Spatial Correlation Length Research Articles

Optical trapping two types of particles using a focused vortex beam

Propagations of Gaussian Schell-model (GSM) vortex beams through a focusing optical system are formulated. The radiation force acting on Rayleigh dielectric sphere with different refractive indices produced by focused GSM vortex beams is investigated theoretically. Numerical results demonstrate that the focused GSM non-vortex beam can not trap the low index of refraction particles, but can capture the high index of refraction particles. The focused GSM vortex beam can be used to trap high index of refraction particles to a bright ring of the focal plane, and simultaneously capture low index of refraction particles to z-axis. The larger the topological charge m is, the larger the value of the spatial correlation length σ0 is, the easier it is to trap two types of particles is. Trapping stability is also analyzed.

Incorporating spatially heterogeneous infiltration capacity into hydrologic models with applications for simulating post‐wildfire debris flow initiation

AbstractSoils in post‐wildfire environments are often characterized by a low infiltration capacity with a high degree of spatial heterogeneity relative to unburned areas. Debris flows are frequently initiated by run‐off in recently burned steeplands, making it critical to develop and test methods for incorporating spatial variability in infiltration capacity into hydrologic models. We use Monte Carlo simulations of run‐off generation over a soil with a spatially heterogenous saturated hydraulic conductivity (Ks) to derive an expression for an aerially averaged saturated hydraulic conductivity ( ) that depends on the rainfall rate, the statistical properties of Ks, and the spatial correlation length scale associated with Ks. The proposed method for determining is tested by simulating run‐off on synthetic topography over a wide range of spatial scales. Results provide a simplified expression for an effective saturated hydraulic conductivity that can be used to relate a distribution of small‐scale Ks measurements to infiltration and run‐off generation over larger spatial scales. Finally, we use a hydrologic model based on to simulate run‐off and debris flow initiation at a recently burned catchment in the Santa Ana Mountains, CA, USA, and compare results to those obtained using an infiltration model based on the Soil Conservation Service Curve Number.

Propagation properties of a partially coherent radially polarized beam in atmospheric turbulence

Based on the extended Huygens–Fresnel integral, second-order moments of the Wigner distribution function of a partially coherent radially polarized beam propagating through atmospheric turbulence are derived. Besides, propagation properties such as the mean-squared beam width, angular width, effective radius of curvature, beam propagation factor and Rayleigh range can also be obtained and calculated numerically. It is shown that the propagation properties are dependent on the spatial correlation length, refraction index structure constant and propagation distance.

Matched-Filter Loss From Time-Varying Rough-Surface Reflection With a Small Effective Ensonified Area

Active sonar sensing often entails propagation paths that include a surface reflection, particularly in shallow-water scenarios. Surface reflection loss, which degrades sonar performance, depends on how rough the surface is with respect to the sensing wavelength and grazing angle. The Rayleigh roughness measure quantifies this relationship with small values representing an acoustically smooth surface and large values an acoustically rough surface. Models predicting surface reflection loss are generally derived assuming the surface shape is not varying over the time in which the pulse is reflecting from it and that the ensonified region of the surface is large in extent relative to the spatial correlation length of the surface. While these models are often appropriate for short-duration narrowband pulses, they are not necessarily applicable to long-duration broadband pulses, which are the focus of this paper. By assuming the effective ensonified area after matched filtering is smaller in extent than the spatial correlation length, a surface-reflection-loss model is derived as a function of pulse duration relative to surface wave period when the net surface displacement is Gaussian distributed. As might be expected the matched filter loss for the small-ensonified-area scenario increases with the Rayleigh roughness, the number of consecutive surface reflections, and the ratio between pulse duration and the surface wave period. With respect to the latter, the loss is predicted to saturate when the pulse duration exceeds one surface wave period. The model was compared with data measurements from the 2013 Target and Reverberation Experiment, as reported by Hines et al. (“The dependence of signal coherence on sea surface roughness for high and low duty cycle sonars in a shallow water channel,” IEEE J. Ocean. Eng. , vol. 42, no. 2, pp. 298–318, Apr. 2017). The data represent both short- and long-duration pulses with respect to the surface wave period. For the short-duration pulses, the model corroborates the data analysis by Hines et al. in predicting a very small matched filter loss. It also compared very favorably with the data for the long-duration pulses in both level and slope as a function of surface roughness. The models presented in this paper should be useful in sonar-equation analysis for predicting surface reflection loss with broadband waveforms when pulse duration is on par with or exceeds the surface wave period.

