Frequency Distribution Function Research Articles

A Snow-Based Hydroclimatic Aggregate Drought Index for Snow Drought Identification

Climate change has increased the risk of snow drought, which is associated with a deficit in snowfall and snowpack. The objectives of this research are to improve drought identification in a warming climate by developing a new snow-based hydroclimatic aggregate drought index (SHADI) and to assess the impacts of snowpack and snowmelt in drought analyses. To derive the SHADI, an R-mode principal component analysis is performed on precipitation, snowpack, surface runoff, and soil water storage. Then, a joint probability distribution function of drought frequencies and drought classes, conditional expectation, and k-means clustering are used to categorize droughts. The SHADI was applied to the Red River of the North Basin (RRB), a typical cold climate region, to characterize droughts in a mostly dry period from 2003 to 2007. The SHADI was compared with the hydroclimatic aggregate drought index (HADI) and U.S. drought monitor (USDM) data. Cluster analysis was also utilized as a benchmark to compare the results of the HADI and SHADI. The SHADI showed better alignment with cluster analysis results than the HADI, closely matching the identified dry/wet conditions in the RRB. The major differences between the SHADI and HADI were observed in cold seasons and in transition periods (dry to wet or wet to dry). The derived variable threshold levels for different categories of drought based on the SHADI were close to, but different from, those of the HADI. The SHADI can be used for short-term lead prediction of droughts in cold climate regions and, in particular, can provide an early warning for drought in the warming climate.

Characterization of the damage mechanism in CFRP composites under mode I based on comprehensive analysis of AE signals

This study utilises several methods centred on acoustic emission (AE) waveform characteristics to conduct in-depth analysis of the damage mechanism of composite materials under mode I. Combined with the peak frequency statistics and continuous wavelet transform (CWT) of AE signals, three damage modes of laminated composites during loading are identified. The cumulative energy of three damage modes separated by variational modal decomposition (VMD) is used to characterize their damage evolution process. Based on the findings, delamination and fiber–matrix debonding are proven to be the dominant damage mechanisms for mode I. The comprehensive analysis results from AE's accumulated energy, peak frequency distribution, CWT, VMD, and sentry function can accurately detect the onset time of delamination in laminates. The equivalent crack length is calculated by the load value determined at the initial time of delamination, and the strain energy release rate calculated by the load value and crack length at this time is used as the interlaminar fracture toughness value of mode I. This research method will provide a new idea for the damage tolerance analysis of mode I delamination in laminated structures.

Direct fringe projection profilometry based on the spatial frequency distribution function in optical 3D imaging

Phase unwrapping has been a big hurdle in conventional optical three-dimensional (3D) measurement technologies, badly affecting speed and accuracy. To skip the complicated step of phase unwrapping, a direct fringe projection profilometry based on the spatial frequency distribution function is presented in this paper. First, the spatial frequency distribution function is defined according to the physical meaning of spatial frequency. Then, direct phase-shift method and direct Fourier transform profilometry are developed respectively with reference to the conventional fringe projection profilometry. Finally, both numerical simulations and experiments were carried out to test the proposed direct fringe projection profilometry. The direct phase-shift method without phase unwrapping combines the advantages of the conventional in terms of high accuracy, while the direct Fourier transform method does not get rid of the drawbacks of the conventional in spectral aliasing although it skips the phase unwrapping procedure.

Is Over-parameterization a Problem for Profile Mixture Models?

