Correlation Length Research Articles

Dynamic Behavior of Poly(N-isopropylmethacrylamide) in Neat Water and in Water/Methanol Mixtures.

We investigate the collective dynamics of thermoresponsive polymer poly(N-isopropylmethacrylamide) (PNIPMAM) in aqueous solution and in water/methanol mixtures in the one-phase region. In neat water, the polymer concentration c is varied in a wide range around the overlap concentration c*, that is estimated at 23 g L-1. Using dynamic light scattering (DLS), two decays ("modes") are consistently observed in the intensity autocorrelation functions for c = 2-150 g L-1 with relaxation rates which are proportional to the square of the momentum transfer. Below c*, these are attributed to the diffusion of single chains and to clusters from PNIPMAM that are formed due to hydrophobic interactions. Above c*, they are assigned to the diffusion of the chain segments between overlap points and to long-range concentration fluctuations. From the temperature-dependent behavior of the overall scattering intensities and the dynamic correlation lengths of the fast mode, the critical temperatures and the scaling exponents are determined. The latter are significantly lower than the static values predicted by mean-field theory, which may be related to the presence of the large-scale inhomogeneities. The effect of the cosolvent methanol on the dynamics is investigated for polymer solutions having c = 30 g L-1 and methanol volume fractions in the solvent mixtures of up to 60 vol %. The phase diagram was established by differential scanning calorimetry. The slow mode detected by DLS becomes significantly weaker as methanol is added, i.e., the solutions become more homogeneous. Beyond the minimum of the coexistence line, which is located at 40-50 vol % of methanol, the dynamics is qualitatively different from the one at lower methanol contents. Thus, going from the water-rich to the methanol-rich side of the miscibility gap, the change of interaction of the PNIPMAM chains with the two solvents has a severe effect on the collective dynamics.

Effects of soil spatial variability on the behaviour of the embankment supported with a combined retaining structure

In this study, the effects of soil spatial variability on the behaviour of the embankment supported with a combined retaining structure (CRS) were investigated. The numerical model of the CRS embankment was established and validated with the field data. An application programming interface (API) was developed to deal with the data exchanging issue between the numerical model and the spatial variability characterization model. Based on the verified numerical model and the API, the probabilistic analysis with 500 Monte Carlo simulations was automatically computed. Three influencing factors of the retained soil (the mean of the friction angle, the variation of the friction angle and the vertical correlation length of the random field) are analysed by parametric analysis. The results show that the vertical correlation length of the random field is most important in the earth pressure calculation process, while the mean of the friction angle is the factor with least impact. On the whole, the spatial variability of soil properties has minimal impact on the distribution and magnitude of earth pressure behind the retaining structure.

A mechano-regulation model to design and optimize the surface microgeometry of titanium textured devices for biomedical applications

In a technological context where, thanks to the additive manufacturing techniques, even sophisticated geometries as well as surfaces with specific micrometric features can be realized, we propose a mechano-regulation algorithm to determine the optimal microgeometric parameters of the surface of textured titanium devices for biomedical applications. A poroelastic finite element model was developed including a portion of bone, a portion of a textured titanium device and a layer of granulation tissue separating the bone from the device and occupying the space between them. The algorithm, implemented in the Matlab environment, determines the optimal values of the root mean square and the correlation length that the device surface must possess to maximize bone formation in the gap between the bone and the device. For low levels of compression load acting on the bone, the algorithm predicts low values of root mean square and high values of correlation length. Conversely, high levels of load require high values of root mean square and low values of correlation length. The optimal microgeometrical parameters were determined for various thickness values of the granulation tissue layer. Interestingly, the predictions of the proposed computational model are consistent with the experimental results reported in the literature. The proposed algorithm shows promise as a valuable tool for addressing the demands of precision medicine. In this approach, the device or prosthesis is no longer designed solely based on statistical averages but is tailored to each patient's unique anthropometric characteristics, as well as considerations related to their metabolism, sex, age, and more.

