Small Correlation Length Research Articles

Planar XY magnetic glass state in the Gd2ScNbO7 pyrochlore

Here a spin glass system with emergent planar ordered spin clusters is investigated. The mixed B-site pyrochlore Gd2ScNbO7has been synthesized and characterized through a variety of techniques, including x-ray diffraction, magnetic susceptibility, muon spin relaxation, heat capacity and neutron scattering. Despite a Curie-Weiss temperature of -3.93(3) K, indicating net antiferromagnetic interactions, no signs of long ranged magnetic ordering are found down toT= 0.3 K. Instead, a disordered magnetic state emerges with a small correlation length of 2.1(1) Å of single tetrahedra. A Reverse Monte Carlo analysis of the polarized neutron scattering data reveals short-range antiferromagnetic order with emergent XY spin ordering similar to the parent pyrochlore compounds. Muon spin relaxation, and AC susceptibility measurements confirm that the magnetization condenses into a glass, with 10 % of the potential entropy missing in the specific heat. This magnetic ground state is similar to what is observed in Gd2Sn2O7just above the ordering temperature, without the eventual long-range ordering at low temperature.

Applicability of the Névot-Croce factor in analysis of X-ray reflection from a rough surface

Usability of the Névot-Croce (NC) formula for calculation of the reflectivity from a surface with high-frequency roughness is critically analyzed. First, the necessary conditions of the NC factor applicability are identified quantitatively in the limiting case of vanishingly small correlation length of roughness. Second, the conditions are established, when the nonzero correlation length of real surface roughness can be reckoned as vanishingly small. Third, basing on available in literature experimental data, these conditions are compared with the experimental values of the correlation length of high-frequency roughness. The final conclusions concerning applicability of the NC formula for hard X-ray to extreme ultraviolet radiation are formulated.

A Reciprocal Heuristic Model for Diffuse Scattering From Walls and Surfaces

Diffuse scattering of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several diffuse scattering models based on different approaches have been proposed over the years, two of the most popular ones being Kirchhoff Theory and the so-called Effective Roughness heuristic model. The latter, although less rigorous than the former, is more flexible and applicable to a wider range of real-world cases, including non-Gaussian surfaces, surfaces with electrically small correlation lengths and scattering from material inhomogeneities that are often present under the surface. Unfortunately, the Effective Roughness model, with the exception of its Lambertian version, does not satisfy reciprocity, which is an important physical-soundness requirement for any propagation model. In the present work, without compromising its effectiveness and its simple and yet sound power-balance approach, we propose a reciprocal version of the Effective Roughness model, which can be easily implemented and replaced to the old version in ray-based propagation models. The new model is analyzed and compared to the old one and to other popular models. Once properly calibrated, it is shown to yield similar - if not better - performance with respect to the old one when checked vs. measurements.

Load and resistance factor design versus reliability-based design of shallow foundations

ABSTRACT The load and resistance factor design (LRFD) approach employed in geotechnical design codes is often calibrated using the reliability-based design (RBD) method. However, the LRFD may not achieve the target safety level exactly. This paper makes comparisons between the LRFD and RBD by considering the ultimate and serviceability limit state design of strip foundations. The RBD is carried out via the Random Finite Element Method. It is found that the failure probability and the resulting foundation width for ULS obtained using the RBD increase with the soil spatial correlation length, gradually reaching a plateau. The comparison between the LRFD and RBD results for ULS suggests that the LRFD is conservative for low to medium soil variability, particularly at smaller correlation lengths. The reliability-based SLS design is less dependent on the soil correlation length, particularly for lower coefficients of variation of the soil elastic modulus. However, a resistance factor of 1.0 for SLS is unconservative, and resistance factors of 0.65, 0.7 and 0.8 are better aligned with the RBD when the target failure probabilities are 1×10−3, 1×10−2 and 1×10−1. The current study can be used to guide the design of shallow foundations and the calibration of the LRFD approach.

