Sigmoidal Form Research Articles

Fold localization at pre-existing normal faults: field observations and analogue modelling of the Achental structure, Northern Calcareous Alps, Austria

Abstract. Within the Northern Calcareous Alps (NCA) fold-and-thrust belt of the Eastern Alps, multiple pre-shortening deformation phases have contributed to the structural grain that controlled localization of deformation at later stages. In particular, Jurassic rifting and opening of the Alpine Tethys led to the formation of extensional basins at the northern margin of the Apulian plate. Subsequent Cretaceous shortening within the Northern Calcareous Alps produced the enigmatic Achental structure, which forms a sigmoidal transition zone between two E–W-striking major synclines. One of the major complexities of the Achental structure is that all structural elements are oblique to the Cretaceous direction of shortening. Its sigmoidal form was, therefore, proposed to be a result of forced folding at the boundaries of the Jurassic Achental basin. This study analyses the structural evolution of the Achental structure through integrating field observations with crustal-scale physical analogue modelling to elucidate the influence of pre-existing crustal heterogeneities on oblique basin inversion. From brittle–ductile models that include a weak basal décollement, we infer that oblique shortening of pre-existing extensional faults can lead to the localization of deformation at the pre-existing structure and predicts thrust and fold structures that are consistent with field observations. Consequently, the Achental low-angle thrust and sigmoidal fold train was able to localize at the former Jurassic basin margin, with a vergence opposite to the controlling normal fault, creating the characteristic sigmoidal morphology during a single phase of NW-directed shortening.

Analysis of the inflection points of height-diameter models

The inflection point is an important feature of sigmoidal height-diameter (H-D) models. It is often cited as one of the properties favoring sigmoidal model forms. However, there are very few studies analyzing the inflection points of H-D models. The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset. The six models were the Wykoff (WYK), Schumacher (SCH), Curtis (CUR), Hossfeld IV (HOS), von Bertalanffy-Richards (VBR), and Gompertz (GPZ) models. The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution. The distributions of the estimated inflection points were similar between the two-parameter models WYK, SCH, and CUR, but were different between the three-parameter models HOS, VBR, and GPZ. GPZ produced some of the largest inflection points. HOS and VBR produced concave H-D curves without inflection points for 12.7% and 39.7% of the tree species. Evergreen species or decreasing shade tolerance resulted in larger inflection points. The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape. Furthermore, HOS could produce concave H-D curves for portions of the landscape. Based on the studied behaviors, the choice between two-parameter models may not matter. We recommend comparing several three-parameter model forms for consistency in estimated inflection points before deciding on one. Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one. Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

Dynamic compaction of cohesive granular materials: scaling behavior and bonding structures.

The compaction of cohesive granular materials is a common operation in powder-based manufacture of many products. However, the influence of particle-scale parameters such as bond strength on the packing structure and the general scaling of the compaction process are still poorly understood. We use particle dynamics simulations to analyze jammed configurations obtained by dynamic compaction of sticky particles under a fixed compressive pressure for a broad range of system parameter values. We show that relative porosity, representing the relative importance of porosity with respect to its minimum and maximum values, is a unique function of a modified cohesion number that combines adhesion force, confining pressure, and particle size, as well as contact stiffness, which is often assumed to be ineffective but is shown here to play an essential role in compaction. An asymmetric sigmoidal form based on two power laws provides an excellent fit to the data. The statistical properties of the bond network reveal self-balanced force structures and an exponential fall-off of the number of both tensile and compressive forces. Remarkably, the properties of the bond network depend on the cohesion number rather than the modified cohesion number, implying that similar bond network characteristics are compatible with a broad range of porosities mainly due to the effect of contact stiffness. We also discuss the origins of data points escaping the general scaling of porosity and show that they reflect either finite system size or rigid confining walls.

