Solar Wind Magnetic Field Correlation Length: Correlation Functions versus Cross-field Displacement Diffusivity Test
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B. R. Ragot↗
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Nucleation and growth of blue phase liquid crystals on chemically-patterned surfaces: a surface anchoring assisted blue phase correlation length
In condensed matter, the correlation length is an essential parameter which describes the distance over which a material maintains its structural properties. In liquid crystals, for the orientational order parameter this characteristic length is of the order of nanometers, while in solid crystals it can extend to macroscopic length scales. Here, we report the measurement of the correlation length, or persistence length, of the crystallographic orientation of blue phases (BPs)—chiral liquid crystals with long-range 3D-crystalline structures and submicron-sized lattice-parameters. These materials exhibit phase transformations that have been identified as the liquid analog of crystal-crystal martensitic transformations. In this work, we use liquid epitaxial growth to achieve spontaneous BP-crystal nucleation and subsequent growth. Specifically, we design patterned substrates made of a binary array of regions with different liquid crystal anchoring, which facilitate a uniform nucleation and growth of BP-crystals with (100)-lattice orientation and a simple cubic symmetry. Furthermore, our results indicate that this simple cubic BP, the so-called blue phase II (BPII), forms first on the patterned surface, thereby propagating the growth of domains in directions parallel or perpendicular to the patterned regions. These results are used to understand the emergence of a surface anchoring assisted BPII-correlation length, taken as the distance over which the BP preserves its lattice orientation, as a function of time and pattern characteristics. We found that BPII single crystals can be achieved on patterned regions whose lateral dimensions are equal to or larger than 10 μm, consistent with our measurements of the BPII-correlation length. This newly acquired understanding of the role of surfaces on the formation of BPs is then used to design processes that permit formation of macroscopically large mono-domain, single-crystal BPs by relying on significantly reduced patterned areas (only part of the area is patterned), a feature that could benefit the applications of this intriguing class of materials.
correlation length↗
Evaluating Multispectral Snowpack Reflectivity With Changing Snow Correlation Lengths
This study investigates the sensitivity of multispectral reflectivity to changing snow correlation lengths. Matzler's ice-lamellae radiative transfer model was implemented and tested to evaluate the reflectivity of snow correlation lengths at multiple frequencies from the ultraviolet (UV) to the microwave bands. The model reveals that, in the UV to infrared (IR) frequency range, the reflectivity and correlation length are inversely related, whereas reflectivity increases with snow correlation length in the microwave frequency range. The model further shows that the reflectivity behavior can be mainly attributed to scattering rather than absorption for shallow snowpacks. The largest scattering coefficients and reflectivity occur at very small correlation lengths (approximately 10(exp -5 m) for frequencies higher than the IR band. In the microwave range, the largest scattering coefficients are found at millimeter wavelengths. For validation purposes, the ice-lamella model is coupled with a multilayer snow physics model to characterize the reflectivity response of realistic snow hydrological processes. The evolution of the coupled model simulated reflectivities in both the visible and the microwave bands is consistent with satellite-based reflectivity observations in the same frequencies. The model results are also compared with colocated in situ snow correlation length measurements (Cold Land Processes Field Experiment 2002-2003). The analysis and evaluation of model results indicate that the coupled multifrequency radiative transfer and snow hydrology modeling system can be used as a forward operator in a data-assimilation framework to predict the status of snow physical properties, including snow correlation length.
Kang, Do Hyuk↗
The role of the spatial heterogeneity and correlation length of surface wettability on two-phase flow in a CO 2 -water-rock system
This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.
58 GEOSCIENCES↗
The correlation length for interplanetary magnetic field fluctuations
It is argued that it is appropriate to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyro-radii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies greater than or approximately equal to several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities, L approximately 2 x 10 to the 11th power. Particles with gyro-radii much less than this mean separation (energies less than or approximately equal to 100 MeV/nucleon) appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. For these particles the correlation length is shown to be L approximately 10 to the 10th power cm. With this system of two correlation lengths the cosmic-ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (approximately 50 MeV/nucleon).
Fisk, L. A.↗
Correlation length for interplanetary magnetic field fluctuations.
It is argued that it is necessary to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyroradii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies of above several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities. Particles with gyroradii much less than this mean separation appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. With this system of two correlation lengths the cosmic ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (about 50 MeV/nucleon).
