Correlation Length Scale Research Articles

Finite-size effects in lead scandium tantalate relaxor thin films

Relaxor ferroelectrics exhibit large electromechanical effects in response to external stimuli, making them promising materials for a variety of energy-harvesting, sensing, and actuating applications. An open question in the field, however, is how the polarization response evolves when the sample size approaches the nanometer length scale of polar correlations. Here, the evolution of polarization response as a function of film thickness is studied in epitaxial thin films of the relaxor lead scandium tantalate, demonstrating a large suppression of polarization response at reduced thickness.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features

Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

We study the finite temperature Fermi-liquid to non-Fermi-liquid crossover in the 2D Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behaviour that is itself characterized by a long, but finite, correlation length scale. We perform fluctuation diagnostics to decompose the single-particle self energy into scattering $q$-vector and bosonic frequency contributions. Within this framework we find that the key contributions to the single-particle self energy that give non-Fermi-liquid character, even at weak coupling, are caused by relatively sharp $q=(\pi,\pi)$ spin fluctuations, while the decomposition in the bosonic frequency channel shows a complicated dependence on the relative strengths of zero, positive and negative frequency contributions. Finally, variation in density suggests that the tendency towards non-Fermi-liquid behavior is not substantially different for electron or hole doped systems.

Magnetic correlations in the disordered ferromagnetic alloy Ni-V revealed with small angle neutron scattering

We present small angle neutron scattering (SANS) data collected on polycrystalline Ni1−xVx samples with x ≥ 0.10 with confirmed random atomic distribution. We aim to determine the relevant length scales of magnetic correlations in ferromagnetic samples with low critical temperatures Tc that show signs of magnetic inhomogeneities in magnetization and μSR data. The SANS study reveals signatures of long-range order and coexistence of short-range magnetic correlations in this randomly disordered ferromagnetic alloy. We show the advantages of a polarization analysis in identifying the main magnetic contributions from the dominating nuclear scattering.

Temporal and Spatial Scales of Correlation in Marine Phytoplankton Communities

AbstractOcean circulation shapes marine phytoplankton communities by setting environmental conditions and dispersing organisms. In addition, processes acting on the water column (e.g., heat fluxes and mixing) affect the community structure by modulating environmental variables that determine in situ growth and loss rates. Understanding the scales over which phytoplankton communities vary in time and space is key to elucidate the relative contributions of local processes and ocean circulation on phytoplankton distributions. Using a global ocean ecosystem model, we quantify temporal and spatial correlation scales for phytoplankton phenotypes with diverse functional traits and cell sizes. Through this analysis, we address these questions: (1) Over what timescales do perturbations in phytoplankton populations persist? and (2) over what distances are variations in phytoplankton populations synchronous? We find that correlation timescales are short in regions of strong currents, such as the Gulf Stream and Antarctic Circumpolar Current. Conversely, in the subtropical gyres, phytoplankton population anomalies persist for relatively long periods. Spatial correlation length scales are elongated near ocean fronts and narrow boundary currents, reflecting flow paths and frontal patterns. In contrast, we find nearly isotropic spatial correlation fields where current speeds are small, or where mixing acts roughly equally in all directions. Phytoplankton timescales and length scales also vary coherently with phytoplankton body size. In addition to aiding understanding of phytoplankton population dynamics, our results provide global insights to guide the design of biological ocean observing networks and to better interpret data collected at long‐term monitoring stations.

Reciprocal space imaging of ionic correlations in intercalation compounds.

The intercalation of alkali ions into layered materials has played an essential role in battery technology since the development of the first lithium-ion electrodes. Coulomb repulsion between the intercalants leads to ordering of the intercalant sublattice, which hinders ionic diffusion and impacts battery performance. While conventional diffraction can identify the long-range order that can occur at discrete intercalant concentrations during the charging cycle, it cannot determine short-range order at other concentrations that also disrupt ionic mobility. In this Article, we show that the use of real-space transforms of single-crystal diffuse scattering, measured with high-energy synchrotron X-rays, allows a model-independent measurement of the temperature dependence of the length scale of ionic correlations along each of the crystallographic axes in sodium-intercalated V2O5. The techniques described here provide a new way of probing the evolution of structural ordering in crystalline materials.