Impact of Combined Assimilation of Wind Profiler and Doppler Radar Data on a Convective-Scale Cycling Forecasting System

Abstract The two types of wind observations, profiler and radar radial velocity, have been successfully assimilated into numerical weather prediction (NWP) systems. However, the added value of profiler data, especially from a densely deployed profiler network, is unknown when assimilated together with Doppler radar radial velocity. In this article, two combined assimilation strategies of profilers along with radar radial winds are compared within a convective-scale data assimilation (DA) framework. In strategy I, the profiler data are assimilated with conventional observations to generate an intermediate analysis that acts as a prior for radar data assimilation. In strategy II, both profiler and radar data are considered as storm-scale and assimilated within the same pass. Single- and dual-observation assimilation experiments indicate that for strategy I, the profiler DA improvement can be partly canceled by the potentially negative impact of the assimilation of single-radar radial velocity afterward, particularly when the radial wind is nearly orthogonal to the prevailing wind. For strategy II, important complements are provided when profilers are assimilated within the same pass along with radial winds. The diagnostics for a low-level jet case demonstrate that both strategies facilitate improved analyses and forecasts. But strategy II may bring more moderate analysis increments, which indicate mutual constraints of the profiler and radial winds when assimilated within the same pass. The results obtained in 1-month, retrospective cycling experiments also show that the strategy II outperforms the strategy I with slightly better wind and precipitation forecasts. Significance Statement Due to the high spatial–temporal wind information provided by profiler and radar radial velocity measurements, their combined assimilation would be expected to improve wind analysis. To fully utilize dense profiler data and radar radial wind in future operational applications, this study proposes a suitable assimilation strategy. If the profilers are defined as synoptic-scale observations, the profiler and Doppler radar data must be assimilated in different passes to adopt different length and variance scales. Whereas it is more reasonable to use a small background correlation length consistent with the radial velocity and, therefore, assimilate in the same pass if the profiler data are considered to better sample storm-scale features. Single- and dual-observation experiments indicate that profiler data provide important complements, while the assimilation of single-radar radial wind may yield analyzed wind results that do not depict the ground truth. A low-level jet case and a 1-month impact study further show that the combined assimilation strategy of assimilating both profiler and Doppler radar using smaller background correlation lengths enhances the analysis and forecasting of wind, resulting in more accurate accumulated precipitation forecasts.

Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wave number, we obtain low-frequency MI sidelobes which converge to those given by a white-noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD.

Role of growth pressure on Structural, optical and electrical properties of indium Nitride thin films prepared by modified activated reactive evaporation

The effect of deposition conditions on the crystal structure and optical and electrical properties of Indium Nitride (InN) films deposited by modified reactive evaporation have been investigated. Substrates are kept at the electrode and thereby subjected to low-energy nitrogen ion bombardment.The effects of pressure on the structural, morphological, and optical properties of the films on Si (100) and glass substrates are investigated by X-ray diffraction analysis, scanning electron microscopy, energy-dispersive X-ray analysis, and UV–Vis transmittance, Photoluminescence, and Raman spectroscopy. All the films show a preferential c-axis orientation with c- lattice constant found decreasing up to 8 mTorr. The bandgap measured from the photoluminescence and optical absorption method shows similar characteristics. Raman spectra reveal broad and asymmetric line shapes for E2(high) and A1(LO) modesdue to the small phonon correlation length. The Indium oxide phase was detected for the film grown at 25 mTorr which alsodeteriorates its electrical and optical properties.

Highly coherent illumination for imaging through opacity

Imaging through opacity has captured extensive attention in recent years for its promising applications in bioimaging systems and information extraction from scrambled light. Many optimized image reconstruction algorithms and advanced imaging scenarios are introduced and intensively studied in previous researches. However, intensity-based image reconstruction under the highly coherent light illumination is still a major challenge due to the strong interference effect. Here, we demonstrate that imaging through opacity can be implemented efficiently even under the highly coherent illumination with the aid of an intensity-based/incoherent deconvolution algorithm. Based on the experimental and theoretical analysis, we find the small phase correlation length of the diffuser plays a pivotal role in enabling the incoherent deconvolution operation for highly coherent illumination. Furthermore, the deconvolution algorithm shows insensitivity to the light coherence since the spatial frequencies of the object are well preserved in the spatial frequency spectrum of the speckle pattern. Our results provide a phase-information-free scheme for imaging through opacity under the highly coherent illumination. We anticipate our work would motivate the deep understanding of imaging using highly coherent illumination, increase the structural robustness of imaging systems and facilitate wavelength-sensitive imaging applications.