Biochemical constraints on the admissible amino acids at specific sites in proteins lead to heterogeneity of the amino acid substitution process over sites in alignments. It is well known that phylogenetic models of protein sequence evolution that do not account for site heterogeneity are prone to long-branch attraction (LBA) artifacts. Profile mixture models were developed to model heterogeneity of preferred amino acids at sites via a finite distribution of site classes each with a distinct set of equilibrium amino acid frequencies. However, it is unknown whether the large number of parameters in such models associated with the many amino acid frequency vectors can adversely affect tree topology estimates because of over-parameterization. Here, we demonstrate theoretically that for long sequences, over-parameterization does not create problems for estimation with profile mixture models. Under mild conditions, tree, amino acid frequencies, and other model parameters converge to true values as sequence length increases, even when there are large numbers of components in the frequency profile distributions. Because large sample theory does not necessarily imply good behavior for shorter alignments we explore the performance of these models with short alignments simulated with tree topologies that are prone to LBA artifacts. We find that over-parameterization is not a problem for complex profile mixture models even when there are many amino acid frequency vectors. In fact, simple models with few site classes behave poorly. Interestingly, we also found that misspecification of the amino acid frequency vectors does not lead to increased LBA artifacts as long as the estimated cumulative distribution function of the amino acid frequencies at sites adequately approximates the true one. In contrast, misspecification of the amino acid exchangeability rates can severely negatively affect parameter estimation. Finally, we explore the effects of including in the profile mixture model an additional "F-class" representing the overall frequencies of amino acids in the data set. Surprisingly, the F-class does not help parameter estimation significantly and can decrease the probability of correct tree estimation, depending on the scenario, even though it tends to improve likelihood scores.

A Novel Approach to Estimate Electrothermal Aging of Epoxy–Alumina Nanocomposites Using Dielectric Relaxation Current Analysis

In this article, an advanced technique is applied to estimate the aging state of epoxy–alumina nanocomposite insulation. For this purpose, several epoxy–alumina nanocomposite samples are prepared in the laboratory. Samples are undergone into artificial electrothermal aging conditioning up to duration of 600 h. After each 100-h instant, the relaxation current is measured under 1-kV/mm dc stress through the developed experimental setup in the laboratory. From the experimentally measured current data, relaxation frequency distribution (RFD) function of the test samples is computed. Based on the relaxation distribution function, two aging sensitive parameters are evaluated. In order to correlate these two aging sensitive parameters with the aging state of insulation, two empirical relationships are proposed based on the experimental investigation. The effectiveness of these two empirical relationships is validated with the laboratory prepared epoxy nanocomposites (EPNCs) insulation having a definite aging state. The experimental investigation shows that the proposed method can effectively be applied for estimating the aging state of nanocomposites insulation used in real-life high-voltage equipment.

A Modified Frequency Distribution Function of Wave-Breaking-Induced Energy Dissipation.

A nonlinear frequency-domain model and a probabilistic wave breaking model have been employed together to simulate the propagation of nearshore wave breaking and to provide estimates of related statistical quantities such as skewness and asymmetry. This combination of models requires a pre-specification of the frequency dependence of dissipation. Prior work has suggested that a frequency-squared weighting for the dissipation term is most appropriate via physical arguments. However, the original frequency distribution function significantly underpredicts the higher-order moments, particularly the accuracy of asymmetry predictions is in need of further improvement. An intensity of frequency dependence for the breaking-induced damping coefficient is introduced here to further adjust the dissipation function in order to increase the accuracy of asymmetry predictions. By correcting the frequency dependence function with a new form of frequency dependence in the breaking coefficient, the model results are in better agreement with the measurements of the spectrum and higher-order statistics, as well as with the free surface elevation measurements. It is also seen from testing the model with three different cases that the more evident the influence of the breaking mechanism is on the wave transformation process, the more pronounced the contribution of this modification is.

The Age and Erosion Rate of Young Sedimentary Rock on Mars

The Medusae Fossae Formation (MFF) is an enigmatic sedimentary unit near the equator of Mars, with an uncertain formation process and absolute age. Due to the heavily wind-eroded surface, it is difficult to determine the absolute model age of the MFF using a one-parameter model based on the crater size–frequency distribution function with existing crater count data. We create a new two-parameter model that estimates both age and a constant erosion rate (β) by treating cratering as a random Poisson process. Our study uses new crater count data collected from Context Camera imagery for both the MFF and other young equatorial sedimentary rock. Based on our new model, the Central MFF formed >1.5 Gyr ago and had low erosion rates (<650 nm yr−1), whereas the East MFF, Far East MFF, and Zephyria Planum most likely formed <1.5 Gyr ago and had higher erosion rates (>740 nm yr−1). The top of Aeolis Mons (informally known as Mount Sharp) in Gale Crater and Eastern Candor have relatively young ages and low erosion rates. Based on the estimated erosion rates (since fast erosion permits metastable shallow ice), we also identify several sites, including Zephyria Planum, as plausible locations for shallow subsurface equatorial water ice that is detectable by gamma-ray spectroscopy or neutron spectroscopy. In addition to confirming <1.5 Gyr sedimentary rock formations on Mars, and distinguishing older and younger MFF sites, we find that fast-eroding locations have younger ages and MFF locations with slower erosion have older best-fit ages.

