Scale Fluctuations Research Articles

Soil Strength Parameters for the Sustainable Design of Unsupported Cuts Under Drained Conditions Using Reliability Analysis

Unsupported excavations are frequently performed in several geological and geotechnical projects, particularly for constructing roads and railways, and they are often carried out in different materials. The design of such cuts in soils needs the determination of representative values of its mechanical properties, particularly of the strength parameters, and the application of adequate safety factors. The procedure should ensure a sustainable design of those cuts, allowing for economical solutions that guarantee a low probability of geological–geotechnical failure. This paper assesses the reliability of unsupported cuts in soils, under drained conditions, assuming a Mohr–Coulomb strength criterion. Statistical meshes are generated considering the spatial variability of the friction angle and of the true effective cohesion, which are assumed to be uncorrelated. In this process, typical values of the coefficients of variation and of the horizontal and vertical scales of fluctuation are applied. Soil characterisation is simulated in each statistical mesh, and the characteristic values of the strength parameters are determined using statistical methods. Unsupported cuts of different heights and inclinations are designed using typical safety factors. Slope stability analyses are carried out using Random Finite Element Limit Analysis. The uncertainty in the actions is considered, and the probability of failure is determined by direct reliability analysis. The results show the relevance of the ratio between the scale of fluctuation and the excavation depth, the slope inclination, and the characteristic value of the soil strength parameters on the probability of failure. Values of adequate safety factors are proposed towards obtaining an appropriate probability of failure, compatible with the sustainable design of the cuts.

Gravitational wave memory imprints on the CMB from populations of massive black hole mergers

Our aim is to showcase and characterise the rich phenomenology of temperature fluctuation patterns that are imprinted on the cosmic microwave background (CMB) by the gravitational wave memory (GWM) of massive black hole mergers. We analysed both individual binaries as well as populations of binaries, distributed in local cosmological boxes at a given redshift. The magnitude of the temperature fluctuations scales primarily as a function of binary total mass and pattern angular scale, and accumulates as a random-walk process when populations of mergers are considered. Fluctuations of order $ $ K are reached across scales of $ 1'$ to $ circ $ for realistic volumetric merger rates of 10$^ $ Mpc$^ $ Gyr$^ $, as is appropriate for massive galaxies at $z=1$. We determined numerically that GWM temperature fluctuations result in a universal power spectrum with a scaling of $P(k) While not detectable given the limitations of current all-sky CMB surveys, our work explicitly shows how every black hole merger in the Universe left us its unique faint signature.

Novel method to estimate horizontal variability of shear wave velocity through multichannel analysis of surface waves

Scale of fluctuations (SOFs) of spatially variable soil properties have been regarded as one of the important parameters for performing reliability-based design in geotechnical engineering. However, the information required to estimate the SOFs in practice is limited, especially in the horizontal direction. In this study, the potential use of Multichannel Analysis of Surface Waves (MASW) to estimate the SOFs of shear wave velocity (VS) in horizontal direction is investigated through a series of numerical investigations. 2D random field models with a vertically increasing trend of VS were first simulated with different levels of variability controlled by the coefficient of variation (COV) and SOF. Afterwards, a large number of numerical MASW tests were performed using a 2D finite difference method, where the survey lines were progressively shifted. Results show that the COV of VS can be determined from the scatter of the dispersion curves, whereas the horizontal SOF of VS can be appropriately estimated from the phase velocity profile presented in the wavelength form. Additionally, in-situ MASW tests were conducted to estimate the horizontal SOF, and the obtained results align with those estimated by different methods. It is highlighted that the accuracy of the estimation depends on survey length. The interpretation using a long array reflects an averaged site condition of the survey area, thus losing the variability information. Favorable predictions are produced when survey length is shorter than 1.0 SOF. However, it should be noted that use of short survey length may limit the depth of investigation.