Electronic transport across extended grain boundaries in graphene

Owing to its superlative carrier mobility and atomic thinness, graphene exhibits great promise for interconnects in future nanoelectronic integrated circuits. Chemical vapor deposition (CVD), the most popular method for wafer-scale growth of graphene, produces monolayers that are polycrystalline, where misoriented grains are separated by extended grain boundaries (GBs). Theoretical models of GB resistivity focused on small sections of an extended GB, assuming it to be a straight line, and predicted a strong dependence of resistivity on misorientation angle. In contrast, measurements produced values in a much narrower range and without a pronounced angle dependence. Here we study electron transport across rough GBs, which are composed of short straight segments connected together into an extended GB. We found that, due to the zig-zag nature of rough GBs, there always exist a few segments that divide the crystallographic angle between two grains symmetrically and provide a highly conductive path for the current to flow across the GBs. The presence of highly conductive segments produces resistivity between 102 to 104 Ω μm regardless of misorientation angle. An extended GB with large roughness and small correlation length has small resistivity on the order of 103 Ω μm, even for highly mismatched asymmetric GBs. The effective slope of the GB, given by the ratio of roughness and lateral correlation length, is an effective universal quantifier for GB resistivity. Our results demonstrate that the probability of finding conductive segments diminishes in short GBs, which could cause a large variation in the resistivity of narrow ribbons etched from polycrystalline graphene. We also uncover spreading resistance due to the current bending in the grains to flow through the conductive segments of the GB and show that it scales linearly with the grain resistance. Our results will be crucial for designing graphene-based interconnects for future integrated circuits.

A variational quantum algorithm for Hamiltonian diagonalization

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational quantum algorithm for Hamiltonian diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality, and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

Nucleation of frictional sliding by coalescence of microslip

The onset of frictional motion is mediated by the dynamic propagation of a rupture front, analogous to a shear crack. The rupture front nucleates quasi-statically in a localized region of the frictional interface and slowly increases in size. When it reaches a critical nucleation length it becomes unstable, propagates dynamically and eventually breaks the entire interface, leading to macroscopic sliding. The nucleation process is particularly important because it determines the stress level at which the frictional interface fails, and therefore, the macroscopic friction strength. However, the mechanisms governing nucleation of frictional rupture fronts are still not well understood. Specifically, our knowledge of the nucleation process along a heterogeneous interface remains incomplete. Here, we study the nucleation of localized slip patches on linear slip-weakening interfaces with deterministic and stochastic heterogeneous friction properties. Using numerical simulations, we analyze the process leading to a slip patch of critical size for systems with varying correlation lengths of the local friction strength. Our deterministic interface model reveals that the growth of the critical nucleation patch at interfaces with small correlation lengths is non smooth due to the coalescence of neighboring slip patches. Existing analytical solutions do not account for this effect, which leads to an overestimation of global interface strength. Conversely, when the correlation length is large, the growth of the slip patch is continuous and our simulations match the analytical solution. Furthermore, nucleation by coalescence is also observed on stochastic interfaces with small correlation length. In this case, the applied load for a given slip patch size is a random variable. We show that its expectation follows a logistic function, which allows us to predict the strength of the interface well before failure occurs. Our model and observations provide new understanding of the nucleation process and its effect on the static frictional strength.

A Priori Error Analysis of a Numerical Stochastic Homogenization Method

This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$, $\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization.

