Ofitserov, and Anna A. Koverda. "The program «Moments of inertia» for calculating the moments of inertia of the rotational motion of molecules." Butlerov Communications 57, no. 3 (March 31, 2019): 42–50. http://dx.doi.org/10.37952/roi-jbc-01/19-57-3-42.

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The moment of inertia of the rotational motion I, as a descriptor of the spatial structure of the molecule, which determines the properties of a substance, in accordance with the works of recent years, begins to acquire significance in the study of the «structure – property» dependencies, allowing one to describe the change in the properties of compounds in homologous series and address odd homologues. The problem is that there is no universal and transparent method for calculating the moments of inertia of the rotational motion of molecules. Researchers are trying to solve this problem in various ways: presenting the molecule as its carbon chain and calculating the moments of inertia only for it, neglecting the contribution of other atoms, manually calculating the moments of inertia for small simple molecules, based on their estimated geometry, extracting intermediate results from quantum chemical calculations of the program packages like Gaussian or Gamess. We have developed a program for the exact calculation of the moments of inertia, which uses the specification of the exact geometry of the molecule in three-dimensional space using Cartesian coordinates. The program is written on Perl programming language and is available under the GNU General Public License v3.0 (free software). The program uses XYZ files as input data. The principle of the program is to iteratively calculate the inertia moments for all possible positions in the space of the axis of rotation passing through the center of mass of the calculated molecule. The minimum and maximum values of the moments of inertia obtained during the calculation correspond to two perpendicular axes of rotation of the molecule (x and z). The moment of inertia with respect to the third remaining y axis is calculated after finding the canonical equation of the straight axis perpendicular to the found x and z axes.

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Lomov, N., and S. Sidyakin. "MORPHOLOGICAL MOMENTS OF BINARY IMAGES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W4 (May 10, 2017): 19–25. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w4-19-2017.

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The concept of morphological moments of binary images is introduced. Morphological moments can be used as a shape descriptor combining an integral width description of an object with a description of its spatial distribution. The relationship between the proposed descriptor and the disc cover of the figure is discussed and an exact analytical method for descriptor calculation is proposed within the continuous morphology framework. The approach is based on the approximation of the shape by a polygonal figure and the extraction of its medial representation in the form of the continuous skeleton and the radial function. The proposed method for calculation of morphological moments achieves high accuracy and it is computationally efficient. Experimentations have been conducted. Obtained results indicate that the morphological moments are a more informative and rich shape descriptor than the area of the disc cover. Application of morphological moments to the font recognition task improves the recognition quality.

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Qiu, Wen Liang, Meng Jiang, and Xing Bo Zhang. "Seismic Response Reduction of Cable-Stayed Bridge with Viscous Dampers." Applied Mechanics and Materials 137 (October 2011): 154–58. http://dx.doi.org/10.4028/www.scientific.net/amm.137.154.

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For floating system cable-stayed bridge, the longitudinal displacement of girder and moments of towers are very large when strong earthquake happens. The dampers installed between girder and towers in longitudinal direction can reduce efficiently displacement of the girder and moments of the towers induced by longitudinal seismic waves. Using spatial finite element model and time history analysis method, the influences of design parameters of viscous damper on seismic responses of cable-stayed bridge are studied in detail. The results of study show that, with the damping constant increasing, the longitudinal displacement of girder and moment of tower decrease, and the forces of damper increase. With velocity exponent increasing, the longitudinal displacement of girder and moment of tower increase, and the force of damper decrease. So, when determining the design parameters of damper, the cost of dampers, difficulty of construction and seismic reduction effects should be considered together.

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Feng, Lei, Fei Wang, Ju Gao, Yu Gang Fan, and Xue Nan Deng. "A New Titanium-Based Heusler Alloy." Applied Mechanics and Materials 380-384 (August 2013): 4276–79. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.4276.

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TheHeusleralloy system is a rich source of functional materials. We studied the ternary alloyTi2NiSbby first-principles calculations to explore for new functional alloy. We performed geometry optimization for the alloy withHg2CuTi-typestructure and the obtained equilibrium lattice parameter isa0=6.21Å. The magnetic moments of atomNiis 0.22μBin one cell. The alloy is a ferromagnet. The little magnetic moment of atomNicomes from the characteristic spatial occupation of the atoms in the space structure of the alloy.