Fisk, L. A.↗
Experimental determination of the critical spin-glass correlation length in single-crystal CuMn
Using high resolution SQUID magnetometry we have made detailed measurements of the waiting time effect of the Thermoremanent Magnetization (TRM) decays on a single crystal CuMn(6%) spin glass sample near T g . In this study, we have systematically mapped the rapid decrease of the characteristic timescale tw eff , approaching T g from below, for waiting times ranging from 100 s to 100000 s. Using tw eff to determine the length scale of the growth of correlations during the waiting time, ξ TRM , (observed in both numerical studies and experiment), we observe both growth of ξ TRM in the spin glass phase and then a rapid reduction very close to T g . We interpret this reduction in ξ TRM , for all waiting times, as being governed by the critical correlation length scale ξ crit = a(T - T c ) -v .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Large-amplitude magnetic variations in quasi-parallel shocks - Correlation lengths measured by ISEE 1 and 2
Wide separations up to more than 1 earth radius between ISEE 1 and 2 during the second half of 1978 have been used to measure the correlation length of magnetic pulsations in quasiparallel shocks. When the two spacecraft were less than a few hundred km apart, magnetic oscillations measured by magnetometers on both spacecraft exhibited virtually identical waveforms, but at distances of several thousand km, the two time series of field variation showed no detailed similarily at all. The correlation coefficients of the pulsations dropped from close to 1.0 for spacecraft separations of less than 100 km to 0.2 for separations of greater than 800 km. A correlation length of several hundred km may be related to the gyroradius of return protons with energy typical of the peaks of diffuse and beam ion distributions.
Greenstadt, E. W.↗
Nematic Correlation Length in Iron-Based Superconductors Probed by Inelastic X-Ray Scattering
Nematicity is ubiquitous in electronic phases of high-T c superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length ξ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe 0.97 Co 0.03 ) 2 As 2 , and optimally doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 . In all cases, we find that. is well described by a power law (T - T 0 ) -1/2 extending over a wide temperature range. Combined with the previously reported Curie-Weiss behavior of the nematic susceptibility, these results point to the mean-field character of the nematic transition, which we attribute to a sizable nematoelastic coupling that is likely detrimental to superconductivity.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Predicted vibration responses of Apollo structure and effects of pressure correlation lengths on response
Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.
R W White↗
On the saturation of the refractive index structure function. II - Influence of the correlation length on astronomical 'seeing'
A physical length scale in the wavefront corresponding to the parameter (r sub 0) characterizing the loss in detail in a long exposure image is identified, and the influence of the correlation scale of turbulence as r sub 0 approaches this scale is shown. Allowing for the effect of 2-point correlations in the fluctuations of the refractive index, Venkatakrishnan and Chatterjee (1987) proposed a modified law for the phase structure function. It is suggested that the departure of the phase structure function from the 5/3 power law for length scales in the wavefront approaching the correlation scale of turbulence may lead to better 'seeing' at longer wavelengths.
Venkatakrishnan, P.↗
Theoretical models for microwave snow response and applications to remote sensing
Two theoretical models were developed to characterize snowpacks: (1) a random medium with a variance, a horizontal correlation length, and a vertical correlation length; and (2) a homogeneous dielectric containing discrete scatters. Theoretical results were matched with experimental data collected from snow ice fields. For snow ice fields the horizontal correlation length is no less than the vertical correlation length signifying a more laminar structure. The correspondence between the continuum random medium and the discrete spherical scatter model can be verified when the vertical correlation length is equal to the horizontal correlation length. The vertically polarized backscattering cross section sigma (sub vv) is always greater than the horizontally polarized backscattering cross section sigma (sub hh) for half space scattering media and may become smaller for a two layer model. In order to account for diurnal change exhibited by snow fields in both the active and passive remote sensing cases, a three layer model with a thin top layer caused by solar illumination must be used.
Kong, J. A.↗
Viscosity of nitrogen near the critical point
The formulation of a quantitative description of the critical enhancement in the shear viscosity of fluids near the gas-liquid critical point is considered. The critical point is a point of marginal thermodynamic stability. In the vicinity of the critical point, large-scale density fluctuations are present in the fluid. The critical enhancement of the transport properties is related to the correlation length. The correlation length is related to the compressibility, thus providing consistency between the equations for the transport properties and the equation of state in the critical region. The critical region parameters for nitrogen are presented in a table. It is found that the critical viscosity enhancement observed by Zozulya and Blagoi (1974) for nitrogen is consistent with current theoretical predictions
Basu, R. S.↗
Interpreting radial correlation Doppler reflectometry using gyrokinetic simulations
A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al 2007 Plasma Phys. Control. Fusion 49 1019) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber $k_{\perp}$ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a nonseparable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber $l_r \sim C k_{\perp}^{-\alpha} (\alpha \approx 1)$ which agrees with the inverse proportionality relationship between the measured $l_r$ and $k_{\perp} $ observed in experiments (Fernández-Marina et al 2014 Nucl. Fusion 54 072001). This new insight indicates that RCDR characterizes the eddy aspect ratio in the perpendicular plane to the magnetic field. It also motivates future use of a nonseparable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location $W_\text n$ satisfies $W_\text n \ll l_r$, while the measurement becomes dominated by $W_\text n$ for $W_\text n \gg l_r$. This suggests that $l_r$ is likely to be inaccessible for electron-scale DBS measurements (${k_{\perp}}{\rho_{\text s}} \gt 1$). The effect of $W_\text n$ on ion-scale radial correlation lengths could be nonnegligible.