Directional channel modelling for millimetre wave communications in urban areas

Integrating Kirchhoff approximation (KA) and a ray-tracing (RT) algorithm, this study develops a new directional three-dimensional channel model for urban millimetre-wave small cells. The authors study the path loss, spatial correlation, coverage distance, and coherence length for line-of-sight (LOS), obstructed LOS, and non-LOS (NLOS) scenarios in urban areas. Exploiting physical optics and geometric optics solutions, closed-form expressions for spatial correlation are derived. It is deduced that LOS availability, frequency, and surface roughness scale highly impact spatial diversity. In addition, using antenna arrays of moderate gain at both sides of the link, even under NLOS conditions, a typical urban cell size of 200 m is achievable.

Damage evolution analysis of coal samples under cyclic loading based on single-link cluster method

In this paper, the acoustic emission (AE) response of coal samples under cyclic loading is measured. The results show that there is good positive relation between AE parameters and stress. The AE signal of coal samples under cyclic loading exhibits an obvious Kaiser Effect. The single-link cluster (SLC) method is applied to analyze the spatial evolution characteristics of AE events and the damage evolution process of coal samples. It is found that a subset scale of the SLC structure becomes smaller and smaller when the number of cyclic loading increases, and there is a negative linear relationship between the subset scale and the degree of damage. The spatial correlation length ξ of an SLC structure is calculated. The results show that ξ fluctuates around a certain value from the second cyclic loading process to the fifth cyclic loading process, but spatial correlation length ξ clearly increases in the sixth loading process. Based on the criterion of microcrack density, the coal sample failure process is the transformation from small-scale damage to large-scale damage, which is the reason for changes in the spatial correlation length. Through a systematic analysis, the SLC method is an effective method to research the damage evolution process of coal samples under cyclic loading, and will provide important reference values for studying coal bursts.

A stability analysis of a layered-soil slope based on random field

This paper details a method for investigating the stability of a layered slope that combines random field theory with horizontal integration. Both the cohesion and friction coefficient are treated as a Gaussian random field. The closed-form solution of the factor of safety and the probability of failure of the layered slope are derived, in which the effects of spatial correlation lengths and spatial correlation parameters on the stability of the layered slope are considered. The derived probability of failure is greatly affected by the input spatial correlation length of the soil parameters. The effectiveness of this proposed method is validated with the results of the Monte Carlo simulation.

Spatial Patterns and Temporal Stability of Throughfall in a Mature Douglas-fir Forest

Forest plays a key role in spatial distribution of rainfall and nutrients at fine spatial scales. Areas of localized rainfall and nutrient input at the soil surface may have a large effect on several hydrological and biogeochemical processes. In this paper, a Douglas-fir stand was revisited to evaluate the changes in the throughfall spatial distribution and its temporal stability due to forest growth and thinning. We used 32 funnel-type collectors distributed in a random stratified array within a 0.2 ha plot to measure throughfall amounts from February to November 2015. The throughfall variability was much lower as compared to the values reported ~25 years ago in the same site. We further assessed the spatial patterns of throughfall in spring and summer. We detected a spatial correlation length of 12 m and 8 m for spring and summer, respectively, which are higher than the values reported for other mature Douglas-fir forests in similar climatic conditions. Temporal stability plots confirmed that detected spatial patterns were stable in time.

Quenched disorder of a nematic liquid crystal under a magnetic field

We report measurements and theoretical predictions on the effect of an aligning magnetic field on the orientational disorder of a nematic liquid crystal in contact with isotropic solid substrates. Different types of substrates present a similar disorder and a similar dependency on the magnetic field amplitude, i.e. a decreasing of the angular distribution widths and spatial correlation lengths. Measurements are in qualitative agreement with a theory where the orientational disorder emerges from the competition between the aligning magnetic torque and the disorienting thermal fluctuations during the adsorption of the liquid crystal molecules on the substrate.

Ultra-Slow Single-Vessel BOLD and CBV-Based fMRI Spatiotemporal Dynamics and Their Correlation with Neuronal Intracellular Calcium Signals

Functional MRI has been used to map brain activity and functional connectivity based on the strength and temporal coherence of neurovascular-coupled hemodynamic signals. Here, single-vessel fMRI reveals vessel-specific correlation patterns in both rodents and humans. In anesthetized rats, fluctuations in the vessel-specific fMRI signal are correlated with the intracellular calcium signal measured in neighboring neurons. Further, the blood-oxygen-level-dependent (BOLD) signal from individual venules and the cerebral-blood-volume signal from individual arterioles show correlations at ultra-slow (<0.1Hz), anesthetic-modulated rhythms. These data support a model that links neuronal activity to intrinsic oscillations in the cerebral vasculature, with a spatial correlation length of ∼2mm for arterioles. In complementary data from awake human subjects, the BOLD signal is spatially correlated among sulcus veins and specified intracortical veins of the visual cortex at similar ultra-slow rhythms. These data support the use of fMRI to resolve functional connectivity at the level of single vessels.

