Scale Fluctuations Research Articles

Insights into the design principles of JF-ED-VTFET for biosensing application

In this research article, we have designed a junction-free electrostatically doped vertical tunnel field-effect transistor (JF-ED-VTEFT) for label-free biosensing applications. We incorporated a nano-cavity within the gate-oxide layer near the source end of the FET to enable the detection of biomolecules based on the principle of dielectric modulation and without the requirement of external labeling. The proposed biosensor is thoroughly analyzed, considering various aspects such as electric field, energy band, transfer characteristics, and sensitivity parameters including energy band diagram, ON-current, ION/IOFF ratio, electrical analysis, and surface potential characteristics. The investigation of sensitivity encompasses practical challenges, such as different filling factors and step-profiles resulting from steric hindrance. In addition, the performance of the biosensor is evaluated by analyzing the temperature and scaling fluctuation in the integrated nanocavities. Additionally, values of biomolecules that are close to standard have been taken to validate the performance and provide insight into the sensitivity of the biosensor for detecting and analyzing the molecules.

Regional scale evaluation of nitrate fluctuations in groundwater using cluster analysis and standardised hydrometeorological indices

Temporal fluctuations in nitrate in groundwater can result in concentrations temporarily exceeding drinking water standards. This can bring about the need for costly water treatment or blending. Despite this, the extent and potential controls on these fluctuations are poorly understood, particularly at regional to national scales. Applied to Southeast England (UK), here we develop the first application of cluster analysis and standardised hydrometeorological indices to evaluate nitrate fluctuations in groundwater at the regional scale. Hierarchical and K-means cluster analysis of 96 groundwater nitrate time series for the period 1995–2022 showed that nitrate time series can be divided into 4 clusters: (1) long term increasing trends (n = 23, mean trend = 0.26 mg NO3/l/a), (2) long term decreasing trends (n = 19, mean trend = − 0.65 mg NO3/l/a), (3) long term increasing trends with seasonal fluctuations (n = 24, mean trend = 0.29 mg NO3/l/a) and (4) long term increasing trends superimposed on near-decadal scale fluctuations (n = 30, mean trend = 0.22 mg NO3/l/a). Boreholes in cluster 1 appear to be deeper than boreholes in cluster 2. In comparison to shallower boreholes, deeper boreholes are likely to be intersecting longer groundwater flow systems where nitrate concentrations are affected by historic “legacy nitrate” leaching. There is weak spatial coherence in the clustering, with clusters 3 and 4 present in the South and North Downs respectively. Cross-correlation analysis between groundwater nitrate time series with precipitation and groundwater level indices showed that rapid seasonal fluctuations in nitrate concentrations in cluster 3 in the South Downs are associated with rapidly responding groundwater level fluctuation. This is likely due to the highly fractured and faulted nature of the Chalk aquifer in this area. This is in contrast with the slower near-decadal fluctuations in cluster 4 in the North Downs. The strongest correlations between groundwater levels and nitrate concentrations in cluster 3 occurred when cross-correlating at a lag of zero months, which would suggest that matrix diffusion is unlikely to be a significant control on nitrate seasonality. Seasonal fluctuations in nitrate concentrations are likely to be associated with a combination of piston displacement at the water table and changing groundwater flow paths to the borehole. Future climate change may change the magnitude and timing of seasonal fluctuations caused by these processes. The methodology developed here is generic and can be applied wherever there is a large body of groundwater nitrate time series data.

Garnet zoning patterns record multiple processes of chemical transfer during subduction

Subduction is the principal mechanism by which volatiles are transferred from the Earth's surface to its interior. In garnets from eclogites and blueschists formed within the subduction setting, fine-scale, oscillatory elemental zoning is a common feature, sometimes considered to record open-system fluid exchange during prograde metamorphism. We present oxygen isotope data for garnets with such zoning from five exhumed subduction zone complexes. Short length scale fluctuations in elemental and oxygen isotope zoning (which are themselves spatially decoupled) cannot be linked to open-system fluid exchange during garnet crystallization in all samples; these data do not provide evidence for a genetic relationship between elemental oscillations and fluid fluxing. However, garnets from one setting do provide clear evidence for syn-growth ingress of elementally and isotopically buffering fluids, a process that operated simultaneously with the formation of elemental oscillations. Our findings indicate multiple mechanisms of chemical transfer operate at the grain–rock scale during subduction, and that some subduction zone rocks may experience only limited interaction with external prograde fluids. These results are consistent with a picture of highly heterogenous volatile transfer during subduction, and suggest that some proportion of the fluid inventory inherited at shallow depths may be transferred to sub-arc depths.