Temperature dependence of aging effect in Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystal

The temperature dependence of the aging effect of permittivity in the paraelectric phase of 70.5%Pb(Mg1/3Nb2/3)O3–29.5%PbTiO3 (PMN–29.5%PT) is investigated. Time dependences of permittivity due to the aging effect at constant temperatures without DC biasing field can be empirically analyzed with the Williams–Watts relaxation function. Using the distribution function of relaxation frequency for the Williams–Watts relaxation function, we discuss the temperature dependence of the characteristic time of the aging effect. We clarify that the distribution width of the characteristic time markedly increases with decreasing temperature.

The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems

The statistics of nonlinear processes in avalanching systems, based on the self-organized criticality (SOC) concept of Bak et al. (1988), predicts power-law-like size (or occurrence frequency) distribution functions. Following up on previous work, we define a standard SOC model in terms of six assumptions: (i) area fractality, (ii) volume fractality, (iii) the flux–volume proportionality, (iv) classical diffusion, (v) the Euclidean maximum at the event peak time, and (vi) the spatiotemporal fluence or energy of an avalanche event. We gather data of the fractal dimension and power-law slopes from 162 publications and assemble them in 28 groups (for instance, solar flare energies, or stellar flare energies), from which we find that 75% of the groups are consistent with the standard SOC model. Alternative SOC models (Lévy flight, flat-world, nonfractal) are slightly less correlated with the data. Outliers are attributed to small number statistics, background definition problems, inadequate fitting ranges, and deviations from ideal power laws.

High-Resolution Direction of Arrival Estimation of Underwater Multitargets Using Swarming Intelligence of Flower Pollination Heuristics

Developing the parameter estimation, particularly direction of arrival (DOA), utilizing the swarming intelligence-based flower pollination algorithm (FPA) is considered an optimistic solution. Therefore, in this paper, the features of FPA are applied for viable DOA in the case of several robust underwater scenarios. Moreover, acoustic waves impinging from the far-field multitarget are evaluated using the different number of hydrophones of uniform linear array (ULA). The measuring parameters like robustness against noise and element quantity, estimation accuracy, computation complexity, various numbers of hydrophones, variability analysis, frequency distribution and cumulative distribution function of root mean square error (RMSE), and resolution ability are applied for analyzing the performance of the proposed model with additive white Gaussian noise (AWGN). For this purpose, particle swarm optimization (PSO), minimum variance distortion-less response (MVDR), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance technique (ESPRIT) standard counterparts are employed along with Crammer–Rao bound (CRB) to improve the worth of the proposed setup further. The proposed scheme for estimating the DOA generates efficient outcomes compared to the state-of-the-art algorithms over the Monte Carlo simulations.

Agricultural Water Optimal Allocation Using Minimum Cross-Entropy and Entropy-Weight-Based TOPSIS Method in Hetao Irrigation District, Northwest China