A radar reflectivity operator with ice-phase hydrometeors for variational data assimilation (version 1.0) and its evaluation with real radar data

Abstract. A reflectivity forward operator and its associated tangent linear and adjoint operators (together named RadarVar) were developed for variational data assimilation (DA). RadarVar can analyze both rainwater and ice-phase species (snow and graupel) by directly assimilating radar reflectivity observations. The results of three-dimensional variational (3D-Var) DA experiments with a 3 km grid mesh setting of the Weather Research and Forecasting (WRF) model showed that RadarVar was effective at producing an analysis of reflectivity pattern and intensity similar to the observed data. Two to three outer loops with 50–100 iterations in each loop were needed to obtain a converged 3-D analysis of reflectivity, rainwater, snow, and graupel, including the melting layers with mixed-phase hydrometeors. It is shown that the deficiencies in the analysis using this operator, caused by the poor quality of the background fields and the use of the static background error covariance, can be partially resolved by using radar-retrieved hydrometeors in a preprocessing step and tuning the spatial correlation length scales of the background errors. The direct radar reflectivity assimilation using RadarVar also improved the short-term (2–5 h) precipitation forecasts compared to those of the experiment without DA.

Observation Error Statistics for Doppler Radar Radial Wind Superobservations Assimilated into the DWD COSMO-KENDA System

AbstractCurrently in operational numerical weather prediction (NWP) the density of high-resolution observations, such as Doppler radar radial winds (DRWs), is severely reduced in part to avoid violating the assumption of uncorrelated observation errors. To improve the quantity of observations used and the impact that they have on the forecast requires an accurate specification of the observation uncertainties. Observation uncertainties can be estimated using a simple diagnostic that utilizes the statistical averages of observation-minus-background and observation-minus-analysis residuals. We are the first to use a modified form of the diagnostic to estimate spatial correlations for observations used in an operational ensemble data assimilation system. The uncertainties for DRW superobservations assimilated into the Deutscher Wetterdienst convection-permitting NWP model are estimated and compared to previous uncertainty estimates for DRWs. The new results show that most diagnosed standard deviations are smaller than those used in the assimilation, hence, it may be feasible to assimilate DRWs using reduced error standard deviations. However, some of the estimated standard deviations are considerably larger than those used in the assimilation; these large errors highlight areas where the observation processing system may be improved. The error correlation length scales are larger than the observation separation distance and influenced by both the superobbing procedure and observation operator. This is supported by comparing these results to our previous study using Met Office data. Our results suggest that DRW error correlations may be reduced by improving the superobbing procedure and observation operator; however, any remaining correlations should be accounted for in the assimilation.

Correlating fracture toughness and fracture surface roughness via correlation length scale

Fracture toughness of a material depends on its microstructure and the imposed loading conditions. Intuitively, the resultant fracture surfaces must contain the information about the interlacing of these intrinsic (microstructure) and extrinsic (imposed loading) characteristics. Mandelbrot’s revelation that fracture surfaces are fractals, excited both the scientific and engineering communities, spurring a series of works focused at correlating the fracture toughness and the fracture surface roughness. Unfortunately, these studies remained inconclusive and later on it was shown that the fractal dimension of the fracture surface roughness is in fact universal. Here, we show that by going beyond the universality, a definite correlation between the fracture toughness and indices of the fracture surface roughness is obtained. To this end, fracture experiments on an aluminum alloy were carried over a wide range of loading rates ( $$10^{-2}$$ – $$10^{6}\,\mathrm{MPa}\sqrt{\mathrm{m}}\mathrm{s}^{-1}$$ ), and the resulting fracture surface were reconstructed using stereography. The correlation lengths, extracted from the reconstructed surfaces, were found to be linearly correlated with the measured fracture toughness. The correlation unraveled in our work, along with the proposed mechanistic interpretation, revives the hope of correlating fracture toughness and fracture surface roughness, allowing quantitative failure analysis and a potential reconstructive approaches to designing fracture resistant materials.

Finite correlation length scaling with infinite projected entangled pair states at finite temperature

We study second order finite temperature phase transitions of the 2D quantum Ising and interacting honeycomb fermions models using infinite projected entangled pair states (iPEPS). We obtain an iPEPS thermal state representation by Variational Tensor Network Renormalization (VTNR). We find that at the critical temperature $T_c$ the iPEPS correlation length is finite for the computationally accessible values of the iPEPS bond dimension $D$. Motivated by this observation we investigate the application of Finite Correlation Length Scaling (FCLS), which has been previously used for iPEPS simulations of quantum critical points at $T=0$, to obtain precise values of $T_c$ and the universal critical exponents. We find that in the vicinity of $T_c$ the behavior of observables follows well the one predicted by FCLS. Using FCLS we obtain $T_c$ and the critical exponents in agreement with Quantum Monte Carlo (QMC) results except for couplings close to the quantum critical points where larger bond dimensions are required.