Extracting electromagnetic signatures of spacetime fluctuations

We present a formalism to discern the effects of fluctuations of the spacetime metric on electromagnetic radiation. The formalism works via the measurement of electromagnetic field correlations, while allowing a clear assessment of the assumptions involved. As an application of the formalism, we present a model of spacetime fluctuations that appear as random fluctuations of the refractive index of the vacuum in single, and two co-located Michelson interferometers. We compare an interferometric signal predicted using this model to experimental data from the Holometer and aLIGO. We show that if the signal manifests at a frequency at which the interferometers are sensitive, the strength and scale of possible spacetime fluctuations can be constrained. The bounds, thus obtained, on the strength and scale of the spacetime fluctuations, are also shown to be more stringent than the bounds obtained previously using astronomical observation at optical frequencies. The formalism enables us to evaluate proposed experiments such as QUEST for constraining quantum spacetime fluctuations and to design new ones.

Stability of Regularized Hastings–Levitov Aggregation in the Subcritical Regime

We prove bulk scaling limits and fluctuation scaling limits for a two-parameter class ALE(α,η)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha },\\eta )$$\\end{document} of continuum planar aggregation models. The class includes regularized versions of the Hastings–Levitov family HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} and continuum versions of the family of dielectric-breakdown models, where the local attachment intensity for new particles is specified as a negative power -η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\eta $$\\end{document} of the density of arc length with respect to harmonic measure. The limit dynamics follow solutions of a certain Loewner–Kufarev equation, where the driving measure is made to depend on the solution and on the parameter ζ=α+η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }={\\alpha }+\\eta $$\\end{document}. Our results are subject to a subcriticality condition ζ⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }\\leqslant 1$$\\end{document}: this includes HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} for α⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }\\leqslant 1$$\\end{document} and also the case α=2,η=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }=2,\\eta =-1$$\\end{document} corresponding to a continuum Eden model. Hastings and Levitov predicted a change in behaviour for HL(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\\alpha })$$\\end{document} at α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }=1$$\\end{document}, consistent with our results. In the regularized regime considered, the fluctuations around the scaling limit are shown to be Gaussian, with independent Ornstein–Uhlenbeck processes driving each Fourier mode, which are seen to be stable if and only if ζ⩽1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\zeta }\\leqslant 1$$\\end{document}.

An investigation of the effect of stratification stability and saltation sand flux on the anisotropy of atmospheric surface layer wall turbulence

In the atmospheric surface layer (ASL), the anisotropic characteristics of turbulence become more complex due to the strong influence of heat flux and particle motion. In this paper, the effects of stratification stability and total saltation sand flux on turbulent anisotropy of ASL wall turbulence are systematically analyzed by using high-frequency 3D velocity, temperature, and saltation sand flux measured in the field. Our results show that the temperature gradient intensifies the spanwise turbulent motion and enhances the vertical motion asymmetry. Although the buoyancy-driven turbulence enhances the spanwise variation, the momentum transfer mode between the streamwise–vertical and spanwise–vertical does not change. With the increase in instability, the large-scale motions (LSM) of the spanwise velocity may be destroyed and more spanwise small-scale motions (SSM) formed. In addition, saltation increases the sharpness, randomness, and extreme frequency of spanwise velocity distribution, but does not change the momentum transfer mode. Saltation may enlarge the fluctuation range and scale of the spanwise velocity, but may not be the main factor affecting the anisotropy of SSM. These results can deepen people's understanding of wind-blown sand movement and turbulence properties in ASL, and provides empirical data and insights that can significantly contribute to the development and refinement of turbulence models, particularly those that need to account for the complex interplay between stratification stability, saltation sand flux, and turbulence anisotropy.