radial correlation Doppler reflectometry↗
Length scales and scale-free dynamics of dislocations in dense solid solutions
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe 0.70 Ni 0.11 Cr 0.19 over a range of stresses and temperatures. These roughness profiles reveal the hallmark features of a depinning transition. Namely, below a temperature-dependent critical stress, the dislocation line exhibits roughness in two different length scale regimes which are divided by a so-called correlation length. This correlation length increases with applied stress and at the critical stress (depinning transition or yield stress) formally goes to infinity. Above the critical stress, the line roughness profile converges to that of a random noise field. Motivated by these results, a physical model is developed based on the notion of coherent line bowing over all length scales below the correlation length. Above the correlation length, the solute field prohibits such coherent line bow outs. Using this model, we identify potential gaps in existing theories of solid solution strengthening and show that recent observations of length-dependent dislocation mobilities can be rationalized.
36 MATERIALS SCIENCE↗
A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications
Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.
GC99↗
Unveiling the Significance of Correlations in K-Space and Configuration Space for Drift Wave Turbulence in Tokamaks
Turbulence and transport phenomena play a crucial role in the confinement and stability of tokamak plasmas. Turbulent fluctuations in certain physical quantities, such as density or temperature fluctuations, can have a wide range of spatial scales, and understanding their correlation length is important for predicting and controlling the behavior of the plasma. The correlation length in the radial direction is identified as the critical length in real space. The dynamics in real space are of significant interest because transport in configuration space is primarily focused on them. When investigating transport caused by the E×B drift, the correlation length in real space represents the size of E×B whirls. It was numerically discovered that in drift wave turbulence, this length is inversely proportional to the normalized mode number of the fastest growing mode relative to the drift frequency. Considerable time was required before a proper analytical derivation of this condition was accomplished. Therefore, a connection has been established between phenomena occurring in real space and those occurring in k-space. Although accompanied by a turbulent spectrum in k-space with a substantial width, transport in real space is uniquely determined by the correlation length, allowing for accurate transport calculations through the dynamics of a single mode. Naturally, the dynamics are subject to nonlinear effects, with resonance broadening in frequency being the most significant nonlinear effect. Thus, mode number space is once again involved. Resonance broadening leads to the detuning of waves from particles, permitting a fluid treatment. It should be emphasized that the consideration here involves the total electric field, including the induction part, which becomes particularly important at higher beta plasmas.
Weiland, Jan (ORCID:0000000253496025)↗
Direct Visualization of Magnetic Correlations in Frustrated Spinel ZnFe 2 O 4
Magnetic materials with the spinel structure (A 2+ B 3+ 2 O 4 ) form the core of numerous magnetic devices, and ZnFe 2 O 4 constitutes a peculiar example where the nature of the magnetism is still unresolved. Susceptibility measurements revealed a cusp around T c = 13 K resembling an antiferromagnetic transition, despite the positive Curie–Weiss temperature determined to be Θ CW = 102.8(1) K. Bifurcation of field-cooled and zero-field-cooled data below T c in conjunction with a frequency dependence of the peak position and a non-zero imaginary component below T c shows it is in fact associated with a spin-glass transition. Highly structured magnetic diffuse neutron scattering from single crystals develops between 50 K and 25 K revealing the presence of magnetic disorder which is correlated in nature. Here, the 3D-mΔPDF method is used to visualize the local magnetic ordering preferences, and ferromagnetic nearest-neighbor and antiferromagnetic third nearest-neighbor correlations are shown to be dominant. Their temperature dependence is extraordinary with some flipping in sign and a strongly varying correlation length. The correlations can be explained by orbital interaction mechanisms for the magnetic pathways and a preferred spin cluster. This study demonstrates the power of the 3D-mΔPDF method in visualizing complex quantum phenomena thereby providing a way to obtain an atomic-scale understanding of magnetic frustration.
36 MATERIALS SCIENCE↗