Developing a thermodynamic model for the circulating air using an opaque system

AbstractThe paper focuses on energy modelling that involves a concatenated structure of a linear time‐invariant system. A block‐structured (BS) technique was adopted for a nonlinear system identification. Using the superimposition principle, the model mapped the thermodynamic state variables as an indirect function of time to the output function. The available energy and degradation of solar radiation are determined through a black box model. For testing and validation purposes, a solar collector with recirculating air was considered. The basic principle is to establish a relation between state variables and the performance parameters, without invoking the conventional thermodynamic relationship between them. The output of the model was compared with the validation data to ensure whether or not there was any affinity between them. The sigmoidal, wavenet, and polynomial forms of nonlinearity provided a good fit to the experimental dataset. The mean absolute percentage error encountered while estimating the collector efficiency was noticed to vary from −4.85 × 10−03% to 1.22 × 10−03%. Similarly, it falls in the domain of −4.73 × 10−04% to 7.78 × 10−02% for the second law efficiency. The maximum heat loss rate (BS model) obtained across the first and second passages of the solar air collector was 235.41 and 218.19 W at the air mass flow rate of 8.10 g/s, which is congruent to the validation dataset.

A discourse on factors influencing the formation of sigmoidal and linear slope-geometries in the deltaic clinoforms of the calciclastic Sobrarbe Delta, Ainsa Basin, Spain

Clinoforms develop at the hearts of prograding sedimentary systems and are an integral part in understanding basin development and sediment partioning. The Eocene Sobrarbe Formation in the Ainsa Basin in Spain, displays well-developed dipping clinoform geometries. The study observes depositional facies, mineralogy, and performs curve-fitting calculations in 2D to better understanding of factors controlling clinoform geometries.The Sobrarbe Formation is a unique prograding calciclastic delta system, in which carbonates are dominant, but depositional environments and sedimentary processes are akin to silicilclastic systems.Four clinothems (CT 1–4) were selected for detailed study. The clinothems display an overall coarsening upward trend. The lowermost clinothems comprise dominantly pro-deltaic marlstone deposited from suspension and dilute hyperpycnal flows, with occasional thin fine-grained episodic turbidite beds. The uppermost clinothems are dominated by reworked remobilized topset deposits comprising bioturbated calcarenites with a variety of trace-fossils, shells and large assemblages of nummulites, and finally proximal subaqueous stacked calcarenites.Three clinothems (1, 2, 4) are characterized by sigmoidal geometry (Gaussian distribution curve), symmetrical sediment distribution, a simple coarsening upward trend, and where calculable, ascending regressive trajectories. Clinothem 3 comprises a more complex stratigraphic development and displays an overall ascending transgressive trajectory, linear slope and asymmetric sediment distribution.The results show that sigmoidal geometries develop in both the distal pro-delta and in the coarser-grained proximal delta, suggesting the sigmoidal form develops naturally granted sufficient accommodation. While speculative it appears that linear slopes might be associated with draping during transgression, and asymmetric distribution associated with high sedimentation rates vis a vis accommodation. Accommodation exerts the dominant control on the location of the rollover and the trajectory. The topset-foreset ratio indicates the relative rate of sedimentation compared to accommodation, as high sedimentation rates increase deposition on the foreset. Results indicate that accommodation appears to be the most important factor controlling foreset slope, with steeper inclination developing in deeper water. Meanwhile sedimentation rate, grain size, and the role of turbidity currents may play a secondary role influencing slope angle.

Noise influence on recurrent neural network with nonlinear neurons

The purpose of this study is to establish the features of noise propagation and accumulation in a recurrent neural network using a simplified echo network as an example. In this work, we studied the influence of activation function of artificial neurons and the connection matrices between them. Methods. We have considered white Gaussian noise sources. We used additive, multiplicative and mixed noise depending on how the noise is introduced into artificial neurons. The noise impact was estimated using the dispersion (variance) of the output signal. Results. It is shown that the activation function plays a significant role in noise accumulation. Two nonlinear activation functions have been considered: the hyperbolic tangent and the sigmoid function with range form 0 to 1. It is shown that some types of noise are suppressed in the case of the second function. As a result of considering the influence of coupling matrices, it was found that diagonal coupling matrices with a large blurring coefficient lead to less noise accumulation in the echo network reservoir with an increase in the reservoir memory influence. Conclusion. It is shown that activation functions of the form of sigmoid with range from 0 to 1 are suitable for suppressing multiplicative and mixed noise. The accumulation of noise in the reservoir was considered for three types of coupling matrices inside the reservoir: a uniform matrix, a band matrix with a small blurring coefficient, and a band matrix with a large blurring coefficient. It has been found that the band matrix echo networks with a high blurring coefficient accumulates the least noise. This holds for both additive and multiplicative noise.