Income Variability of Agricultural Households in Poland: A Descriptive Study

Among the different types of households, agricultural ones are perceived as the most exposed to the problem of income instability. Income fluctuations pose a threat not only to the financial stability of farming families but also to the sustainable development of the agriculture sector. Investigating the scale and factors of the variability of farmers’ household incomes is important in designing and monitoring agricultural policy measures that aim to stabilize farmers’ incomes. In this context, the main objective of this article is to assess the income variability of agricultural households in Poland and to identify the main correlates of farmers’ income fluctuations in the period 1996–2022. To emphasize the significance of the problem of income instability for agricultural households, a comparative assessment of income variability was performed (relative to non-agriculture households). Furthermore, two research subperiods (1996–2003; 2004–2022; before and after EU accession) were distinguished to capture the association between the Common Agriculture Policy (CAP) and the stability of agricultural income. The study focusses on associations between variables (regression and correlation analyses were used). The income of agricultural households was shown to exhibit greater variability (year-on-year) than the income of households of workers and of self-employed people, with a lower scale of fluctuations after 2004. Furthermore, the study reveals a group of factors that could be correlated with the variability of the income of agricultural households: income structure (share of income from agriculture), natural and climatic conditions (variability of the yields and agricultural production), and changes in prices of the means of agricultural production. The findings raise, however, a question about the effectiveness of CAP instruments in stabilizing agricultural income.

Entropy-driven nonequilibrium phonon-stimulated electron-phonon coupling in tin dioxide nanorods.

Nonequilibrium (NEQ) phonon fluctuation in a nanosystem has been studied through the statistical assessment of the entropy-production and -consumption events in ultrasmall tin dioxide (SnO_{2}) nanorods. Size- and shape-dependent alteration in free energy leading to modulation of the probability distribution function of the phonon dynamics has been observed from the x-ray diffraction and Raman scattering characterizations. The Gallavotti-Cohen nonequilibrium fluctuation theorem has been utilized to qualitatively describe the aforementioned behaviors under the influence of a global flux. The observation of entropy consumption and thermodynamically favorable entropy-production events indicates the presence of NEQ fluctuations in the phonon modes. The effective energy scale of fluctuation in driven phonon modes, dissipating energy faster than relaxation time, is quantified on the order of nanojoules. From optical absorption and photoluminescence studies, the observation of the electron-phonon coupled state confirms the interaction of the NEQ phonons with electrons. The strength of the coupling has been estimated from the temperature-independent Barry center shift and found to be enhanced to 5.35. Valence band x-ray photoelectron spectroscopy and Fourier transformed infrared spectroscopy analyses reconcile NEQ phonon mediated alteration of the valence band density of states, activation of silent phonon modes, and superior excitonic transitions, suitable for the new generation of ultrafast quantum device applications.

Evolution of temporal fluctuation scaling exponent in nonstationary time series using supersymmetric theory of stochastic dynamics.

Temporal fluctuation scaling (TFS) is an emergent property of complex systems that relates the variance (Ξ_{2}) and the mean (M_{1}) from an empirical data set in the form Ξ_{2}∼M_{1}^{α_{TFS}}, where the dispersion (fluctuation) of the data has been described in terms of Ξ_{2}. At present, it has been shown that this law of complex systems has different multidisciplinary applications such as characterizing the market rate based on its exponent, explaining the spatial spread of a pandemic or measuring dispersion in a counting process, among others, if it is known how the average value M_{1} of a representative quantity in a system changes. Then, using the path integral formalism and Parisi-Sourlas method, we propose an extension of path integral formalism to understand the origin of the temporal fluctuation scaling and the evolution of its exponent over time in nonstationary time series. To this end, we first show how the probability of transition between two states of a stochastic variable x(t) can be expressed once it is known its cumulant generating function. Also, we introduce a nonlinear term in a cumulant generating function of the form H^{(n)}(p,t;γ)∼p^{n} to obtain a model where the nth moment of the probability distribution evolves arbitrarily. Subsequently, in order to reproduce the temporal fluctuation scaling, a linear combination of H^{(n)}(p,t;γ) with n∈{1,2} is used. Therefore this allows describing how the mean M_{1}(t) and the variance Ξ_{2}(t) of empirical time series evolve. Thence, an analytical expression is deduced for the evolution of the temporal evolution of the temporal fluctuation scaling exponent α_{TFS}(t). Likewise, the validity of the expression found for α_{TFS}(t) is verified with a toy model based on white noise. Finally, this approach is verified in two stock indices (Dow Jones and Sao Paulo stock index) and two currencies (GBP-USD and EUR-USD) with daily data. It is found that this approach accurately captures the evolution of the mean and variance of these four financial derivatives after contrasting the results with a coefficient of determination that depends on H^{(n)}(p,t;γ). Also, it is shown that the temporal fluctuation scaling exponent is a measure of uncertainty or volatility in financial time series.

