Beyond “greening” and “browning”: Trends in grassland ground cover fractions across Eurasia that account for spatial and temporal autocorrelation
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Katarzyna Ewa Lewińska↗
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Results for “AUTOCORRELATION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Accounting for spatial autocorrelation in disease modeling feature selection
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Mathematics↗
Accounting for spatial autocorrelation in disease modeling feature selectio
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Li, Katherine Jia↗
Operator dynamics in Floquet many-body systems
We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025
Yoshimura, Takato (ORCID:0000000309159846)↗
Non-Gaussian wave packet dynamics in anharmonic potential: Cumulant expansion treatment
This manuscript utilizes cumulant expansion as an alternative algebraic approach to evaluating integrals and solving a system of nonlinear differential equations for probing anharmonic dynamics in condensed phase systems using Morse oscillator. These integrals and differential equations become harder to solve as the anharmonicity of the system goes beyond that of Morse oscillator description. This algebraic approach becomes critically important in case of Morse oscillator as it tends to exhibit divergent dynamics and numerical uncertainties at low temperatures. The autocorrelation function is calculated algebraically and compared to the exact one for they match perfectly. It is also compared to the approximate autocorrelation function using the differential equations technique reported in Toutounji (2014) for weak and strong electron–phonon coupling cases. It is found that the present cumulant method is more efficient, and easier to use, than the exact expression. Deviation between the approximate autocorrelation function and the exact autocorrelation function starts to arise as the electron–phonon coupling strength increases. The autocorrelation function obtained using cumulants identically matches the exact autocorrelation function, thereby surpassing the approach presented in Toutounji (2014). The advantage of the present methodology is its applicability to various types of electron–phonon coupling cases. Additionally, the herein approach only uses algebraic techniques, thereby avoiding both the divergence integral and solving a set of linear first- and second-order partial differential equations as was done in previous work. Model calculations are presented to demonstrate the accuracy of the herein work.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices
The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components are described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different {sup 29}Si concentrations in magnetic fields directed along three crystallographic axes is considered.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Effects of sample design and landscape features on a measure of environmental heterogeneity
Environmental heterogeneity, an important influence on organisms and ecological processes, can be quantified by the variance of an environmental characteristic over all locations within a study extent. However on landscapes with autocorrelation and gradient patterns, estimating this variance from a sample of locations may lead to errors that cannot be corrected with statistical techniques. We analytically derived the relative expected sampling error of sample designs on landscapes with particular gradient pattern and autocorrelation features. We applied this closed-form approach to temperature observations from an existing study. The expected heterogeneity differed, both in magnitude and direction, amongst sample designs over the study site's likely range of autocorrelation and gradient features. We conducted a simulation study to understand the effects of (i) landscape variability and (ii) design variability on an average sampling error. On 10 000 simulated landscapes with varying gradient and autocorrelation features, we compared estimates of variance from a variety of structured and random sample designs. While gradient patterns and autocorrelation cause large errors for some designs, others yield near-zero average sampling error. Sample location spacing is a key factor in sample design performance. Random designs have larger range of possible sampling errors than structured designs due to the potential for sample arrangements that over- and under-sample certain areas of the landscape. Furthermore, when implementing a new sample design to quantify environmental heterogeneity via variance, we recommend using a simple structured design with appropriate sample spacing. For existing designs, we recommend calculating the relative expected sampling error via our analytical derivation.
54 ENVIRONMENTAL SCIENCES↗
Theory and modeling of molecular modes in the NMR relaxation of fluids
Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Temporal Error Correlations in a Terrestrial Carbon Cycle Model Derived by Comparison to Carbon Dioxide Eddy Covariance Flux Tower Measurements
Abstract Atmospheric CO 2 flux inversions require as input an estimate of spatial and temporal correlations of errors in their estimate of the prior mean. Some previous studies have used the differences in CO 2 daily average flux estimates produced by terrestrial carbon cycle models and eddy covariance measurements to constrain the flux error correlations. Since inversions are starting to resolve the daily cycle, we set out to examine the correlations at sub‐daily time scales, as well as the correlations across years. To this end, we examine the autocorrelations in the difference between net ecosystem‐atmosphere exchange measurements from 75 AmeriFlux towers and temporally downscaled high‐spatial‐resolution flux estimates from the Carnegie‐Ames‐Stanford Approach (CASA) terrestrial carbon cycle model. We find that the daily cycle is prominent in these hourly autocorrelations and that these autocorrelations persist across years. We propose a family of functions to model these temporal correlations in atmospheric inversions, and use cross validation to determine which of the correlation functions best fits autocorrelation data from towers not in the training set. Correlation functions with a component that attempts to model the daily cycle in the differences match correlations from other towers better than those without. Those models that reproduce the same correlation structures at 1‐year intervals while modulating the amplitudes of the correlations between those intervals improve the fit still further.