Normal modes of weak colloidal gels.

The normal modes and relaxation rates of weak colloidal gels are investigated in calculations using different models of the hydrodynamic interactions between suspended particles. The relaxation spectrum is computed for freely draining, Rotne-Prager-Yamakawa, and accelerated Stokesian dynamics approximations of the hydrodynamic mobility in a normal mode analysis of a harmonic network representing several colloidal gels. We find that the density of states and spatial structure of the normal modes are fundamentally altered by long-ranged hydrodynamic coupling among the particles. Short-ranged coupling due to hydrodynamic lubrication affects only the relaxation rates of short-wavelength modes. Hydrodynamic models accounting for long-ranged coupling exhibit a microscopic relaxation rate for each normal mode, λ that scales as l^{-2}, where l is the spatial correlation length of the normal mode. For the freely draining approximation, which neglects long-ranged coupling, the microscopic relaxation rate scales as l^{-γ}, where γ varies between three and two with increasing particle volume fraction. A simple phenomenological model of the internal elastic response to normal mode fluctuations is developed, which shows that long-ranged hydrodynamic interactions play a central role in the viscoelasticity of the gel network. Dynamic simulations of hard spheres that gel in response to short-ranged depletion attractions are used to test the applicability of the density of states predictions. For particle concentrations up to 30% by volume, the power law decay of the relaxation modulus in simulations accounting for long-ranged hydrodynamic interactions agrees with predictions generated by the density of states of the corresponding harmonic networks as well as experimental measurements. For higher volume fractions, excluded volume interactions dominate the stress response, and the prediction from the harmonic network density of states fails. Analogous to the Zimm model in polymer physics, our results indicate that long-ranged hydrodynamic interactions play a crucial role in determining the microscopic dynamics and macroscopic properties of weak colloidal gels.

Nonuniversal and anomalous critical behavior of the contact process near an extended defect.

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of λ(l)-λ(∞)=Al^{-s}, with l being the distance from the surface. We concentrate on the marginal situation s=1/ν_{⊥}, where ν_{⊥} is the critical exponent of the spatial correlation length, and study the local critical properties of the one-dimensional model by Monte Carlo simulations. The system exhibits a rich surface critical behavior. For weaker local activation rates A<A_{c}, the phase transition is continuous, having an order-parameter critical exponent, which varies continuously with A. For stronger local activation rates A>A_{c}, the phase transition is of mixed order: the surface order parameter is discontinuous; at the same time the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. The mixed-order transition regime is analogous to that observed recently at a multiple junction and can be explained by the same type of scaling theory.

The influence of uncertain local subsoil conditions on the response of buildings to ground vibration

This paper examines the influence of imperfect knowledge of the local subsoil conditions on the prediction of building response to ground-borne vibration. The focus is on problems of environmental ground vibration in the wide frequency range between 1 Hz and 80 Hz. A probabilistic finite element-perfectly matched layers model is developed for the analysis of the dynamic soil-structure interaction problem where the shear modulus of the soil is modeled as a conditional random field. A subdomain formulation is employed to impose loading by an incident wave field in the model. The uncertainty on the subsoil properties is propagated to the response of a building by means of Monte Carlo simulation. A case study is considered to investigate the influence of the spatial correlation length of the random field representing the shear modulus of the subsoil, and the foundation type of the building. The structural response uncertainty varies over frequency bands but as a general trend increases with frequency. The foundation type of the building is a crucial parameter determining the structural response and the associated uncertainty bounds.