Time-varying and multi-scale analysis of copper price influencing factors based on LASSO and EMD methods

In this paper, we select 75 indicators to conduct a comprehensive analysis of the factors influencing the copper price along six dimensions: inventory, supply, demand, the macroeconomy, finance, and geopolitics. Facing the high-dimensionality problem, we use the least absolute shrinkage and selection operator (LASSO) regression model to select variables to measure the contribution of each category of factors. Furthermore, we identify the time-varying nature of the relationship among factors with rolling windows. Then, we decompose copper prices into different scales of fluctuations by means of empirical mode decomposition (EMD) and investigate the driving factors at each scale. The results show that financial and geopolitical factors have played an important role in copper pricing in recent years. The long-run fluctuation trend of copper prices is mainly determined by fundamental factors, while financial and geopolitical factors have a more direct impact on short-term fluctuations.

Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition.

Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance. Several such quantities are length scales (ξ or l) that characterize the size of excitations, the decay of spatial correlations, the response to perturbations, or the effect of physical constraints in the boundary or bulk of the material. Additionally, the spatial and sample-to-sample fluctuations of macroscopic observables such as contact statistics or elastic moduli diverge approaching unjamming. Here, we discuss important connections between all of these quantities and present numerical results that characterize the scaling properties of sample-to-sample contact and shear modulus fluctuations in ensembles of low-coordination disordered sphere packings and spring networks. Overall, we highlight three distinct scaling regimes and two crossovers in the disorder quantifiers χz and χμ as functions of system size N and proximity to unjamming δz. As we discuss, χX relates to the standard deviation σX of the sample-to-sample distribution of the quantity X (e.g., excess coordination δz or shear modulus μ) for an ensemble of systems. Importantly, χμ has been linked to experimentally accessible quantities that pertain to sound attenuation and the density of vibrational states in glasses. We investigate similarities and differences in the behaviors of χz and χμ near the transition and discuss the implications of our findings on current literature, unifying findings in previous studies.

Probabilistic analysis of tunnel convergence in spatially variable soil based on Gaussian process regression

Traditional probabilistic analysis of tunnel convergence in spatially variable soil typically involves using the random finite difference method, which is computationally intensive. In this study, we propose an efficient machine learning method based on the Gaussian Process Regression (GPR) model for predicting the horizontal and vertical convergences of a high-speed railway tunnel. In the proposed approach, the soil Young's modulus random field is simplified from a 2D matrix to a 1D vector, which serves as the input of the GPR model. Considering the prior knowledge about the probability distribution of the tunnel convergence, the horizontal and vertical convergences are transformed into two random variables that can be predicted effectively by the GPR model. Notably, the developed GPR model requires only 1.97% of the computational cost to achieve similar prediction accuracy as the 2D-convolutional neural network model. A training dataset comprising 1400 samples can deliver satisfactory prediction performance of the surrogate model under a certain scale of fluctuation (SOF). Moreover, selecting 700 samples from each random field optimally composes a mixed dataset for training the GPR model. The findings of this study suggest that the trained GPR model provides excellent performance for the probabilistic analysis of the tunnel convergences considering the spatially variable soil Young's modulus.

A novel general method for simulating a one dimensional random field based on the active learning Kriging model

Random fields are widely used to represent the uncertainty of some parameters in engineering, and numerous simulation approaches have been developed for Gaussian and non-Gaussian random fields. However, the unified methods among them suffer from low computational accuracy and efficiency or discontinuities in the simulated random fields. Therefore, an easy-to-implement general simulation method based on the active learning Kriging model is proposed for a one dimensional(1D) Gaussian or non-Gaussian random field in this paper. In the proposed method, there are two stages. One stage, called the inner loop, is to construct the Kriging approximation of a random field sample with enough accuracy by some samples of the random variables at some discretized locations, in which an active learning strategy based on the error estimation for the Kriging model is introduced to select adaptively the added locations, and a fast sampling method is presented to determine efficiently the samples at the added locations. In the other stage, called the outer loop, some random field samples are represented accurately by their corresponding Kriging approximations through training iteratively. Furthermore, several numerical examples are presented to show the accuracy, effectiveness and generality of the proposed method for 1D Gaussian and non-Gaussian random fields by comparing with the Karhunen–Loève(KL) expansion method. Meanwhile, the effects of the types of correlation function and the scales of fluctuation on the simulation results are analyzed.