Experimental study on the concentration fluctuation of dust particles with different sizes during a dust storm

The particle size distribution (PSD) and concentration fluctuation were analyzed during different stages of a dust event. Our results show that dust smaller than 0.5 μm were dominant during the development stage; dust less than 0.5 μm decreased and dust from 0.5 μm to 10 μm increased in the high and low concentration stage; dust from 0.5 μm to 10 μm decreased and dust less than 0.5 μm increased in the dissipation stage. PSD of the first and fourth stages shows the unimodal distribution, but that of the other stages shows the distribution of 4 peaks. For large scale fluctuation with a period larger than 300 s, the concentration fluctuation of particles with size less than 0.4 μm and size larger than 0.4 μm has a high correlation. For small scale fluctuation with period less than 300 s, some particle size segments have high correlation at different stages, while some particle size segments have poor correlation at different stages. At the same stage, the size of the benchmark particle that is highly correlated in different particle size segments fluctuates with increasing particle size. In addition, the concentration fluctuation in 0.01276 Hz ∼ 0.02084 Hz and 0.00285 Hz ∼ 0.01096 Hz has significant contributions.

Exact results on the dynamics of the stochastic Floquet-East model*

Abstract We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size, this model has a large deviation phase transition between active and inactive dynamical phases. We also compute the finite time and size scaling of general space-time fluctuations, which for the case of inactive regions gives rise to dynamical hydrophobicity. We also discuss how, through the Trotter limit, these exact results also hold for the continuous-time East model, thus proving long-standing observations in kinetically constrained models. Our results here illustrate the applicability of exact tensor network methods for solving problems in many-body stochastic systems.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations.

Large stochastic population abundance fluctuations are ubiquitous across the tree of life, impacting the predictability and outcomes of population dynamics. It is generally thought that abundance fluctuations with a Taylor's law exponent of two do not strongly impact evolution. However, we argue that such abundance fluctuations can lead to substantial genotype frequency fluctuations if different genotypes in a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related Escherichia coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from genetic drift. We develop an effective model explaining that the abundance fluctuations arise from correlated offspring numbers between individuals, and the large frequency fluctuations result from (even slight) decoupling in offspring number correlations between genotypes. The model quantitatively predicts the observed abundance and frequency fluctuation scaling. Initially close trajectories diverge exponentially, suggesting that chaotic dynamics may underpin the excess frequency fluctuations. Our findings suggest that decoupling noise is also present in mixed-genotype Saccharomyces cerevisiae populations. Theoretical analyses demonstrate that decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of these frequency fluctuations, we expect them to be widespread across biological populations.

ResnetCPS for Power Equipment and Defect Detection

Routine visual inspection is fundamental to the preventive maintenance of power equipment. Convolutional neural networks (CNNs) substantially reduce the number of parameters and efficiently extract image features for classification tasks. In the actual production and operation process of substations, due to the limitation of safety distance, camera monitoring, inspection robots, etc., cannot be very close to the target. The operational environment of power equipment leads to scale variations in the main target and thus compromises the performance of conventional models. To address the challenges posed by scale fluctuations in power equipment image datasets, while adhering to the requirements for model efficiency and enhanced inter-channel communication, this paper proposed the ResNet Cross-Layer Parameter Sharing (ResNetCPS) framework. The core idea is that the network output should remain consistent for the same object at different scales. The proposed framework facilitates weight sharing across different layers within the convolutional network, establishing connections between pertinent channels across layers and leveraging the scale invariance inherent in image datasets. Additionally, for substation image processing mainly based on edge devices, smaller models must be used to reduce the expenditure of computing power. The Cross-Layer Parameter Sharing framework not only reduces the overall number of model parameters but also decreases training time. To further enhance the representation of critical features while suppressing less important or redundant ones, an Inserting and Adjacency Attention (IAA) module is designed. This mechanism improves the model’s overall performance by dynamically adjusting the importance of different channels. Experimental results demonstrate that the proposed method significantly enhances network efficiency, reduces the total parameter storage space, and improves training efficiency without sacrificing accuracy. Specifically, models incorporating the Cross-Layer Parameter Sharing module achieved a reduction in the number of parameters and model size by 10% to 30% compared to the baseline models.