The interactive effects of environmental gradient and dispersal shape spatial phylogenetic patterns

IntroductionThe emergence and maintenance of biodiversity include interacting environmental conditions, organismal adaptation to such conditions, and dispersal. To understand and quantify such ecological, evolutionary, and spatial processes, observation and interpretation of phylogenetic relatedness across space (e.g., phylogenetic beta diversity) is arguably a way forward as such patterns contain signals from all the processes listed above. However, it remains challenging to extract information about complex eco-evolutionary and spatial processes from phylogenetic patterns.MethodsWe link environmental gradients and organismal dispersal with phylogenetic beta diversity using a trait-based and eco-evolutionary model of diversification along environmental gradients. The combined effect of the environment and dispersal leads to distinct phylogenetic patterns between subsets of species and across geographical distances.Results and discussionSteep environmental gradients combined with low dispersal lead to asymmetric phylogenies, a high phylogenetic beta diversity, and the phylogenetic diversity between communities increases linearly along the environmental gradient. High dispersal combined with a less steep environmental gradient leads to symmetric phylogenies, low phylogenetic beta diversity, and the phylogenetic diversity between communities along the gradient increases in a sigmoidal form. By disentangling the eco-evolutionary mechanisms that link such interacting environment and dispersal effects and community phylogenetic patterns, our results improve understanding of biodiversity in general and help interpretation of observed phylogenetic beta diversity.

Impact of local timescales in a cellular automata model of excitable media

A cellular automata system known as the Greenberg-Hastings cellular automata (GHCA), with cyclic and excitable individual dynamics, provides a useful paradigm for modeling emergent phenomena in an excitable medium. Most past studies of GHCA have investigated the asymptotic dynamics of the system, assuming fixed extents for the active and passive dynamical phases. This study is a systematic investigation of the relationship between the dynamical properties of individual cells of a small system implementing excitable dynamics, and the emergent system wide asymptotic state. The impact of the temporal extents of individual dynamical phases (τa, τp), on the probability of persistence P(τa,τp), defined as the fraction of initial configurations which sustain spatiotemporal oscillations asymptotically, is examined for each unique configuration of the system. The main result obtained is that the probability of persistence P(τa, τp) assumes a characteristic sigmoidal form, as the dynamical behaviour of the system transitions from absolute quiescence to persistent spatiotemporal oscillations, with respect to the parameters (τa, τp). A plot of the numerical findings in the (τa, τp) space provides a consolidated view of their impact on the emergent behaviour of the system. In conclusion, some implications of the methods and results presented in this work, to the study of emergent phenomena in excitable systems, are discussed.

Understanding plankton ecosystem dynamics under realistic micro-scale variability requires modeling at least three trophic levels

Plankton ecosystems are complex, multi-trophic networks of biotic and abiotic interactions among physical and chemical components. Still, nutrient-phytoplankton (NP) interactions are in many cases assumed to be representative of higher trophic-level interactions in plankton ecosystems. Here, we investigate the degree to which NP interactions capture the overall dynamics of multi-trophic plankton ecosystems when accounting for realistic levels of micro-scale variability. Plankton models are typically developed based on the mean-field approach, which considers only first central moments (i.e., spatio-temporal means). Such conventional plankton models may be appropriate for meso‑ or larger-scales, but inappropriate for the highly intermittent spatial fluctuations of phytoplankton that are ubiquitous at the micro (mm) scale. Using Reynold's decomposition, the closure approach accounts for spatial variability and temporal fluctuations (higher central moments) of the phytoplankton distributions. We apply closure models of various combinations of Nutrient (N), Phytoplankton (P), and Zooplankton (Z), each with linear, hyperbolic, sigmoidal and quadratic phytoplankton mortality forms to test i) the previously advanced hypothesis ‘fluctuations enhance higher trophic level biomass in plankton models’ and ii) the suitability of nutrient-phytoplankton interactions as a proxy for higher trophic ecological processes. We find that in NP models with linear, hyperbolic and sigmoidal phytoplankton mortality (P-mortality), phytoplankton biomass (P-biomass) increases with variability, but in the NP model with quadratic P-mortality, P-biomass decreases with variability. The results are robust in the sense that similar qualitative behavior is obtained for a wide range of biologically feasible parameter sets. We investigate the characteristics of the measurable quantity coefficient of variation of phytoplanktonCVp for models with different numbers of compartments. The NP models with density-independent form (linear form) and density-dependent forms (hyperbolic, sigmoidal and quadratic) for P-mortality term behave quite opposite to each other: NP models with linear P-mortality produce coefficient of variation CVp > 1 for all stable solutions while NP models with hyperbolic, sigmoidal and quadratic P-mortality forms produce CVp < 1 for all stable solutions. Depending on the mortality rate assumed, the NP model produces qualitatively different results at both micro- and macro-scales, and therefore is unable to consistently capture the true underlying dynamics of plankton ecosystems. By contrast, NPZ models behaved consistently and supported the previously advanced hypotheses, regardless of the functional form assumed for P-mortality.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows for repulsive and/or attractive contributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