Probing nuclear structure at the Electron-Ion Collider and in ultra-peripheral nuclear collisions

Within the Color Glass Condensate framework, we demonstrate that exclusive vector meson production at high energy is sensitive to the geometric deformation of the target nucleus and subnucleon scale fluctuations. Deformation of the nucleus enhances the incoherent cross section in the small |t| region. Subnucleon scale fluctuations increase the incoherent cross section in the large |t| region. In ultra-peripheral collisions (UPCs), larger deformation leads to a wider distribution of the minimal impact parameter Bmin required to produce a UPC. This, together with larger incoherent cross sections for larger deformation, results in smaller extracted radii. Our results demonstrate great potential for future studies of nuclear structure in UPCs and electron-ion collisions.

Seasonality and Lithic Investment in the Oldowan

Seasonality is a critical driver of resource availability within individual generations and is therefore likely to have exerted selective pressures on hominin evolution. Nonetheless, it has frequently been overlooked in discussions of early technological variability. This paper examines the relationship between seasonality and lithic investment in the Oldowan of eastern Africa, to broaden our understanding of hominin behavioural adaptability. We develop a framework for the identification of seasonal signatures in the archaeological record and examine the nature of lithic variability across 12 Early Pleistocene localities. In combining these insights, we suggest that seasonality played a pivotal role in shaping the pattern of lithic investment in the Oldowan, with peak investment related to greater wet season processing of plant resources and mobility across the landscape. The productivity of cores, retouching of flakes, and use of percussive implements may each play a role in this seasonal patterning of tool use. Our analysis provides further evidence that Oldowan hominins were able to adapt their technological behaviours to changing environmental conditions, even at the scale of intra-seasonal fluctuations in resource availability, and how this interacts with landscape familiarity over longer timescales.

Modeling the single particle crushing behavior by random discrete element method

Microscopic properties of granular materials typically exhibit significant heterogeneity. Realistic particle crushing simulation in granular materials requires the use of model that incorporate the spatial heterogeneity of its microscopic properties. This study introduces a novel approach, the Random Field Theory-Discrete Element Method (RFT-DEM) model, to simulate the single-particle crushing behavior of granular materials, considering the spatial heterogeneity of microscopic properties within particles. The material heterogeneity was characterized through Random Field Theory, demonstrating reasonable consistency between simulated and experimental results. The size-dependent characteristics of crushing strength and Weibull modulus were confirmed through a series of single-particle crushing simulations, emphasizing the model's capability to capture such features. Systematic analyses explored the impact of coefficient of variation (COV) and scale of fluctuation (SOF) on single-particle crushing behavior. Increasing COV resulted in reduced characteristic crushing strength and Weibull modulus, with larger particles exhibiting greater sensitivity. Furthermore, increasing SOF initially increased these parameters until a threshold SOF value of 0.0005 m, beyond which they stabilized. Reduced COV or increased SOF diminished the size effect in characteristic crushing strength, and once COV exceeded a threshold of 0.03, the size effect became independent of its variations. These findings contribute to a comprehensive understanding of the intricate interplay between microscopic properties and crushing behavior in granular materials.

Visualization of Mesoscopic Conductivity Fluctuations in Amorphous Semiconductor Thin-Film Transistors.

Charge transport in amorphous semiconductors is considerably more complicated than the process in crystalline materials due to abundant localized states. In addition to device-scale characterization, spatially resolved measurements are important to unveiling electronic properties. Here, we report gigahertz conductivity mapping in amorphous indium gallium zinc oxide (a-IGZO) thin-film transistors by microwave impedance microscopy (MIM), which probes conductivity without Schottky barrier's influence. The difference between the dc and microwave conductivities reflects the efficacy of the injection barrier in an accumulation-mode transistor. The conductivity exhibits significant nanoscale inhomogeneity in the subthreshold regime, presumably due to trapping and release from localized states. The characteristic length scale of local fluctuations, as determined by the autocorrelation analysis, is about 200 nm. Using a random-barrier model, we can simulate the spatial variation of the potential landscape, which underlies the mesoscopic conductivity distribution. Our work provides an intuitive way to understand the charge transport mechanism in amorphous semiconductors at the microscopic level.