Reliability and landslide consequence analysis of long heterogeneous soil infrastructure slopes: A parallel computing investigation

Long infrastructures, like flood defense levees, built upon diverse soils, often face complex landslide failures. Risk assessments for such structures involve evaluating slope stability reliability and potential landslide consequences. Historically, embankment slope reliability and failure assessments focused on shorter sections due to computational limitations. This study, however, delves into a longer 3D soil slope section, 100 times the height, using the random finite element method to analyze the size effect. It conducts a parametric study varying the soil strength’s horizontal correlation length to understand slope failure initiation in heterogeneous soils. In contrast to prior work, this paper emphasizes several facets: the realized factor of safety (FOS) distribution, quantification of discrete unstable zones, failures, and the size impact on long embankment slopes. Findings indicate the Weibull distribution better fits the realized FOS, aiding in predicting long embankment slope system reliability when combined with the weakest link theory. While multiple failures are possible for very long soil embankment slopes, practical observations suggest a likelihood of a single localized failure despite this potential.

Modeling stochastic elastic wave diffraction by the tips of randomly rough defects

Elastic wave scattering from a randomly rough surface of a finite length includes surface reflections and diffractions from the tips. Previous research has focused upon reflection waves with applications in ultrasonic defect detection, seismic wave exploration and phonon boundary transport. However, waves diffracted from the tips/edges have been largely neglected so far for rough defects, despite their importance in engineering applications including ultrasonic defect sizing and imaging for assessment of structural integrity. Currently understanding the statistical nature of elastic wave tip diffraction and the role of roughness is limited due to the lack of theoretical studies. In this article, we develop a statistical geometrical tip diffraction (SGTD) theory to rapidly predict the stochastic properties of tip diffraction amplitude as a function of surface roughness and incident angle. By applying a small slope perturbation to the model, a simplified analytical solution of tip diffraction is obtained. It is found that for defects with small to medium roughness, the diffraction amplitude explicitly follows a Gamma distribution, and its mean and the standard deviation are both proportional to the square of the rms slope. High-fidelity Monte Carlo finite element simulations are then run to evaluate the accuracy of the theoretical model. The range of validity of the analytical solution with respect to the level of roughness and the incident angle is obtained. The SGTD method is accurate when the correlation length is approximately equivalent or larger than one wavelength, for a wide range of angles. It is also applicable for a correlation length as short as half wavelength, but only for small rms values and when the beam angle is larger than 45∘. In addition, at large angles, the tip diffraction is almost not affected by roughness, being very similar to that from a smooth crack. This is explained by the significant dependence on the beam angle factor explicitly shown in the theoretical solution.

Using the AIEM and Radarsat-2 SAR to Retrieve Bare Surface Soil Moisture

Taking the Jiefangzha irrigation area of the Inner Mongolia Autonomous Region as the research area, the response relationships between the backscattering coefficient and radar frequency, radar incidence angle, root-mean-square height, correlation length, and soil water content under different conditions were simulated using advanced integral equations. The backscattering characteristics of exposed surfaces in cold and dry irrigation areas were discussed, and the reasons for the different effects were analyzed. Based on this, surface roughness models and statistical regression moisture inversion models were constructed through co-polarized backscatter coefficients and combined surface roughness. The correlation between the inverted surface roughness values and the measured values was R2 = 0.7569. The correlation between the soil moisture simulation values and the measured values was R2 = 0.8501, with an RMSE of 0.04. The findings showed a strong correlation between the values from the regression simulation and the measured data, indicating that the model can be applied to soil moisture inversion and has a good inversion accuracy. Compared with previous studies in the same area, the inversion model proposed in this paper has a higher accuracy and is more suitable for the inversion of soil moisture in the Jiefangzha irrigation area. These findings can support research on the water cycle and water environment assessment in the region.

Shear viscosity of a near-critical binary system analyzed with variable-temperature atomic force microscopy

Variation in shear viscous drag in a near-critical binary mixture was measured between a hydrophilic probe sphere and a hydrophilic substrate down to a distance range comparable to or smaller than the correlation length ξ using a magnetic excitation method of atomic force microscopy at temperatures T=Tc−∆T with ∆T varying from 0.1 to 0.7 K. As the temperature approached the Tc, the increase in the drag coefficient toward the zero distance was observed to be less pronounced in the distance range below ca. 100 nm. The data was discussed as arising from suppression in a concentration gradient in the intersurface region due to the overlap of the affected layers on similar surfaces.