Evolution of Plasma Composition in an Eruptive Flux Rope

Abstract Magnetic flux ropes are bundles of twisted magnetic field enveloping a central axis. They harbor free magnetic energy and can be progenitors of coronal mass ejections (CMEs). However, identifying flux ropes on the Sun can be challenging. One of the key coronal observables that has been shown to indicate the presence of a flux rope is a peculiar bright coronal structure called a sigmoid. In this work, we show Hinode EUV Imaging Spectrometer observations of sigmoidal active region (AR) 10977. We analyze the coronal plasma composition in the AR and its evolution as a sigmoid (flux rope) forms and erupts as a CME. Plasma with photospheric composition was observed in coronal loops close to the main polarity inversion line during episodes of significant flux cancellation, suggestive of the injection of photospheric plasma into these loops driven by photospheric flux cancellation. Concurrently, the increasingly sheared core field contained plasma with coronal composition. As flux cancellation decreased and a sigmoid/flux rope formed, the plasma evolved to an intermediate composition in between photospheric and typical AR coronal compositions. Finally, the flux rope contained predominantly photospheric plasma during and after a failed eruption preceding the CME. Hence, plasma composition observations of AR 10977 strongly support models of flux rope formation by photospheric flux cancellation forcing magnetic reconnection first at the photospheric level then at the coronal level.

S1R agonist modulates rat platelet eicosanoid synthesis and aggregation

Sigma-1 receptor (S1R) is detected in different cell types and can regulate intracellular signaling pathways. S1R plays a role in the pathomechanism of diseases and the regulation of neurotransmitters. Fluvoxamine can bind to S1R and reduce the serotonin uptake of neurons and platelets. We therefore hypothesized that platelets express S1R, which can modify platelet function. The expression of the SIGMAR1 gene in rat platelets was examined with a reverse transcription polymerase chain reaction and a quantitative polymerase chain reaction. The receptor was also visualized by immunostaining and confocal laser scanning microscopy. The effect of S1R agonist PRE-084 on the eicosanoid synthesis of isolated rat platelets and ADP- and AA-induced platelet aggregation was examined. S1R was detected in rat platelets both at gene and protein levels. Pretreatment with PRE-084 of resting platelets induced elevation of eicosanoid synthesis. The rate of elevation in thromboxane B2 and prostaglandin D2 synthesis was similar, but the production of prostaglandin E2 was higher. The concentration-response curve showed a sigmoidal form. The most effective concentration of the agonist was 2 µM. PRE-084 increased the quantity of cyclooxygenase-1 as detected by ELISA. PRE-084 also elevated the ADP- and AA-induced platelet aggregation. S1R of platelets might regulate physiological or pathological functions.

Controllable SiOx Nanorod Memristive Neuron for Probabilistic Bayesian Inference.

Modern artificial neural network technology using a deterministic computing framework is faced with a critical challenge in dealing with massive data that are largely unstructured and ambiguous. This challenge demands the advances of an elementary physical device for tackling these uncertainties. Here, wedesigned and fabricated a SiOx nanorod memristive device by employing the glancing angle deposition (GLAD) technique, suggesting a controllable stochastic artificial neuron that can mimic the fundamental integrate-and-fire signaling and stochastic dynamics of a biological neuron. The nanorod structure provides the random distribution of multiple nanopores all across the active area, capable of forming a multitude of Si filaments at many SiOx nanorod edges after the electromigration process, leading to a stochastic switching event with very high dynamic range (≈5.15 × 1010 ) and low energy (≈4.06 pJ). Different probabilistic activation (ProbAct) functions in a sigmoid form are implemented, showing its controllability with low variation by manufacturing and electrical programming schemes. Furthermore, as an application prospect, based on the suggested memristive neuron, wedemonstrated the self-resting neural operation with the local circuit configuration and revealed probabilistic Bayesian inferences for genetic regulatory networks with low normalized mean squared errors (≈2.41 × 10-2 ) and its robustness to the ProbAct variation.