Characterisation of the spatial variability of underconsolidated Singapore Marine Clay using random field theory

ABSTRACT This paper characterised the spatial variability of Singapore Kallang Formation Marine Clays using piezocone penetration test (CPT) data from the Marina South area. Both vertical and horizontal scales of fluctuation in undrained shear strength for two distinct clay units, Upper Marine Clay (UMC) and Lower Marine Clay (LMC), are calibrated for autocorrelation and semi-variogram functions. The Marina South area was reclaimed from the sea using fills placed in three phases from 1970s to 1990s and remains underconsolidated up to date. This study identified variations in the degree of consolidation across the area, which has led to variations in the undrained shear strength in this area. However, the variations in the degree of consolidation were found to have no noticeable influence on the vertical and horizontal scales of fluctuation of either UMC or LMC unit. The vertical scales of fluctuation of UMC and LMC units are 0.57 ± 0.3 m and 0.48 ± 0.17 m , respectively, while the horizontal scales of fluctuations are 148 ± 26 m and 138 ± 28 m , respectively. The present study contributes to the database of the statistical and spatial variability of marine clays and can provide useful guidance for assessing reliability of excavations and foundations in Marina South as well as other areas with similar geological settings.

Active fluctuations of axoneme oscillations scale with number of dynein motors

Fluxes of energy generate active forces in living matter, yet also active fluctuations. As a canonical example, collections of molecular motors exhibit spontaneous oscillations with frequency jitter caused by nonequilibrium phase fluctuations. We investigate phase fluctuations in reactivated Chlamydomonas reinhardtii axonemes, which are accessible to direct manipulation. We quantify the precision of axonemal oscillations after controlled chemical removal of dynein motors, providing an experimental test for the theory prediction that the quality factor of motor oscillations should increase with motor number. Our quantification reveals specialized roles of inner and outer arm dynein motors. This supports a model in which inner dyneins serve as master pace-makers, to which outer arm dyneins become entrained, consistent with recent insight provided by structural biology.

Deciphering the effects of STN DBS on neuropsychiatric fluctuations in Parkinson’s disease

The impact of subthalamic nucleus (STN) deep brain stimulation (DBS) on neuropsychiatric fluctuations in Parkinson´s disease (PD) remains unclear. The Neuropsychiatric Fluctuations Scale (NFS) can help to fill this gap, directly measuring fluctuations between the OFF- and ON-medication conditions. The NFS provides NFS-plus (hyperdopaminergic) and NFS-minus (hypodopaminergic) sub-scores. Based on these, the NFS global scores express the overall magnitude of neuropsychiatric symptoms in both the OFF- and ON-medication states. The total fluctuation score (TFS) represents the difference between ON- vs. OFF-medication NFS global scores, thus assessing fluctuations amplitude. The NFS was used to evaluate changes in neuropsychiatric fluctuations between the OFF- and ON-medication conditions before and 1-year after bilateral STN-DBS in 45 PD patients (32 males; mean age, 61.3 ± 7.2 years; PD duration, 10.2 ± 3.0 years). After surgery, the amplitude of neuropsychiatric fluctuations was significantly reduced (p < 0.001), confirming the efficacy of STN-DBS on these symptoms.

Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

Effects of saturation and fluctuating hotspots for flow observables in ultrarelativistic heavy-ion collisions

We investigate the effects of saturation dynamics on midrapidity flow observables by adding fluctuating hotspots into the novel Monte Carlo EKRT (MC-EKRT) event generator for high-energy nuclear collisions. We demonstrate that the intensity of the saturation effects significantly affects the ratio between the flow coefficients v3 and v2 at the LHC. Adding a hotspot substructure to the nucleons enhances the saturation effects and improves the agreement with the measured data. We show that the collision-energy dependence of the flow coefficients obtained using the MC-EKRT initial states with hotspots is improved in comparison with the earlier event-by-event EKRT model. In addition, we present the results for the charged hadron multiplicity distribution in Pb+Pb collisions at the LHC, and show that the minijet multiplicity originating fluctuations of the saturation scale included in MC-EKRT, as well as the presence of hotspots, are necessary for describing the measured large-multiplicity tail in the distribution. Published by the American Physical Society 2024

Influence of subgrade spatial variability on strain-alleviating ability of geogrids and rutting life in flexible pavement