Inter-ELM pedestal turbulence dynamics dependence on q95 and temperature gradient

Abstract A series of dedicated experiments from DIII-D tokamak provide spatially and temporally resolved measurements of electron density and temperature, and multiscale and multichannel fluctuations over a wide range of conditions. Measurements of long wavelength density fluctuations in the type-I ELMing H-mode pedestal routinely revealed a coexistence of multiple instabilities that exhibit dramatic different dynamic behaviors as q95 and temperature gradient are varied, apparently responsible for limiting pedestal temperature profiles. Two distinct frequency bands of density fluctuations are modulated with ELM cycle with frequency above 200kHz propagating in the electron diamagnetic direction in the lab frame (electron mode) and below 200kHz propagating in the ion diamagnetic direction (ion mode). The electron mode amplitude peaks near the electron temperature gradient region and increases with q95 which seems to be correlated with the increased χe at higher q95, similar to the characteristics expected for Micro-tearing Mode (MTM). At higher q95, during the inter-ELM period, the ion mode decays at later phase of the ELM cycle. Consistently, the poloidal correlation length of the ion mode is also found to reduce which suggests the possible E×B flow shear suppression of ion mode at later phase of the ELM cycle as the Er well recovers. In contrast, the electron mode grows during the ELM cycle and reaches saturation at around 50-60% of ELM period. Linear gyrokinetic simulations find the MTMs as the most unstable mode in the pedestal electron temperature gradient region. The higher q95 and lower magnetic shear destabilize MTMs. These observations provide key insights of the underlying physics of multifield properties and rich dataset of experimental ‘fingerprints’ that enable new tests of the theoretical pedestal models and lead to developing a predictive model for pedestal formation on ITER and future burning plasma experiments.

The average transmitted wave in random particulate materials

Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon is not unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding the average transmission in particle-filled environments is central to improve data extraction or even to create materials that can selectively block or absorb certain wave frequencies. Most methods that calculate the average transmitted field assume that it satisfies a wave equation with a complex effective wavenumber. However, recent theoretical work has predicted more than one effective wave propagating even in a material which is statistically isotropic and for scalar waves. In this work we provide the first clear evidence of these predicted multiple effective waves by using high-fidelity Monte-Carlo simulations that do not make any statistical assumptions. To achieve this, it was necessary to fill in a missing link in the theory for particulate materials: we prove that the incident wave does not propagate within the material, which is usually taken as an assumption called the Ewald–Oseen extinction theorem. By proving this we conclude that the extinction length—the distance it takes for the incident wave to be extinct—is equal to the correlation length between the particles.

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase’s resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions

The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to the growth rule, and compare the estimated values with the previous numerical and experimental results. For the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these discrete models with quenched disorder. For full comparisons in the physically relevant spatial dimensions, we also perform numerically two distinct universality classes, including the quenched Edwards–Wilkinson, and the quenched Kardar–Parisi–Zhang equations with and without external driving forces. The critical exponents of these systems in the presence of quenched disorder are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these discrete systems with quenched disorder in the (2+1)-dimensional cases, we present surface morphologies with various external driving forces during the saturated time regimes. The relationships between surface morphologies, scaling exponents and correlation length are also revealed.

Sedimentation dynamics of passive particles in dilute bacterial suspensions: emergence of bioconvection

Microorganisms are ubiquitous in nature and technology. They inhabit diverse environments, ranging from small river tributaries and lakes, to oceans, as well as wastewater treatment plants and food manufacturing. In many of these environments, microorganisms coexist with settling particles. Here, we investigate the effects of microbial activity (swimming E. coli) on the settling dynamics of passive colloidal particles using particle tracking methods. Our results reveal the existence of two distinct regimes in the correlation length scale ( $L_u$ ) and the effective diffusivity of the colloidal particles ( $D_{eff}$ ), with increasing bacterial concentration ( $\phi _b$ ). At low $\phi _b$ , the parameters $L_u$ and $D_{eff}$ increase monotonically with increasing $\phi _b$ . Beyond critical $\phi _b$ , a second regime is found where both $D_{eff}$ and $L_u$ are independent of $\phi _b$ . We demonstrate that the transition between these regimes is characterized by the emergence of bioconvection. We use experimentally measured particle-scale quantities $L_u$ and $D_{eff}$ to predict the critical bacterial concentration for the diffusion–bioconvection transition.