Efficient uncertainty quantification for dynamic subsurface flow with surrogate by Theory-guided Neural Network

Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty quantification for dynamic subsurface flow with a surrogate constructed by the Theory-guided Neural Network (TgNN). The TgNN here is specially designed for problems with stochastic parameters. In the TgNN, stochastic parameters, time and location comprise the input of the neural network, while the quantity of interest is the output. The neural network is trained with available simulation data, while being simultaneously guided by theory (e.g., the governing equation, boundary conditions, initial conditions, etc.) of the underlying problem. The trained neural network can predict solutions of subsurface flow problems with new stochastic parameters. With the TgNN surrogate, the Monte Carlo (MC) method can be efficiently implemented for uncertainty quantification. The proposed methodology is evaluated with two-dimensional dynamic saturated flow problems in porous medium. Numerical results show that the TgNN based surrogate can significantly improve the efficiency of uncertainty quantification tasks compared with simulation based implementation. Further investigations regarding stochastic fields with smaller correlation length, larger variance, changing boundary values and out-of-distribution variances are performed, and satisfactory results are obtained.

A New Method of Roughness Construction and Analysis of Construct Parameters

In micro-manufacturing, roughness is unavoidable due to the tolerance of micro-machining methods. Roughness in microchannel could have a significant influence on flow and heat transfer since the size of microchannel is very small. In our work, roughness is modeled as a superposition of waves. A simple Fourier series method is proposed to construct the rough surface. With this method, roughness is constructed on the bottom of the rectangular microchannel which has a hydraulic diameter of 0.5 mm. Two important parameters during roughness construction, triangulate size and correlation length are studied under the same relative roughness 1%. Results show that flow and heat transfer characteristics are not sensitive to triangulate size. While triangulate size is changing from 0.1 mm to 0.05 mm, the variations of pressure drop and average Nusselt number are less than 1%. Correlation length could influence the topography of roughness surface a lot, smaller correlation length will lead to more pressure drop and lower Nusselt number.

Probabilistic bearing capacity of strip footing on reinforced anisotropic soil slope

The probabilistic bearing capacity of a strip footing placed on the edge of a purely cohesive reinforced soil slope is computed by combining lower bound finite element limit analysis technique with random field method and Monte Carlo simulation technique. To simulate actual field condition, anisotropic random field model of undrained soil shear strength is generated by using the Cholesky-Decomposition method. With the inclusion of a single layer of reinforcement, dimensionless bearing capacity factor, N always increases in both deterministic and probabilistic analysis. As the coefficient of variation of the undrained soil shear strength increases, the mean N value in both unreinforced and reinforced slopes reduces for particular values of correlation length in horizontal and vertical directions. For smaller correlation lengths, the mean N value of unreinforced and reinforced slopes is always lower than the deterministic solutions. However, with the increment in the correlation lengths, this difference reduces and at a higher correlation length, both the deterministic and probabilistic mean values become almost equal. Providing reinforcement under footing subjected to eccentric load is found to be an efficient solution. However, both the deterministic and probabilistic bearing capacity for unreinforced and reinforced slopes reduces with the consideration of loading eccentricity.

Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

Abstract We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressure field inside the tumor. The permeability field is modeled as a log-Gaussian random field with a prespecified covariance function. We numerically explore dimension reduction of the input parameter and model output. Specifically, truncated Karhunen–Loève (KL) expansions are used to decompose the log-permeability field, as well as the resulting random pressure field. We find that although very high-dimensional representations are needed to accurately represent the permeability field, especially in presence of small correlation lengths, the pressure field is not sensitive to high-order KL terms of the input parameter. Moreover, we find that the pressure field itself can be represented accurately using a KL expansion with a small number of terms. These observations are used to guide a reduced-order modeling approach to accelerate computational studies of biotransport in tumors.

Probabilistic bearing capacity of strip footing on reinforced soil slope

The probabilistic bearing capacity of the strip footing placed on the edge of a reinforced cohesionless soil slope is computed by combining lower bound finite element limit analysis method with anisotropic random field modelling and Monte Carlo simulation technique. Friction and dilation angle of purely cohesionless soil are considered as log-normally distributed random variables. The mean value of the bearing capacity factor Nγ reduces with the increasing randomness of the soil friction angle for particular values of correlation length in the horizontal and vertical directions. At smaller correlation lengths, the mean Nγ values of unreinforced and reinforced slopes are always lower than the deterministic values. However, the difference reduces with the increasing values of correlation lengths. At a higher correlation length, the deterministic and probabilistic mean values become almost equal. With the increasing value of correlation lengths and factor of safety, the failure probability of the bearing capacity factor associated with the reinforced slope reduces. Failure mechanisms of unreinforced and reinforced slopes obtained from the deterministic and probabilistic analysis are illustrated.