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Kyriakou, Kalliopi, and Bernd Resch. "Spatial Analysis of Moments of Stress Derived from Wearable Sensor Data." Advances in Cartography and GIScience of the ICA 2 (November 6, 2019): 1–8. http://dx.doi.org/10.5194/ica-adv-2-9-2019.

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Abstract. Over the last years, we have witnessed an increasing interest in urban health research using physiological sensors. There is a rich repertoire of methods for stress detection using various physiological signals and algorithms. However, most of the studies focus mainly on the analysis of the physiological signals and disregard the spatial analysis of the extracted geo-located emotions. Methodologically, the use of hotspot maps created through point density analysis dominates in previous studies, but this method may lead to inaccurate or misleading detection of high-intensity stress clusters. This paper proposes a methodology for the spatial analysis of moments of stress (MOS). In a first step, MOS are identified through a rule-based algorithm analysing galvanic skin response and skin temperature measured by low-cost wearable physiological sensors. For the spatial analysis, we introduce a MOS ratio for the geo-located detected MOS. This ratio normalises the detected MOS in nearby areas over all the available records for the area. Then, the MOS ratio is fed into a hot spot analysis to identify hot and cold spots. To validate our methodology, we carried out two real-world field studies to evaluate the accuracy of our approach. We show that the proposed approach is able to identify spatial patterns in urban areas that correspond to self-reported stress.

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Chae, Seungheon, Ahnryul Choi, Hyunwoo Jung, Tae Hyong Kim, Kyungran Kim, and Joung Hwan Mun. "Machine Learning Model to Estimate Net Joint Moments during Lifting Task Using Wearable Sensors: A Preliminary Study for Design of Exoskeleton Control System." Applied Sciences 11, no. 24 (December 10, 2021): 11735. http://dx.doi.org/10.3390/app112411735.

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Accurately measuring the lower extremities and L5/S1 moments is important since L5/S1 moments are the principal parameters that measure the risk of musculoskeletal diseases during lifting. In this study, protocol that predicts lower extremities and L5/S1 moments with an insole sensor was proposed to replace the prior methods that have spatial constraints. The protocol is hierarchically composed of a classification model and a regression model to predict joint moments. Additionally, a single LSTM model was developed to compare with proposed protocol. To optimize hyperparameters of the machine learning model and input feature, Bayesian optimization method was adopted. As a result, the proposed protocol showed a relative root mean square error (rRMSE) of 8.06~13.88% while the single LSTM showed 9.30~18.66% rRMSE. This protocol in this research is expected to be a starting point for developing a system for estimating the lower extremity and L5/S1 moment during lifting that can replace the complex prior method and adopted to workplace environments. This novel study has the potential to precisely design a feedback iterative control system of an exoskeleton for the appropriate generation of an actuator torque.

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Saavedra, Luz A. "Tests for spatial lag dependence based on method of moments estimation." Regional Science and Urban Economics 33, no. 1 (January 2003): 27–58. http://dx.doi.org/10.1016/s0166-0462(01)00106-5.

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Wang, Zujin, and Xiaodiao Huang. "Visual positioning method of printed circuit boards based on spatial moments." Optical Engineering 53, no. 3 (March 20, 2014): 033102. http://dx.doi.org/10.1117/1.oe.53.3.033102.

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Sharma, Pramod Kumar, and Rajesh Srivastava. "Concentration Profiles and Spatial Moments for Reactive Transport through Porous Media." Journal of Hazardous, Toxic, and Radioactive Waste 16, no. 2 (April 2012): 125–33. http://dx.doi.org/10.1061/(asce)hz.2153-5515.0000112.

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Rämö, Hans. "Moments of trust: temporal and spatial factors of trust in organizations." Journal of Managerial Psychology 19, no. 8 (December 2004): 760–75. http://dx.doi.org/10.1108/02683940410568248.

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Dagan, Gedeon. "Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion." Water Resources Research 26, no. 6 (June 1990): 1281–90. http://dx.doi.org/10.1029/wr026i006p01281.

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