Affected by the temporal and spatial changes of natural resources, human activities, and social economic system policies, there are many uncertainties in the development, utilization, and management process of irrigation district agricultural water resources, which will increase the complexity of the use of irrigation district agricultural water resources. Decision makers find it challenging to cope with the complexity of fluctuating water supplies and demands that are critical for water resources’ allocation. In response to these issues, this paper presents an optimization modeling approach for agricultural water allocation at an irrigation district scale, considering the uncertainties of water supply and demand. The minimum cross-entropy method was used to estimate the parameters of hydrologic frequency distribution functions of water supply and demand, which are the basis for agricultural water resources’ optimal allocation and the evaluation of water resources’ carrying capacity in the Hetao Irrigation District. Interval Linear Fractional Programming was used to find water availability, shortage, and use efficiency in different irrigation areas of the Hetao Irrigation District (HID) under different scenarios. The denominator of fractional planning is the environmental goal, and the numerator is the economic goal; so, the objective function of fractional programming is the utility rate required in the post-optimization analysis. Future water availability and shortage scenarios are adopted consistent with the Representative Concentration Pathways’ (RCPs’) framework, and future water use scenarios are developed using the Shared Socioeconomic Pathways’ (SSPs’) framework. Results revealed that under SSP1, the annual water consumption increased from 30 billion m3 to 60 billion m3, almost doubling in Urad. The annual water consumption under SSP2 and SSP3 increased slightly, from 30 billion m3 to about 50 billion m3. The amount of water available for well irrigation in Urad decreased from 300 to 250 billion m3, while the amount of water available for canal irrigation in Urad remained at 270 billion m3 from 2010 s to 2030 s, only dropping to 240 billion m3 in 2040 s. The entropy-weight-based Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method was applied to evaluate agricultural water resources’ allocation schemes because it can avoid the subjectivity of weight determination and can reflect the dynamic changing trend of irrigation district agricultural water resources’ carrying capacity. The approach is applicable to most regions, such as the Hetao Irrigation District in the Upper Yellow River Basi with limited precipitation, to determine water strategies under the changing environment.

Neutron Scattering in Nanotubes

Abstract: Neutron scattering has got numerous applications in various fields of research like material research, crystallography etc. Thermal neutron scattering in randomly un-aligned multi walled carbon nanotubes is based on its anisotropic frequency distribution function. This frequency distribution function is obtained using a dynamical model which includes the presence of both the surface modes and intertube coupling. Experimentally measured values of specific heat for randomly un-aligned multi walled carbon nanotubes has been studied to detect the phonon frequency distribution function. Elastic scattering is used for analyzing structures. Inelastic scattering is applied for the study of atomic vibrations. The dynamical model has been used to find the scattering values. Both scattering values are calculated and compared. It was concluded that the difference in their values is large. This difference would affect the transport processes in randomly un-aligned multi walled carbon nanotubes Keywords: Specific heat, Elastic scattering, Inelastic scattering, Neutron Diffraction, Frequency Distribution Function

Flood Hazard Assessment of the Bangshi River Floodplain using an Integrated 1D/2D Coupled Hydraulic Model

In the present study, the flood hazard of the Bangshi River, located in the Savar Industrial Area of Dhaka District, has been evaluated. The historical flood extent analysed from the Landsat satellite images suggests that most parts of the study area were flooded during the major flood events in Bangladesh. The flood flow data were fitted with different analytical frequency distribution functions, and it is found that the Pearson III distribution function best fits with the observed data based on the Chi-Squared statistical test. Then, the flood flow model of the Bangshi River as well as the surrounding floodplain area was developed using the HEC-RAS 1D-2D coupled hydraulic model. The model was simulated with an estimated flow of 100-year and 500-year return periods. The analysis of the historical flood data shows that the water level exceeds the danger level at the nearby monitoring station of the study area in different years. In the study area, devastating floods occurred in the years 1988 and 1998. The maximum flood level was 9.9 m during the flood event of 1988. The analysis of Landsat satellite images also shows that about 69% and 58% of the study area were flooded during the floods of 1988 and 1998, respectively. The roadways provide flood protection barriers in the western side of the study area for the flood water coming from the Bangshi River system unless the road is overtopped. The simulated result shows that about 68% and 79% of the study area will be inundated for the 100-year and 500-year return periods, respectively. The simulated maximum flood velocity for the 100-year and 500-year return period is 2.31 m/s and 4.52 m/s, and the flood duration for the same return periods is about 32.5 days and 48.95 days, respectively. The simulated flood depth, duration, and velocity maps can be used for any development activities within the study area. The Dhaka University Journal of Earth and Environmental Sciences, Centennial Special Volume June 2022: 167-186