Drag Coefficient of a Circular Inclusion in a Near-Critical Binary Fluid Membrane

We calculate the drag coefficient of a circular liquid domain, which is put in a flat fluid membrane composed of a binary fluid mixture lying in the homogeneous phase near the demixing critical point. Assuming a sufficiently small correlation length, we regard the domain dynamics as independent of the critical fluctuation and use the Gaussian free-energy functional for the mixture. Because of the near-criticality, the preferential attraction between the domain component and one of the mixture components generates the composition gradient outside the domain significantly and can affect the drag coefficient. We first consider a domain having the same membrane viscosity as the domain exterior. The drag coefficient is expanded with respect to a dimensionless strength of the preferential attraction. It is numerically shown that the magnitude of the expansion coefficient decreases much as the order of the strength increases and that the first-order term of the series usually gives a good approximation for practical material constants. The effect of the preferential attraction is shown to be able to become significantly large in practice. We second consider cases where the membrane viscosities of the domain interior and exterior are different. The first-order term of the expansion series decreases to approach zero as the domain viscosity increases to infinity. This agrees with previous numerical results showing that the hydrodynamics makes the effect of the preferential attraction negligibly small for a rigid disk.

Evaluation of microstructure and residual stress in W/B4C multilayer optics

The microstructure and residual stress are investigated in W/B4C x-ray multilayer (ML) mirrors as a function of the number of layer pairs (N) varying from 20 to 400 at a fixed period, d ≈ 1.9 nm. The microstructure is analyzed using the x-ray reflectivity (XRR) and rocking scan methods. The total residual stress in the ML film is derived using the substrate curvature measurement method, whereas the stress in W layers of MLs is separately determined by grazing incidence x-ray diffraction measurements based on the sin2 χ method using synchrotron. The successive order Bragg peaks in XRR measured curves indicate good quality of the ML structure in terms of interface roughness and thickness errors. As N increases, the interface width of B4C and W varies in the range of 0.15–0.22 nm and 0.26–0.44 nm, respectively. The contribution of physical roughness to the interface width is significantly lower (∼sub-angstrom) compared to interfacial diffuseness (angstrom level) along with a small (few nanometers) correlation length in the ML structures as observed by rocking scan measurements. The residual stresses both in the W layers and in the ML film are compressive in nature. The total stress in the ML film decreases from −1.444 GPa to −0.389 GPa with increasing N. Measured residual stress in the ML film and W layers is correlated considering a net combined tensile stress arising from B4C layers and interfaces. The ML film with N = 400 shows the least residual stress and is suitable for large layer pair ML optics. Microstructure and stress are correlated considering the mechanism of film growth at the early stage and is discussed.

The Solvent Distribution Effect on the Self-Assembly of Symmetric Triblock Copolymers during Solvent Vapor Annealing

Using a combination of systematic experiments and Monte Carlo simulations, this report demonstrates that the distribution of neutral solvent has a strong impact on the quality and kinetics of the self-assembly of block copolymers in thin films. Both methyl ethyl ketone (MEK, a good solvent) and acetone (a relatively poor solvent) were used for the solvent vapor annealing (SVA) of thin films of poly(2-vinylpyridine)-block-polystyrene-block-poly(2-vinylpyridine) (VSV) triblock copolymer. Acetone, the poorer solvent, accumulated at the interface of the VSV domains, while MEK was distributed more uniformly throughout the VSV. As a result, acetone screened the interactions between the blocks of the copolymer more than MEK. Because MEK afforded less screening of the different blocks, solvent annealing with MEK led to self-assembly of lower molecular weight VSV triblock copolymers than was possible with acetone. Solvent annealing with MEK also led to slower self-assembly kinetics and smaller correlation lengths ...