Effects of correlated morphological and topological heterogeneity of pore network on effective transport and reaction parameters

The effective diffusivity and the effective Thiele modulus of reactive porous matrices are determined by using a hybrid discrete and continuum model. The model describes static heterogeneity with weak noise on both morphology and topology of the matrix. Variations in diffusivity with respect to pore size (radius and length) and network connectivity up to second order are analyzed to assess the effect of stochastic media on catalytic reaction and transition of a single species. The porous medium is simulated by several building blocks (BB) which are regular in topology and morphology. A methodology is presented to construct a BB such that it fits the true matrix. Permutation of several regular pore networks in series constructs the porous media. Local mass balances over each BB yields model equations for reaction and transport in the matrix. Correlated random walk theory is used in each BB in order to relate the diffusivity to the coordination number.The Gaussian correlation function is assumed to model the autocorrelation of independent variables which are used to characterize the correlated porous media. The contribution of the fluctuating parameters in the mass conservation of the matrix yields a new closure equation in which ensemble average concentration of the reactant depends on different cross-correlations. The model is stable as long as the Thiele modulus at the correlation length scale is small. It predicts that geometrical heterogeneities lead to correction in effective diffusivity while the reaction rate is unaffected due to small Thiele modulus at correlation length scale. The model is verified by assessing the Thiele modulus of a pore network under Knudsen regime during a first order catalytic reaction; a good agreement was found especially for moderate Thiele modulus of correlated network. However, it fails to simulate random networks. Our systematic study revealed that the pore radius statistics impact significantly the diffusivity and the Thiele modulus while the topological parameters are important in weakly connected networks. The model predictions show that the diffusion constant decreases sharply as pore radius variance increases but increases smoothly with Thiele modulus.

Omori law for foreshocks and aftershocks in a realistic earthquake model

We study a physical model for earthquakes which extends the standard spring-block model. It is able to quantitatively describe the observations which detect differences between the statistics of foreshocks and aftershocks and the properties of main shocks. The model uses two layers to provide an intrinsic mechanism for stress relaxation and a stochastic equation to describe the contacts of crustal plates which should be treated at the scale of the elastic correlation length of the rocks and therefore result from the combined dynamics of many local contacts. The model parameters are derived from the physical properties of rocks to provide a realistic picture of the mechanisms involved in earthquakes. We show that the Omori law has different exponents for foreshocks and aftershocks, in agreement with observations. Similarly the model detects the differences in the b coefficient of the Gutenberg-Richter law for main shocks, foreshocks and aftershocks. Moreover, the dynamics of the model exhibits various classes of events such as swarm of small earthquakes and major earthquakes extending over a broader fault range, suggesting that it might be the basis for further studies of the phenomena at the contact of crustal plates.

Stress‐Induced Anomalous Transport in Natural Fracture Networks

AbstractWe investigate the effects of geological stress on fluid flow and tracer transport in natural fracture networks. We show the emergence of non‐Fickian (anomalous) transport from the interplay among fracture network geometry, aperture heterogeneity, and geological stress. In this study, we extract the fracture network geometry from the geological map of an actual rock outcrop, and we simulate the geomechanical behavior of fractured rock using a hybrid finite‐discrete element method. We analyze the impact of stress on the aperture distribution, fluid flow field, and tracer transport properties. Both stress magnitude and orientation have strong effects on the fracture aperture field, which in turn affects fluid flow and tracer transport through the system. We observe that stress anisotropy may cause significant shear dilation along long, curved fractures that are preferentially oriented to the stress loading. This, in turn, induces preferential flow paths and anomalous early arrival of tracers. An increase in stress magnitude enhances aperture heterogeneity by introducing more small apertures, which exacerbates late‐time tailing. This effect is stronger when there is higher heterogeneity in the initial aperture field. To honor the flow field with strong preferential flow paths, we extend the Bernoulli Continuous Time Random Walk model to incorporate dual velocity correlation length scales. The proposed upscaled transport model captures anomalous transport through stressed fracture networks and agrees quantitatively with the high‐fidelity numerical simulations.