Stereochemistry and chiroptical properties of bimetallic single helicates of hexapyrrole-α,ω-dicarbaldimines with high diastereoselectivity

Bimetallic complexes of hexapyrrole-[Formula: see text],[Formula: see text]-dicarbaldimines consisting of a pair of four-coordinate metal sites adopt a helical closed [Formula: see text]-symmetric form or sigmoidal open forms depending on whether the 2,2[Formula: see text]-bipyrrole subunit at the center of the hexapyrrole chain takes cis- or trans-conformation. X-ray crystallography of a bisNi complex having N-[([Formula: see text]-1-cyclohexylethyl]carbaldimine units at both ends of the hexapyrrole chain revealed a non-symmetric heterohelical open form where the metal coordination sites of opposite helical sense sit on opposite sides of the central 2,2[Formula: see text]-bipyrrole subunit. BisPd complexes preferred a closed [Formula: see text] form and a steric bulk at the 3,3[Formula: see text]-position of the 2,2[Formula: see text]-bipyrrole subunit improved the helical sense bias. A bisPd complex with N-[([Formula: see text]-1-cyclohexylethyl]carbaldimine units adopts a helical closed [Formula: see text] form exclusively with full bias for a [Formula: see text]-helical sense. These bimetallic single stranded helicates were reversibly oxidized to [Formula: see text]-cation radicals at 0.1∼0.3 V vs. a ferrocene/ferrocenium couple and spectroelectrochemistry revealed remarkable absorption and CD spectral changes in the Vis-NIR region.

Investigation of the Relationship between the Motor Unit Number Estimate (MUNE) and the Mean Slope of the Stimulus-Response (SR) Curve of the Compound Muscle Action Potential (CMAP) Scan

Objective: The goal of this study is to elicit the relationship between the MUNE and the Mean Slope of the SR Curve of the CMAP Scan. Introduction: MUNE is used to diagnose and to monitor the Neuromuscular Disorders. CMAP Scan is a neurophysiological method based on the gradual stimulation of motor neurons and on recording their responses. As a result, a Stimulus-Response (SR) curve is plotted to study the progress of these diseases. In healthy subjects, SR curve is in the sigmoid form. As Motor Unit (MU) loss takes place, higher stimulus intensities are required in CMAP Scan. In addition, the shape of the SR curve becomes different form rather than sigmoid. This affects the slope of the SR curve. Therefore, a new more integrative variable called Mean Slope can be defined which might be correlated with MUNE. Material and Methods: Motor neuron groups including 5- to-300 axons were created through a simulator software and they were stimulated gradually with incrementally increasing currents from 0 to 99 mA. . The voltage differences were computed by utilizing the CMAPs being the responses in the SR curve. The average of all slopes corresponding to each voltage differences was computed to find the Mean Slope. The correlation between MU number the Mean Slope was investigated statistically. Results and Discussion: The coefficient of determination and the Pearson correlation coefficient between MU number and the Mean Slope were found as 0.9974 and 0.999 respectively. A linear relationship between MU number and the Mean Slope was suggested. Conclusion and Recommendation: The mean slope can be taken into account as a new feature while building mathematical models for the MUNE methods. Besides, new variables in conjunction with the slope of the SR curve might be defined in future studies.

Efficient free vibration analysis of FGM sandwich flat panels with conventional shell elements

An efficient finite element model based on conventional shell elements available in ABAQUS software has been developed for free vibration analysis of FGM monolayer and sandwich flat panels. Applications to sandwich plates with an FGM layer embedded as either a core or face sheets with different through-the-thickness material gradations in the form of power (P-FGM), sigmoid (S-FGM), and exponential (E-FGM) distributions are considered. A user-defined material subroutine UMAT was used to implement functionally graded properties of the constitutive FGM layer. Numerical studies are given for free vibrations of monolayer and sandwich plates subjected to various boundary conditions and with different structural parameters such as span-to-thickness, face sheet-core-face sheet thickness and aspect ratios, and volume fraction index. The studies showed very good agreement between the present results and those existing in the literature that confirmed the accuracy of the developed model at minimal computational costs. This emphasizes the efficiency of the shell-based modeling strategy proposed for the calculations. A series of numerical solutions obtained in the research extends the results of known testing examples and may serve as additional benchmark data for other analysts.