Experimental assessment of the variability of concrete air permeability: repeatability, reproducibility and spatial variability

To study the effect of spatial variability of some influential parameters on the durability of the building envelopes, some important information are required: the mean, the standard deviation and the spatial correlation of the studied fields defined by the correlation lengths. In this paper, the characterization of the concrete spatial variability was performed which included a significant number of test allowing the characterization of concrete air permeability. For this a concrete wall of 2 m of height, 1.20 m of width and 15 cm of thickness was manufactured in laboratory in which concrete specimens were periodically taken and tested. Firstly, results repeatability was performed. For these purpose, three tests per sample was carried out in order to assess the repeatability of the measurements. Secondly, the reproducibility of the measurements was carried out by testing two samples for each cored specimen.Good repeatability of the intrinsic permeability measurements on each tested sample is recorded. Indeed, the standard deviation does not exceed 0.67x10–17 m². Also, the concrete intrinsic permeability depends on the spatial location of the studied sample. It was found to be ranging between 2.38x10-17 and 5.91x10-17 m2 with an average value equal to 3.66x10-17 m2.The obtained results enable to quantify the spatial variability of concrete air permeability, particularly in terms of mean value and standard deviation. Also, it allowed highlighting the spatial correlation length of the studied fields and for probabilistic approaches regarding the prediction of the concrete durability.

Constructing regional climate networks in the Amazonia during recent drought events.

Climate networks are powerful approaches to disclose tele-connections in climate systems and to predict severe climate events. Here we construct regional climate networks from precipitation data in the Amazonian region and focus on network properties under the recent drought events in 2005 and 2010. Both the networks of the entire Amazon region and the extreme networks resulted from locations severely affected by drought events suggest that network characteristics show slight difference between the two drought events. Based on network degrees of extreme drought events and that without drought conditions, we identify regions of interest that are correlated to longer expected drought period length. Moreover, we show that the spatial correlation length to the regions of interest decayed much faster in 2010 than in 2005, which is because of the dual roles played by both the Pacific and Atlantic oceans. The results suggest that hub nodes in the regional climate network of Amazonia have fewer long-range connections when more severe drought conditions appeared in 2010 than that in 2005.

Text mining by Tsallis entropy

Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms’ relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods.

Wigner distribution function and kurtosis parameter of vortex beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel integral, the analytical expressions for the Wigner distribution function (WDF) and kurtosis parameter of partially coherent flat-topped vortex (PCFTV) beams propagating through atmospheric turbulence and free space are derived. The WDF and kurtosis parameter of PCFTV beams through turbulent atmosphere are discussed with numerical examples. The numerical results show that the beam quality depends on the structure constants, the inner scale turbulence, the outer scale turbulence, the spatial correlation length, the wave length and the beam order. PCFTV beams are less affected by turbulence than partially flat-topped coherent (PCFT) beams under the same conditions, and will be useful in free-space optical communications.

Transverse-to-transverse diffuse ultrasonic scattering.

Ultrasonic scattering occurs when elastic waves interact with interfaces within heterogeneous media. Diffuse ultrasonic backscatter measurements are used to capture the effective grain scattering within a polycrystal for extracting microstructural information. Recently, a mode-conversion scattering model was developed to describe the longitudinal-to-transverse ultrasonic scattering within polycrystalline materials and successfully applied to determine the material spatial correlation length L by fitting experimental results with the theoretical model. The mode-conversion model may allow additional microstructural information, such as grain shape, to be assessed. In this article, a theoretical extension of the previous mode-conversion ultrasonic scattering model is presented. The transverse-to-transverse (T-T) scattering can be measured by an experimental configuration with both source and receiving transducers oriented at angles between the first and second critical angles, including pitch-catch and pulse-echo measurements. The model is used to determine the correlation length from a sample of 1040 steel through pulse-echo T-T scattering measurements using 7.5 and 10 MHz transducers. The results show that the derived T-T model works well for lower frequencies but the results for higher frequencies reveal deficiencies in the model.

Viscosity of a sheared correlated (near-critical) model fluid in confinement

Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau–Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green–Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness L. In addition, at the critical point the viscosity is proportional to , where is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.

Trapping two types of particles using a focused partially coherent circular edge dislocations beam

A focused partially coherent circular edge dislocations beam used to trap Rayleigh dielectric sphere with different refractive indices is studied. The dependence of radiation forces on the number of circular edge dislocations p, the spatial correlation length σ0, relative refractive index nr, and particle radius a are analyzed and illustrated by numerical examples. It is shown that the focused partially coherent circular edge dislocations beam can be used to trap high index of refraction particles at focus F and bright ring R2, and simultaneously to capture low index of refraction particles at dark ring R1. It is much easier to capture the high index of refraction particles at focus F and the low index of refraction particles at dark ring as for the larger number of circular edge dislocations p and the spatial correlation length σ0, therefore it is necessary to optimally choose on p and σ0 for obtaining an optimal optical guiding. The ranges of the radius for two types of particles stably captured also have been determined. The obtained results are useful for analyzing the trapping efficiency of circular edge dislocations beams applied in micromanipulation technology.