Correlated spin canting in ordered core-shellFe3O4/MnxFe3−xO4nanoparticle assemblies

Polarization-analyzed small-angle neutron-scattering methods are used to determine the spin arrangements and experimental length scales of magnetic correlations in ordered three-dimensional assemblies of $\ensuremath{\sim}7.4$-nm-diam core-shell ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}/{\mathrm{Mn}}_{x}{\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{O}}_{4}$ nanoparticles. In moderate to high magnetic fields, the assemblies display a canted magnetic structure where the canting direction is coherent from nanoparticle to nanoparticle, in contrast to the less extended, more single-particle-like behavior for similar ferrite assemblies. The observed magnetic scattering is modeled by assuming that the interparticle dipolar coupling combined with Zeeman effects in a field leads to nanoparticle domains with preferred net spin alignments relative to packing symmetry axes. Over a range of fields and temperatures, the model qualitatively explains the observed scattering anomalies in terms of clusters that vary in area and thickness, highlighting the complex structures adopted in real, dense nanoparticle systems. The clusters often have a strong two-dimensional magnetic character which is attributed to structural stacking faults and the resulting influence of interparticle dipolar interactions for these magnetically soft nanoparticles.

Dependence of Vertical Alignment of Cloud and Precipitation Properties on Their Effective Fall Speeds

AbstractThe vertical structure of clouds unresolved in large‐scale weather prediction and climate models is controlled by an overlap assumption. When a binary representation (cloud or no cloud) of subgrid horizontal variability is replaced by a probability density function (PDF) treatment of cloud‐related variables, a cloud occurrence overlap needs to be replaced by a PDF overlap. The PDF overlap can be quantified by a correlation length scale, z0, indicating how rapidly rank correlation of distributions at two levels diminishes with increasing level separation. In this study, we show that z0 varies widely for different properties (e.g., number and mass mixing ratios) and different hydrometeor types (cloud liquid and ice, rain, snow, and graupel) and that corresponding fall speed, Vf, is the primary factor controlling the degree of their vertical alignment, with vertical shear of the horizontal wind playing a smaller role. Linear and power law parametric relationships between z0 and Vf are derived using cloud‐resolving simulations of convection under midlatitude continental and tropical oceanic conditions, as well as observations from vertically pointing dual‐frequency radar profilers near Darwin, Australia. The functional form of z0‐Vf relationship is further examined using simple conceptual models that link variability in horizontal and vertical directions and provide insights into the role of Vf and wind shear. Being based on a physical property (i.e., fall speed) of hydrometeors rather than artificially defined and model‐specific hydrometeor types, the proposed parameterization of vertical PDF overlap can be applied to a wide range of microphysics treatments in regional and global models.

Bayesian inverse estimation of urban CO2 emissions: Results from a synthetic data simulation over Salt Lake City, UT

Top-down, data-driven models possess ample power to improve the accuracy of bottom-up carbon dioxide (CO2) emission inventories, and more work is needed to explore the merger of top-down and bottom-up estimates to better inform the metrics used to monitor global CO2 fluxes. Here we present a Bayesian inverse modeling framework over Salt Lake City, Utah, which utilizes available CO2 emission inventories to establish a synthetic data simulation aimed at exploring model uncertainties. Prescribing a high-resolution, urban-scale data product (Hestia) as the “true” emissions in the model, we combine prior emissions with an atmospheric transport model to derive modeled afternoon CO2 enhancements at six monitoring sites within the Salt Lake Valley during the month of September 2015. A global high-resolution gridded emissions data product (ODIAC) is used as the prior, and objective uncertainty structures are defined for both the a priori estimates and the transport model-data relationship which consider non-negligible spatial and temporal covariances. Optimized (posterior) emissions over the Salt Lake Valley agree closely with the assumed “true” emissions during afternoon times, while results including unconstrained times (e.g. night-time) lack such agreement. Both spatial and temporal correlations of prior errors were found to be necessary for obtaining a robust posterior estimate. Model sensitivity analyses are performed, which examine correlation length and time scales, model-data mismatch error, and measurement site network variability. Through these analyses, one measurement site is identified as being particularly prone to introducing bias into posterior emissions due to influences from a nearby point source. Increasing model-data mismatch error at this site is shown to reduce bias in the posterior without significantly compromising agreement with monthly averaged true emissions.

Data fusion and data assimilation of ice thickness observations using a regularisation framework