Thermal Neutron Scattering of Un-Aligned Multi-walled Carbon Nanotubes

Abstract: Neutron scattering is the scattering of free neutrons by matter. This process is used for the investigation of materials. Neutron scattering is an experimental technique which is applied in various areas of physics, physical chemistry, biophysics, crystallography and materials research. Neutron diffraction (elastic scattering) is used for determination of structures of materials. In this paper we attempted to study thermal neutron scattering in randomly un-aligned multi walled carbon nanotubes making use of an anisotropic dynamical model. This model includes the presence of both the surface modes and intertube coupling. Comparison of scattering cross section of un-aligned multiwalled carbon nanotubes has been done with fullerene and graphite. It was concluded that there is a significant difference between the values of scattering cross section for randomly un-aligned multiwalled carbon nanotubes and fullerene at higher values of energy. Keywords: Carbon nanotubes, Elastic scattering, Neutron Diffraction, Frequency distribution function, Specific heat

Climate change impact on extreme value and its frequency distribution function in a karst basin, Southwest China

Abstract Studying extreme meteorology and its frequency under climate change is helpful to guide flood and drought control. The original achievements and objective of this study are to further contribute to the literature on how to analyze the impact of climate change on extreme rainfall and extreme temperature more reasonably and comprehensively for a karst basin. The Mann–Kendall method, Heuristic segmentation method, cross-wavelet analysis method, generalized extreme value (GEV) model, and generalized Pareto distribution (GPD) model were applied in this paper. The 55-year (1963–2017) extreme rainfall and temperature data recorded in the Chengbi River Basin were applied. The results show that extreme rainfall showed a downward trend (−0.169 and −8.735 mm/10a), while the trends of extreme temperatures were not obvious (Sen's slope estimate is 0). The mutation points range from 1981 to 2002 and the mutation point of extreme rainfall series is earlier than that of extreme temperatures. Compared with the GEV model, the parameters of the GPD model show a smaller variation before and after climate change, and the extreme meteorology values corresponding to the same recurrence period show a decreasing trend after climate change. The performance of GEV and GPD models after climate change is generally more fit than that before climate change.

A population balance model for the chocolate roller refining process

A study was performed to analyze the evolution of particle size distribution in the chocolate roller refining process. A mathematical model based on the continuity and population balance equations was developed to interpret industrial data. The industrial data were provided for chocolate pastes with powder/crystalline sugar particles at low/high shear rates. The parameters of the breakage frequency and fragment distribution function were estimated using industrial data. After parameter fitting, the model shows good agreement with the experimental results for varying conditions with a single consistently chosen set of parameters. This provides confidence that the general model structure is suitable for process evaluation. The population balance model was used to analyze the influence of changing some process variables on the efficiency of grinding. The results show that there might exist optimum values of the roll’s diameter and rotational velocity for a specific configuration of the equipment.

Probability distribution function of crossover frequency of operational amplifiers

For the first time the cumulative distribution function and histogram of the crossover frequency of a contemporary operational amplifier ADA4898-2 is experimentally studied. Using a USB lock–in amplifier, which allows automatic frequency sweep of the current response of a non-inverting amplifier with significant static amplification, we measure the crossover frequency of 200 samples of ADA4898-2 operational amplifiers. This new method gives a significant advantage in accuracy and speed of study of every operational amplifier. The theory we use is based on the universal relation between time dependent output and input voltages. This common relation for all operational amplifiers is applicable for frequencies much smaller than the crossover frequency and the frequencies of non-dominant poles. In other words, this approximation is adequate, when an operational amplifier is included in a circuit with significant amplification.

Erosion-reducing effects of plant roots during concentrated flow under contrasting textured soils