X-Ray Crystallographic Analysis of Pr Modified BaTiO3 Ceramics with a Theoretical Perspective for Potential Applications in Microelectronics

By examining the diffraction data, the microstructure of the ball-milled synthesized powder sample ([Formula: see text][Formula: see text]TiO3) was characterized. Through the application of Rietveld’s powder structure refinement approach to analyze X-ray powder diffraction data of ball-milled powder mixes, structural and microstructural alterations in terms of lattice defects have been assessed in the formation of single-phase praseodymium-modified BaTiO3. Bond lengths, bond angles, and generated locations of the [Formula: see text]Pr0[Formula: see text]TiO3 ceramic have been discussed about its generated structure. X-ray diffraction with respect to the first sharp diffraction peak (FSDP) is used to study the nanostructure of void species. General equations were utilized to determine various FSDP characteristics such as interlayer separation, correlation length, nanovoid diameter and scattering vector magnitude. Although the literature reports on many properties of Pr-modified barium titanate ceramic, this sample’s quantitative analysis and nanovoid determination are presented for the first time.

Two distinct charge density waves in the quasi-one-dimensional metal Sr0.95NbO3.37 revealed by resonant soft X-ray scattering

The interplay of electron-electron and electron-lattice interactions plays an important role in determining exotic properties in strongly correlated electron systems. Of particular interest is quasi-one-dimensional SrNbOx metals, which are perovskite-related layered Carpy-Galy phases. Quasi-one-dimensional metals often exhibit a charge density wave (CDW) accompanied by lattice distortion; however, to date, the presence of a CDW in a quasi-one-dimensional metallic Carpy-Galy phase has not been detected. Here, we report the discovery of two distinct and simultaneous commensurate CDWs in Sr0.95NbO3.37 using resonant soft X-ray scattering (RSXS), namely, an electronic-(001) superlattice below ~ 200 K and an electronic-(002) Bragg peak. We also observe a non-electronic-(002) Bragg peak showing lattice distortion below ~ 150 K. Through the temperature dependence and resonance profile of these CDWs and the lattice distortion, as well as the relationship between the wavelength and charge density, these CDWs are determined to be Wigner crystals and Peierls-like instabilities, respectively. The electron‒electron interaction is strong and dominant even up to 350 K, and upon cooling, it drives the electron–lattice interaction. The correlation length of the electronic-(001) superlattice is surprisingly larger than that of the electronic-(002) Bragg peak, and the superlattice is highly anisotropic. Supported by theoretical calculations, the CDWs are determined by the charge anisotropy and redistribution between the O-2p and Nb-4d orbitals, and the strength of the electronic-(001) superlattice is within the strong coupling limit.

Elastic-plastic collision mechanism of micron-sized particle impacting rough surfaces

The interaction between micron-sized particles and rough surfaces represents a common natural phenomenon. Diverse Gaussian rough surfaces are reconstructed by utilizing inverse Fourier transformation, and the impact of surface roughness on the collision of micron-sized particles is investigated, scrutinized through the sizes of RMS roughness and correlation length from 0.025 μm to 0.2 μm. Given the relevance of surface roughness to particle size, it focuses on 1 μm particles collision—a dimension representative size ingested in the turbine blade cooling passage. The results indicate that RMS roughness primarily influences the height of asperities, whereas correlation length predominantly affects the density of asperities. COR diminishes with increasing roughness, and does not exhibit a decline with escalating speed, when the correlation length is small. The maximum contact area remains relatively constant with the larger roughness. Rotational velocity and rebound angle are predominantly impacted by the RMS roughness, less influence of the correlation length.

Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

We study the response of critical resonating valence bond (RVB) spin liquids to doping with longer-range singlets, and more generally of U(1)-symmetric tensor networks to nonsymmetric perturbations. Using a field theory description, we find that in the RVB, doping constitutes a relevant perturbation that immediately opens up a gap, contrary to previous observations. Our analysis predicts a very large correlation length even at significant doping, which we verify using high-accuracy numerical simulations. This emphasizes the need for careful analysis, but it also justifies the use of such states as a variational ansatz for critical systems. Finally, we give an example of a projected entangled pair state where nonsymmetric perturbations do not open up a gap and the U(1) symmetry reemerges. Published by the American Physical Society 2024

Wave-Function Network Description and Kolmogorov Complexity of Quantum Many-Body Systems