A continuum shell element in layerwise models for free vibration analysis of FGM sandwich panels

A finite element model based on continuum shell elements available in ABAQUS software has been developed for the free vibration analysis of FGM sandwich panels. Applications to sandwich plates with different combinations of FGM core and/or FGM face sheets satisfying through-the-thickness material gradations in the form of either power (P-FGM) or sigmoid (S-FGM) or exponential (E-FGM) distributions are considered. A user-defined material subroutine UMAT was used to implement functionally graded properties of the constitutive FGM layer. Numerical studies are given for free vibrations of sandwich plates subjected to different boundary conditions and with different structural parameters such as span to thickness, face sheet–core–face sheet thickness and aspect ratios, and volume fraction exponent. The studies showed very good agreement between the present results and those existing in the literature that confirmed the accuracy of the developed model. A series of numerical solutions obtained in the research extends the results of testing examples and may serve as additional benchmark data for other researchers.

Reflection Absorption Infrared Spectroscopy Characterization of SAM Formation from 8-Mercapto-N-(phenethyl)octanamide Thiols with Phe Ring and Amide Groups.

Multifunctional amide-containing self-assembled monolayers (SAMs) provide prospects for the construction of interfaces with required physicochemical properties and distinctive stability. In this study, we report the synthesis of amide-containing thiols with terminal phenylalanine (Phe) ring functionality (HS(CH2)7CONH(CH2)2C6H5) and the characterization of the formation of SAMs from these thiols on gold by reflection absorption infrared spectroscopy (RAIRS). For reliable assignments of vibrational bands, ring deuterated analogs were synthesized and studied as well. Adsorption time induced changes in Amide-II band frequency and relative intensity of Amide-II/Amide-I bands revealed two-state sigmoidal form dependence with a transition inflection points at 2.2 ± 0.5 and 4.7 ± 0.5 min, respectively. The transition from initial (disordered) to final (hydrogen-bonded, ordered) structure resulted in increased Amide-II frequency from 1548 to 1557 cm−1, which is diagnostic for a strongly hydrogen-bonded amide network in trans conformation. However, the lateral interactions between the alkyl chains were found to be somewhat reduced when compared with well-ordered alkane thiol monolayers.

Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm

The paper studies a ψ-Caputo space-time-fractional moisture transport model stated in terms of water head. We consider a functional parameter of ψ-Caputo derivatives in power and sigmoid forms and use particle swarm optimization algorithm to identify model’s parameters. Input data for the identification were acquired on the irrigated field in the South of Ukraine within one irrigation cycle. Direct problems were solved using a finite-difference scheme. In these conditions, application of a fractional model with the classic Caputo derivative allowed more than ~ 2-times lowering of average absolute error compared to the integer-order model. The usage of functional parameter in power form allowed up to 19% accuracy enhancement compared to the classic Caputo derivative while the usage of sigmoid function up to 2.6-times lowers the error. Such behaviour remains when predicting soil moisture dynamics within the following irrigation cycles.

Nonlinear models based on enhanced Kriging interpolation for prediction of rock joint shear strength

One of the most basic topics in rock mechanic is the shear strength criteria for rock joints. Thus, it is of high importance to accurately predict the shear strength of rock joints. In this study, the abilities for accuracy and agreement of Kriging model-based nonlinear interpolation strategy are investigated in terms of predicting the shear strength of rock joints. Totally 84 datasets were used to construct the Kriging models; the datasets were divided into two main parts: training and testing. The prepared database was applied to the training phase in the Kriging model; this way, several nonlinear basic functions were introduced to enhance the predictions of the Kriging model. The examined functions in this paper were linear, 2-order, 3-order, exponential, logarithmic, logistic, hyperbolic tangent, and hyperbolic sine. The sigmoid forms of the basic functions, including logistic and hyperbolic tangent, provide the superior predictions compared to other mathematical functions, while the 2-order and 3-order forms provide the worst performances than the linear, exponential, and logarithmic functions. According to the obtained results, the logistic-based model with coefficient of determination (R2) of 0.916 was found the optimal model that can be successfully applied to estimating the shear strength of rock joints.