This study employs the Random Field Finite Difference Analysis to assess how subgrade spatial variability impacts geogrid reinforcement’s strain-alleviating ability and the reinforced pavement’s rutting life. The geogrid’s abilities to reduce critical strains are evaluated using a strain-alleviating ratio and compared between deterministic and spatially variable scenarios. The analysis involves six geogrid reinforcement arrangements, considering two kinds of geogrid stiffness (G1 and G2) and three typical positions: top (L1), mid-depth (L1-2) and bottom (L2) of the base course. Key findings include: (a) Subgrade spatial variability significantly amplifies mean critical strains and leads to irregular strain and stress distributions, which in turn impacts the strain-alleviating ability of the geogrid reinforcements and potentially changes the optimal geogrid position. (b) The impacts of subgrade spatial variability on the geogrids’ strain-alleviating ability vary with the type of critical strains, the geogrid position, and the coefficient of variation and scale of fluctuation of subgrade modulus. When the geogrid is located at L2 (G_L2), its ability to alleviate critical subgrade strain is significantly compromised. (c) The adverse effect of subgrade spatial variability on the rutting life of G_L2 reinforced pavement is significant and can be mitigated by homogenising a very thin sublayer at the subgrade surface.

Study of Site Investigation Sample Quality and Worst-Case Scale of Fluctuation for Monopiles Based on Conditional Random Fields

Study of Site Investigation Sample Quality and Worst-Case Scale of Fluctuation for Monopiles Based on Conditional Random Fields

A reliability analysis framework coupled with statistical uncertainty characterization for geotechnical engineering

Reliability analysis plays an important role in the risk management of geotechnical engineering. For the random field-based method, it is expected that the uncertainty characterization of geo-material parameters and the realization of random field can be integrated effectively. Moreover, as the increase in measured data size is generally difficult in the field investigation of geotechnical engineering due to limitation of budget and time etc., the statistical uncertainty resulting from sparse data should be paid great attention. Therefore, taking the determination of hyper-parameters for Bayesian-based conditional random field as the breakthrough, this study proposed a reliability analysis framework to achieve the expectation above. In this proposed reliability analysis framework, the present characterization method of statistical uncertainty is improved by setting the lognormal distribution as the prior distribution of scale of fluctuation (SOF). Subsequently, the performance of statistical uncertainty characterization method is tested by a set of unconfined compressive strength (UCS) database about rocks. Then, a case study about the stability analysis of slope is employed to demonstrate the beneficial effect of the proposed reliability analysis framework. It is found that the uncertainty in both the realization of random field and the reliability analysis results can be significantly mitigated by the proposed reliability analysis framework.

Information and entropy in the labor market: Frictional and involuntary unemployment and the neutrality of money

AbstractWe re‐examine the concept of involuntary and frictional unemployment and the neutrality of money in a statistical equilibrium model of the labor market in which boundedly rational workers' and employers' interactions have a non‐zero impact on wages. From this perspective both the degree of involuntary unemployment and the neutrality of money depend on the adjustment of both expectations of the average level of wages and prices and the further adjustment of anticipations of the scale of fluctuations in prices and wage offers. Shocks to the economy can produce new long‐run equilibrium levels of unemployment and short‐run increases in involuntary unemployment arising from unevenness in the adjustment of expectations.

A novel efficient RFEM for reliability analysis and design of multi-line dynamically installed anchor for floating offshore wind turbines

A novel multi-line dynamically installed anchor was previously proposed by the authors to allow for the mooring of multiple floating offshore wind turbine, resulting in a significant reduction in the total number and cost of anchors required for floating wind farms. Considering the spatial variability of soil properties and the uncertainty of environmental loads, the present study performs reliability analysis and design of the multi-line dynamically installed anchor. Firstly, a strategy to repeatedly use fundamental random variables is proposed and validated for reducing the number of random variables used in Karhunen-Loève expansion in the simulation of random field of soil properties when the ratio of the soil domain dimension to the scale of fluctuation is large. Then, the efficiency, accuracy, and robustness of the RFEM (random finite element method) combined with K-MCS (Kriging model and Monte Carlo simulation) based on the proposed strategy are validated through examples of random capacity of foundations. Next, the random capacities and probabilistic VHMT failure envelopes of the multi-line dynamically installed anchor in spatially variable soil are investigated. Finally, the reliability design of multi-line dynamically installed anchors is conducted and compared with that of multi-line pile anchors, in which both the spatial variability of soil and the uncertainty of loads are condidered. The results show that the costs for multi-line dynamically installed anchors are obviously less than those of multi-line pile anchors.