Accurate estimates of sharp features in the sea ice cover, such as leads and ridges, are critical for shipping activities, ice operations and weather forecasting. These sharp features can be difficult to preserve in data fusion and data assimilation due to the spatial correlations in the background error covariance matrices. In this article, a set of data fusion and data assimilation experiments are carried out comparing two objective functions, one with a conventional l2-norm and one that imposes an additional l1-norm on the derivative of the ice thickness state estimate. The latter is motivated by analysis of high resolution ice thickness observations derived from an airborne electromagnetic sensor demonstrating the sparsity of the ice thickness in the derivative domain. Data fusion and data assimilation experiments (using a 1 D toy sea-ice model) are carried out over a wide range of background and observation error correlation length scales. Results show the superiority of using an l1–l2 regularisation framework. For the data fusion experiments it was found when both background and observation error correlation length scales are zero, the ice thickness root mean squared error for the l1–l2 method was 0.16 m as compared to 0.20 m for the l2 method. The differences between the methods were greater when the background error correlation length scale was relatively short (approximately five times the analysis grid spacing), and were not significant for larger background error correlation length scales (e.g. 10 times the analysis grid spacing). For data assimilation experiments it was found that openings in the ice cover were captured better with the l1–l2 regularisation, with reduced errors in ice thickness, concentration and velocity. In addition, the ice thickness derivatives in the analyses were found to be more sparse when the l1–l2 method was used and are closer to the those from the true model run.

Precise Extrapolation of the Correlation Function Asymptotics in Uniform Tensor Network States with Application to the Bose-Hubbard and XXZ Models

We analyze the problem of extracting the correlation length from infinite matrix product states (MPS) and corner transfer matrix (CTM) simulations. When the correlation length is calculated directly from the transfer matrix, it is typically significantly underestimated for finite bond dimensions used in numerical simulation. This is true even when one considers ground states at a distance from the critical point. We introduce extrapolation procedure to overcome this problem. To that end we quantify how much the dominant part of the MPS/CTM transfer matrix spectrum deviates from being continuous. The latter is necessary to capture the exact asymptotics of the correlation function where the exponential decay is typically modified by an additional algebraic term. By extrapolating such a refinement parameter to zero, we show that we are able to recover the exact value of the correlation length with high accuracy. In a generic setting, our method reduces the error by a factor of $\sim 100$ as compared to the results without extrapolation and a factor of $\sim 10$ as compared to simple extrapolation schemes using bond dimension. We test our approach in a number of solvable models both in 1d and 2d. Subsequently, we apply it to 1d XXZ spin-$\frac32$ and the Bose-Hubbard models in a massive regime in the vicinity of BKT critical point. We then fit the scaling form of the correlation length and extract the position of the critical point and obtain results comparable or better than those of other state-of-the-art numerical methods. Finally, we show how the algebraic part of the correlation function asymptotics can be directly recovered from the scaling of the dominant form factor within our approach. Our method provides the means for detailed studies of phase diagrams of quantum models in 1d and, through the finite correlation length scaling of projected entangled pair states, also in 2d.

Structure-property interplay of asymmetric membranes comprising of soft polydimethylsiloxane chains and hard silica nanomaterials

Silica nanomaterials modified with monomolecular C18-alkyl silane or oligomeric dimethylsiloxane units were loaded in-situ during the formation of PDMS membrane. The small-angle neutron scattering (SANS) study was performed to probe structural compatibility between the modified silica and PDMS. The Ornstein-Zernike (OZ) and Debye-Anderson-Brumberger (DAB) models were excellently fit to the SANS data describing nanoscale structure morphology in terms of correlation length scales of the soft and hard segmental units. The polymeric chain was stretched or contracted depending upon the type and amount of silica incorporation. This indicated limiting amount of silica incorporation in the PDMS membrane structure depending upon structural compatibility between the silica and PDMS. The C18-alkyl silylated silica was found to be the best compatible with the membrane structure. The membrane with 30% (w/w) C18-alkyl silylated -silica loading exhibited the best performance in pervaporation separation of alcohol/water.

Three-dimensional instabilities and negative eddy viscosity in thin-layer flows

The stability of flows in layers of finite thickness H is examined against small-scale three-dimensional (3D) perturbations and large-scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of energy while the latter indicate an inverse transfer and the possibility of an inverse cascade. The analysis is performed using a Floquet-Bloch code that allows examination of the stability of modes with arbitrary large-scale separation. For thin layers, the 3D perturbations become unstable when the layer thickness H becomes larger than H>c1(νℓU/U)1/2=c1ℓURe−1/2, where U is the rms velocity of the flown, ℓU is the correlation length scale of the flow, ν is the viscosity, and Re=ℓUU/ν is the Reynolds number. At the same time, large-scale 2D perturbations also become unstable by an eddy viscosity mechanism when Re>c2, where c1,c2 are order 1 nondimensional numbers. These relations define different regions in parameter space where 2D and 3D instabilities can (co)exist and this allows us to construct a stability diagram. Implications of these results for fully turbulent flows that display a change of direction of cascade as H is varied are discussed.3 MoreReceived 1 June 2018DOI:https://doi.org/10.1103/PhysRevFluids.3.114601©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFlow instabilityTurbulenceFluid Dynamics