Programmable quantum devices are now able to probe wave functions at unprecedented levels. This is based on the ability to project the many-body state of atom and qubit arrays onto a measurement basis which produces snapshots of the system wave function. Extracting and processing information from such observations remains, however, an open quest. One often resorts to analyzing low-order correlation functions—that is, discarding most of the available information content. Here, we introduce wave-function networks—a mathematical framework to describe wave-function snapshots based on network theory. For many-body systems, these networks can become scale-free—a mathematical structure that has found tremendous success and applications in a broad set of fields, ranging from biology to epidemics to Internet science. We demonstrate the potential of applying these techniques to quantum science by introducing protocols to extract the Kolmogorov complexity corresponding to the output of a quantum simulator and implementing tools for fully scalable cross-platform certification based on similarity tests between networks. We demonstrate the emergence of scale-free networks analyzing experimental data obtained with a Rydberg quantum simulator manipulating up to 100 atoms. Our approach illustrates how, upon crossing a phase transition, the simulator complexity decreases while correlation length increases—a direct signature of buildup of universal behavior in data space. Comparing experiments with numerical simulations, we achieve cross-certification at the wave-function level up to timescales of 4 μs with a confidence level of 90% and determine experimental calibration intervals with unprecedented accuracy. Our framework is generically applicable to the output of quantum computers and simulators with access to the system wave function and requires probing accuracy and repetition rates accessible to most currently available platforms. Published by the American Physical Society 2024

Seismic analysis of gravity dam-foundation systems using stochastic spectral finite element method

Seismic analysis of dam-foundation systems is inherently complex due to uncertainties in material properties. This study investigates the effects of material randomness and heterogeneity on the seismic response of gravity dam-foundation systems using the stochastic spectral finite element method (SSFEM) based on the Karhunen Loève expansion and the polynomial chaos expansion. The Pine Plane dam is taken as an analysis example. First, the appropriate Karhunen Loève expansion modes and polynomial chaos order are determined for SSFEM by comparing them with the Monte-Carlo simulations. Subsequently, the seismic response of the dam is analyzed in the stochastic and deterministic models, respectively. Results indicate that material randomness and heterogeneity may reduce the seismic response of gravity dams, and the deterministic model may overestimate dynamic responses. Subsequently, the parametric analysis of the correlation length, which measures the spatial correlation between variables in different positions and indicates the size of heterogeneity material patches, is conducted. It is demonstrated that the correlation length would not significantly affect the mean responses, but a larger correlation length leads to greater dispersions in responses. Finally, the effects of randomness in the foundation are investigated. The heterogeneities in the foundation affect the response of the dam in the high-frequency range. Therefore, the uncertainty in material properties should be fully considered in a structural assessment and risk analysis.

Three-dimensional variational assimilation with a multivariate background error covariance for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS 2.0.0-beta)

Abstract. This paper describes the three-dimensional variational (3D-Var) data assimilation (DA) system for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal- and meridional-wind components, a vertical linear regression representing wind–mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the “unbalanced” variables utilize the Background error on Unstructured Mesh Package (BUMP), which is one of the generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3D-Var systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3D-Var, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance, which combines that used in 3D-Var with the ensemble covariance, significantly outperforms both 3D-Var and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3D-Var system can be useful for the research community.

Thermal Density Fluctuations and Polymorphic Phase Transitions of Ethane (C2D6) in the Gas/Liquid and Supercritical States.

The phase behavior of the liquid C2D6 below and above the critical point was investigated using small-angle neutron scattering (SANS) in temperature and pressure ranges from 10 to 45 °C and 20 to 126 bar, respectively. The scattering of thermal fluctuations of the molecular density was determined and thus the gas-liquid and Widom lines. At the same time, we observed additional scattering of droplets of more densely packed C2D6 molecules above the gas-liquid line and in the supercritical fluid regime from just below the critical point for all temperatures at about ΔP = 10 bar above the Widom line. This line is interpreted as the Frenkel line. These results are consistent with our previous studies on CO2 and thus indicate a universal phase behavior for monomolecular liquids below and above the critical point. The interpretation of the Frenkel line as the lower limit of a polymorphic phase transition is in contrast to the usual interpretation as the limit of a dynamic process. The correlation lengths (ξ) of the thermal density fluctuations at the critical point and at the Widom line are determined between 20 and 35 Å and thus in the range of the droplet radius between 60 and 80 Å. These long-range fluctuations appear to suppress the formation of droplets, which can only form at about 10 bar above the critical point and the Widom line when ξ becomes smaller than 10 Å.