Right anterior insula ASL hypoperfusion as a diagnostic biomarker of prodromal and mild dementia with Lewy bodies: preliminary evidence using a Bayesian approach.

Identifying and validating a biomarker with high specificity in early-stage dementia with Lewy bodies (DLB) using a feasible method is crucial to enhance the current suboptimal diagnostic procedure. Previous research revealed abnormalities, including hypoperfusion in the right anterior insular cortex at group level, in prodromal DLB. Exploring hypoperfusion of the right anterior insula, at an individual-level and assessing its relevance as a potential imaging biomarker in early DLB, has, to our knowledge, not been investigated. Our preliminary study aims to assess the feasibility of the technique and to provide a methodological framework for further investigation. We assessed the feasibility and accuracy of the hypoperfusion of the right anterior insula per arterial spin labelling magnetic resonance imaging (ASL-MRI) as a diagnostic biomarker in early DLB and provided rough estimates of its sensitivity and specificity. Defining the region of interest based on previous research, we established the biomarker as the hypoperfusion of the right anterior insula. Discriminative and analytical performances were assessed in comparison to a control group of treatment-resistant depression patients. Bayesian diagnostic reasoning was employed to assess the biomarker diagnostic usability in early DLB in two scenarios: healthy elderly controls and mild cognitive impairment. Additionally, we updated probabilities by integrating data from the Mayo-clinic cognitive fluctuations scale and real-time quaking-induced conversion (RT-QuIC) α-synuclein data. Lastly, a whole-brain perfusion analysis of DLB patients was conducted to identify further brain regions with discriminative abilities. We successfully replicated the right anterior insular hypoperfusion (RAI-Hypo) in all DLB patients at the individual level. The overall sensitivity of the biomarker was 96%, and the specificity was 92%. Bayesian testing revealed the biomarker's highest performance in early-stage DLB with cognitive fluctuations, showcasing a diagnostic potential associated with a high precision and moderate accuracy. In a cognitively non-impaired population, the RAI-Hypo showed a limited usability and lacked in selectivity to qualify as a screening tool. The exploratory whole-brain analysis revealed perfect discriminative capacities in the bilateral anterior insulae and the left inferior parietal lobule. Further studies are needed to confirm our preliminary results. If performance is maintained in subsequent studies and is compared to a more suitable control population, the proposed biomarker may be eventually sufficient to discriminate early-stage DLB from non-DLB.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations.

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution, as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate that they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

Development of a toroidally resolved broadband ECE imaging system for measurement of turbulent fluctuations on the KSTAR.

The two electron cyclotron emission imaging (ECEI) systems installed at adjacent ports (G and H) on the KSTAR tokamak incorporate large-aperture mm-wave optics, broadband electronics, and high speed digitization (up to 1 MSa/s) for 2D and quasi-3D visualization of MHD-scale fluid dynamics. Recently, the ECEI systems have been proved to be capable of visualization of smaller scale fluctuations albeit with a limited spatiotemporal resolution and even capable of measurement of ion cyclotron harmonic waves by direct high-speed sampling of the ECE IF signals. A four-channel prototype subsystem with a higher sampling rate up to 16 GS/s has been integrated into the G-port ECEI system, enabling the measurement of plasma waves in the GHz range in the form of modulated ECE signals and characterization of high-frequency turbulence during the evolution of pedestal. To achieve higher toroidal resolution in the turbulence measurement, the H-port ECEI system is now being upgraded to have a toroidally dual detector array of 2(toroidal) × 12(vertical) × 8(radial) channel configuration and a high-speed subsystem of 2(toroidal) × 4 channel configuration. The new mm-wave optics has been designed via beam propagation simulation, and the measured performance of the fabricated lens indicates a toroidal resolution of 8-10cm depending on the focus position and zoom factor, allowing for the measurement of parallel wavenumber up to k‖ ∼ 0.8cm-1.