54 ENVIRONMENTAL SCIENCES↗
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nanoscale dynamics and aging of fibrous peptide-based gels
Solutions of the aromatic dipeptide derivative molecule fluorenylmethoxycarbonyl-diphenylalanine (Fmoc-FF) in dimethyl sulfoxide produce fibrous gels when mixed with water. We study the evolution of density fluctuations of this three-component system using X-ray photon correlation spectroscopy (XPCS) and compare these results to the macroscopic rheology of the gels and optical observations of the microstructure evolution. At the investigated scattering angles, the intensity autocorrelation functions do not follow behavior expected for simple diffusion of individual Fmoc-FF molecules localized within cages of nearest neighbors. Instead, the dynamics are associated with density fluctuations on length scales of ∼10–100 nm arising from disaggregation and reformation of fibers, leading to an increasingly uniform network. This process is correlated with the growth of the elastic modulus, which saturates at long times. Autocorrelation functions and relaxation times acquired from XPCS measurements are consistent with relaxation rates of structures at dynamic equilibrium. This study provides further support to the concept of exploring peptide-based gelators as valence-limited patchy particles capable of forming equilibrium gels.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model
A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Spectrometer technology recommendations
A typical heterodyne remote sensing system contains three major elements: the antenna, the radiometer, and the spectrometer. The radiometer consists of the local oscillator, the mixer, and the intermediate frequency amplifiers. This subsystem performs the function of down converting the high frequency incident thermal emission signal to a lower intermediate frequency. The spectrometer measures the power spectrum of the down-converted signal simultaneously in many contiguous frequency channels. Typical spectrum analysis requirements involve measurement of signal bandwidths of 100 to 1000 MHz with a channel resolution of 0.5 to 10 MHz. Three general approaches are used for spectrometers: (1) filter banks, (2) Acousto-Optic Spectrometers (AOS's), and (3) digital autocorrelators. In contrast to the two frequency domain techniques, an autocorrelator works in the time domain. The autocorrelation function (ACF) of the incoming signal is computed and averaged over the integration time. The averaged ACF is then Fourier transformed to obtain the signal power spectrum. Significant progress was made in the development of sub mm antennas and radiometers. It is now time to begin research in the development of low power spaceborne spectrometers and to reduce their size and weight. The near-term research goal will be to develop a prototype digital autocorrelation spectrometer, using VLSI gate array technology, which will have a small size, low power requirements, and can be used in spacecraft mm and sub mm radiometer systems. The long-range objective of this technology development is to make extremely low power, less than 10 mW/channel, small and stable wideband spectrometers which can be used in future mm and sub mm wavelength space missions such as the Large Deployable Reflector.
Wilson, William J.↗
Advanced Sine Wave Modulation of Continuous Wave Laser System for Atmospheric CO2 Differential Absorption Measurements
NASA Langley Research Center in collaboration with ITT Exelis have been experimenting with Continuous Wave (CW) laser absorption spectrometer (LAS) as a means of performing atmospheric CO2 column measurements from space to support the Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) mission.Because range resolving Intensity Modulated (IM) CW lidar techniques presented here rely on matched filter correlations, autocorrelation properties without side lobes or other artifacts are highly desirable since the autocorrelation function is critical for the measurements of lidar return powers, laser path lengths, and CO2 column amounts. In this paper modulation techniques are investigated that improve autocorrelation properties. The modulation techniques investigated in this paper include sine waves modulated by maximum length (ML) sequences in various hardware configurations. A CW lidar system using sine waves modulated by ML pseudo random noise codes is described, which uses a time shifting approach to separate channels and make multiple, simultaneous online/offline differential absorption measurements. Unlike the pure ML sequence, this technique is useful in hardware that is band pass filtered as the IM sine wave carrier shifts the main power band. Both amplitude and Phase Shift Keying (PSK) modulated IM carriers are investigated that exibit perfect autocorrelation properties down to one cycle per code bit. In addition, a method is presented to bandwidth limit the ML sequence based on a Gaussian filter implemented in terms of Jacobi theta functions that does not seriously degrade the resolution or introduce side lobes as a means of reducing aliasing and IM carrier bandwidth.