Fractal dimension of heights facilitates mesoscopic mechanical properties in ternary hard film surfaces

Hardness of thin films is a noteworthy property in the electronic and mechanical industry and is generally observed to be dependent on the degree of roughening facilitated from surface heights' surface spatial heterogeneity at the mesoscopic observation scale. Nonetheless, owing to enhanced scale fluctuations and higher-order central moments, conventional parameters provide limitations and errors in capturing the spatial heterogeneity of surfaces. Herein, we have utilized scale-independent fractal parameters to analyze the spatial heterogeneity of surface heights in Ti1−xSixN ternary hard films deposited with varying Si doping concentrations using sputtering technique. The fractal dimension, lacunarity coefficient, Moran index, surface entropy, Otsu's separability, and fractal succolarity were computed to provide an overarching understanding of the surface heights' spatial heterogeneity. Principal component analysis was employed on the data sets to identify the parameter(s) accounting for the maximum variance and accordingly, the structure–property relation between spatial heterogeneity of surface and hardness is analyzed and discussed in the context of the fractal dimension of surface heights. The results indicate the possibility of mesoscopic surface engineering and, consequently, tuning of hardness and modulus of elasticity in Ti1−xSixN hard films by mere changing of surface spatial heterogeneity facilitated by the fractal dimension of surface heights.

Reliability-based factor of safety for bearing capacity of square foundations on 3D cohesive-frictionless soils considering samples

Reliability-based design concepts have been widely adopted in structural engineering but remain less prevalent in geotechnical practice due to the challenges of characterising ground uncertainties. To facilitate the unification of structural and geotechnical designs in complex engineering systems, we focus on square shallow foundations as crucial elements. Before a complete transition to load and resistance factor design, understanding the reliability of foundations designed using traditional factors of safety is essential. This paper presents a simplified analytical method for evaluating the probability of failure of square shallow foundations on 3D cohesive soils, utilising local average theory. The approach efficiently computes local averages and covariances of soil properties without the need for time-consuming 3D finite element computations. Verified against random finite element analysis, the method accurately determines required factors of safety for bearing capacity designs. Site-specific parameters, including sample location, shear strength coefficient of variation, and spatial variability fluctuation scale, influence the derived factors of safety. We advocate a pragmatic approach that calibrates traditional factor of safety methods with rigorous reliability theories, easing the transition to reliability-based design for practicing engineers. Moreover, the determined factors of safety can aid in establishing appropriate resistance factors by considering suitable load factors.

Effect of copula dependence structure on the failure modes of slopes in spatially variable soils

The copula dependence structure underlying the correlated shear strength parameters of soils can significantly affect the results of slope reliability analysis and risk assessment of slope failure. Currently, how do copula dependence structures affect the failure modes of slopes in spatially variable soils still remains an open question. This study systematically investigates the effect of copula dependence structures on the failure modes of a cohesive-frictional slope in spatially variable soils via an adapted random finite difference method (RFDM) that incorporates the copula-based random fields. The proposed RFDM proceeds with the simulation of cross-correlated random fields considering the copula dependence between the shear strength parameters of the slope. The strength reduction analyses are then performed within the framework of Monte Carlo simulation to obtain the stability analysis results, including the critical slip surface (CSS) and associated factor of safety (FS) and sliding volume. Finally, various statistical analyses on the number and distribution of CSS, FS and sliding volume as well as the failure modes versus different statistics of soil properties are analyzed considering different dependence structures. The results show that the overall distribution range of CSS obtained by the commonly used Gaussian copula is more concentrated, whereas the result by the No. 16 copula is the widest. The differences in the overall distribution range of CSS among different copulas decrease with the increase of the scale of fluctuation, coefficient of variation, and cross-correlation coefficient of the strength parameters. The proportions of different failure modes are comparable for the Gaussian, Plackett and Fran copulas, whereas the No.16 copula has the smallest proportion for the shallow failure and largest proportions for the deep and multi-slip failures. The influence of copula dependence structure on the slope failure mode is more significant than the statistical parameters of soil properties. The results provide useful references for copula selection when the underlying dependence structure is difficult to be determined.