The effects of plant roots on water erosion are likely to vary according to the range of root traits and soil textures. However, little is known about the erosion-reducing potential of roots under different soil textures due to the lack of sufficient texture variations which come from a comparable system. In this study, we systematically investigate how root functional traits respond to soil sand contents and their combined effects on rill erosion. Seeding of Cynodon dactylon (L.) Pers. were grown in a greenhouse under varied proportions of sand mass (ranging from 14% to 83%) by mixing silty clay soil (Ultisols derived from quaternary red clay) and engineering sand. After six months growing, the root-soil composites were subjected to concentrated flow in a hydraulic flume to obtain soil detachment capacity (Dc), then roots were separated to measure their morphology and architecture traits. The results showed that sand content significantly affected root morphology traits (e.g., RD and RLD) (p < 0.01). In contrast, root architecture traits (e.g., root fractal dimension, topological index and radius frequency distribution function) showed no significant changes with soil texture (p > 0.05). Generally, root strongly promoted soil cohesion and they mitigated rill erodibility in a coordinated way. Rill erodibility was mostly determined by soil texture even in soils with dense roots, and the erosion-reducing effects of roots were less efficient in heavy-textured soils. Moreover, no significant correlations were found between critical flow shear stress (τc) and root traits, and soil with a loam texture displayed the lowest τc. Those relationships are likely to exist elsewhere, but its strength and direction could be changed according to the root trait variability and the varied root-soil feedbacks. The results of this study would be quite relevant for soil erosion modeling and imply the bare sandy soils are more urgent to be recovered during engineering constructions. Moreover, the inclusion of plant with dense fibrous roots could be the optimal species mixtures to stable sandy slopes.

Application of Remote Sensing Techniques to Discriminate the Effect of Different Soil Management Treatments over Rainfed Vineyards in Chianti Terroir

The work aimed to discriminate among different soil management treatments in terms of beneficial effects by high-resolution thermal and spectral vegetation imagery using an unmanned aerial vehicle and open-source GIS software. Five soil management treatments were applied in two organic vineyards (cv. Sangiovese) from Chianti Classico terroir (Tuscany, Italy) during two experimental years. The treatments tested consisted of conventional tillage, spontaneous vegetation, pigeon bean (Vicia faba var. minor Beck) incorporated in spring, mixture of barley (Hordeum vulgare L.) and clover (Trifolium squarrosum L.) incorporated or left as dead mulch in late spring. The images acquired remotely were analyzed through map-algebra and map-statistics in QGIS and correlated with field ecophysiological measurements. The surface temperature, crop water stress index (CWSI) and normalized difference vegetation index (NDVI) of each vine row under treatments were compared based on frequency distribution functions and statistics descriptors of position. The spectral vegetation and thermal-based indices were significantly correlated with the respective leaf area index (R2 = 0.89) and stem water potential measurements (R2 = 0.59), and thus are an expression of the crop vigor and water status. The gravel and active limestone soil components determined the spatial variability of vine biophysical (e.g., canopy vigor) and physiological characteristics (e.g., vine chlorophyll content) in both farms. The vine canopy surface temperature, and CWSI were lower on the spontaneous and pigeon bean treatments in both farms, thus evidencing less physiological stress on the vine rows derived from the cover crop residual effect. In conclusion, the proposed methodology showed the capacity to discriminate across soil management practices and map the spatial variability within vineyards. The methodology could serve as a simple and non-invasive tool for precision soil management in rainfed vineyards to guide producers on using the most efficient and profitable practice.

Hydroclimatic aggregate drought index (HADI): a new approach for identification and categorization of drought in cold climate regions

Drought identification is crucial to water resources management and planning. Different drought indices have been developed and their complexity and applicability vary. The objectives of this research are to develop a new integrated drought index with the capability of identification of drought and to further customize drought categorization for cold climate regions. Specifically, a new hydroclimatic aggregate drought index (HADI) is developed by coupling with a grid-based hydrologic model and applying the R-mode correlation-based principal component analysis. The HADI is a composite drought index, which assesses the anomalies of rainfall, surface runoff, snowmelt, and soil moisture in the root zone. Furthermore, joint probability distribution function of drought frequencies and classes as well as conditional expectation are used for drought categorization. The HADI was applied to the Red River of the North Basin (RRB) and its performance was evaluated by comparing with the Palmer Drought Severity Index (PDSI) and the U.S. Drought Monitor (USDM) products. Based on the impacts of drought on agriculture, the HADI outperformed the PDSI in identification of droughts in the RRB. Although the HADI and USDM showed a good agreement in identification of drought periods, the drought area coverages for each drought category from the two methods differed. The new customized drought categorization based on variable threshold levels accounted for the variations in both time and geographical locations. The new HADI, together with the customized drought categorization, is able to provide more accurate drought identification and characterization, especially for cold climate regions.