Campbell, Joel F.↗
ATMS Radiometric Noise Characterization
The Advanced Technology Microwave Sounder (ATMS), on SNPP and NOAA-20, provides vertical atmospheric temperature and moisture profiles that are a key input to numerical weather prediction. Full characterization of radiometric noise is critical to error modeling, algorithm development and the potential development of performance requirements and product improvements. This paper presents estimates of white noise and low-frequency 1/f noise as derived from the Allan variance and scan-to-scan autocorrelations of data from the internal hot calibration. This approach allows direct comparison of on-orbit performance of the two units as well as comparison between ground calibration test data and on-orbit performance. The autocorrelation at multiple scan intervals is used as input to a theoretical model of the NET of inferred scene brightness temperature, when using weighted samples of calibration data over multiple scans. This will support selection of optimized calibration weighting functions for each channel, as well as providing further insight into the striping phenomenon. These measured autocorrelations are also compared to the autocorrelations derived from the 1/f spectra obtained both in special ground and on-orbit tests that characterize gain fluctuation. Channel cross-correlations are also presented, which can have a significant impact on effectiveness of direct assimilation performance.
instrument calibration↗
Calculation of mode lifetimes in weakly anharmonic solids using self-consistent ensemble eigenstates of the Liouvillian
Recent schemes for the efficient calculation of vibrational mode frequencies and lifetimes in weakly anharmonic systems such as solid crystal structures have shown promise, with simple relationships being observed between low order moments of the Liouvillian and the observed lifetime. While only shown empirically, two parameters seemed sufficient to determine the lifetime to high accuracy over a large range of temperatures for a few simple low degree of freedom models and a Lennard–Jones solid. In this paper we analytically reproduce the numerically observed relationship using a few generally applicable assumptions about the density of states. This advance is made by studying the autocorrelation based on an “ensemble eigenstate” of the Liouvillian. We propose the use of this ensemble eigenstate as the basis for autocorrelations to simplify calculations in richer systems. Finally, an analysis is also performed of the relationship between canonical and microcanonical autocorrelation functions and a long standing error in the long time behavior of such functions originally presented by Sen, Sinkovits, and Chakravarti is corrected.
36 MATERIALS SCIENCE↗
The biogeography of soil and airborne fungi in the Southwestern USA in relation to climate and vegetation
To assess how fungal dispersal might respond to climate change, we examined how climate and geography influence the regional distribution of fungi in soil and air. Specifically, we hypothesized that neighboring fungal communities should be more similar than distant communities (i.e. spatially autocorrelated) and that fungal dispersal should be more limited in soil than in air. We collected soil and air samples from 60 sites across five states in the Southwestern USA. Then, we sequenced the ITS2 region to identify fungal taxa in each sample. Next, we used distance-based redundancy analysis to partition variation in fungal community composition between climate variables and spatial structure. Fungi were indeed spatially autocorrelated. Moreover, precipitation, maximum vapor pressure deficit, and soil moisture were significantly related to fungal community composition in soils. In comparison, only precipitation was significantly related to community composition in the air. After accounting for climate, the strength of spatial autocorrelation did not differ significantly in soilborne versus airborne fungi. Dispersal limitation was evident in soilborne fungi at short distances (<100 km) and was not observed at any distance in airborne fungi. Altogether, climate may influence which fungal taxa are present in soil and air, and fungi could feasibly wind disperse over regional scales.
54 ENVIRONMENTAL SCIENCES↗
Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches
Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.
Weix, Derek↗