Cluster Perimeter Research Articles

Growth Simulation of Lyophyllum decastes and Coprinus comatus and Their Influencing Factors in a Forested Catchment

Wild edible mushrooms are an important food source globally and have a crucial role in forest ecosystems. However, there is limited research on the growth characteristics and the contribution of agronomic traits to biomass, and the environmental factors affecting mushroom growth are limited. This study was conducted in the Qilian Mountains, China, and focused on investigating the growth patterns and agronomic traits of Lyophyllum decastes and Coprinus comatus. The results revealed that the growth of these mushrooms followed a logical growth curve. By calculating the model parameters, we obtained the maximum daily growth of height (PH), pileus diameter (PD), and cluster perimeter (CP) of L. decastes on the 5th, 7th, and 7th days, respectively, with values of 0.55 cm d−1, 0.54 cm d−1, and 4.54 cm d−1, respectively. However, the maximum daily growth of PH, pileus length (PL), and PD of the C. comatus appeared on the 3rd day, 2nd day, and 2nd day of the observation, respectively. This study identified near-surface relative humidity, air relative humidity, and rainfall as the primary factors influencing mushroom growth, as indicated by Pearson’s correlation analysis, redundancy analysis (RDA), and multiple linear and stepwise regression. Additionally, land surface temperature and air temperature were also identified as important factors affecting mushroom growth. By utilizing random forest and stepwise regression analysis, this study identified PH and stipe diameter (SD) as the most crucial agronomic traits affecting mushroom biomass. Overall, this study offers insights for industrial mushroom cultivation and basic fungal research.

A formula for the minimal perimeter of clusters with density

This paper deals with the isoperimetric problem for clusters in a Euclidean space with double density. In particular, we show that a limit of an isoperimetric minimizing sequence of clusters with volumes \mathbf{V} is always isoperimetric for its own volumes (which may be smaller than \mathbf{V} ). In particular, if it is strictly smaller, we provide an explicit formula.

Hydration at Highly Crowded Interfaces.

Understanding the molecular and electronic structure of solvated ions at surfaces requires an analysis of the interactions between the surface, the ions, and the solvent environment on equal footing. Here, we tackle this challenge by exploring the initial stages of Cs^{+} hydration on a Cu(111) surface by combining experiment and theory. Remarkably, we observe "inside-out" solvation of Cs^{+} ions, i.e., their preferential location at the perimeter of the water clusters on the metal surface. In addition, water-Cs complexes containing multiple Cs^{+} ions are observed to form at these surfaces. Established models based on maximum ion-water coordination and conventional solvation models cannot account for this situation, and the complex interplay of microscopic interactions is the key to a fundamental understanding.

Anatomical Assessment of Skin Separation in Date Palm (Phoenix dactylifera L. var. Mejhoul) Fruit during Maturation and Ripening Stages

Skin separation (puffiness) is a critical physiological disorder that significantly reduces the date palm (Phoenix dactylifera L.) fruit’s visual appearance and quality. The objectives of this study were to analyze fruit anatomy in skin-separated and normal date palm (var. Mejhoul) fruit and to assess the microclimatic conditions (temperature and relative humidity) during the fruit developmental stages and their association with skin separation. Fruit anatomy analysis was carried at different growth stages (Kimri-Khalal, Khalal, Rutab and Tamr) for two growing seasons. In addition, microclimatic conditions (specifically, temperature, and relative humidity) as well as soil moisture content were assessed across the study period 2020 and 2021. The anatomical analysis of the date palm fruit revealed that the exocarp or skin (cuticle, epidermis, hypodermis) thickness were quite similar across the developmental stages and over the study period (2020, 2021). Conversely, significantly more sclereid cells were found in skin-separated fruit (compared to normal fruit) at the Tamr stage. At that stage (Tamr), the percentage increase in sclereid cell number in skin-separated fruit ranged from 34–183%, sclereid clusters number 23–92%, cluster area 37–206%, and cluster perimeter 25–64%, as compared to normal fruit. In addition, sclereid cells at skin-separated areas of the fruit were clustered together, forming a chain of aggregates underneath the fruit skin, and were closer (42–50%, than normal) to the cuticle, leading to the partial separation of the exocarp from the fruit mesocarp. Although the weather data were similar across the growing seasons (temperatures, 33–34 °C; relative humidity, 45–46%), skin separation occurred in 14–15% of total fruit in 2020 and 30–34% in 2021. Therefore, we believe that skin separation disorder is not as heavily weather dependent as it seems to have been thought. In conclusion, changes in microclimate conditions were not the conclusive component for inducing the skin separation physiological disorder in date palm fruit. Further studies are required to identify the main factors that stimulate the development of sclereid clusters aggregates and the potential of agricultural practices to reduce skin separation.

Relationships between Tomato Cluster Growth Indices and Cumulative Environmental Factors during Greenhouse Cultivation

Growth characteristics of plants are mainly defined by genetic information and affected by environmental factors, such as air temperature, solar radiation, and humidity. There is a strong potential and demand to predict plant growth by environmental factors. Therefore, this study established mathematical models via multiple linear regression analysis (MLR) to describe the relationship between tomato cluster's growth indices and environmental factors in greenhouse cultivation. The Japanese tomato variety (Solanum lycopersicum L. Var. Culta. Momotarou Haruka) was cultivated in a hydroponic culture system using a porous solid medium from September 2019 to June 2020 in a glass greenhouse. The significant correlations among growth indices and environmental factors showed that the cumulative solar radiation (CSR) had a stronger effect on the number of flowers (NFl) rather than the cumulative heat unit (CHU) and vapor pressure deficit (VPD). Meanwhile, the number of fruits (NFr) relied much on VPD than CHU and CSR. Also, pollination condition was sensitive to VPD; NFr and enlargement of fruit cells during fruit maturation might be important factors in fruit-cluster weight (CWt). Mathematical models via MLR of cumulative environmental factors, such as CHU, CSR, and VPD could explain tomato cluster's growth indices, such as NFl, NFr, fruit perimeter (PFr), CWt, and duration of tomato clusters with the coefficient of determination (R2) ranging from 0.742 in the fruit maturation duration (FM) model to 0.953 in the PFr model. In MLR models, CHU was the most important factor in the duration of tomato clusters and PFr with the relative importance metrics (RIM) of ranging 29.47%–43.66%; CSR for NFl with RIM was 36.83%; and VPD for NFr and CWt with RIM were 37.37% and 29.37%, respectively. By MLR analysis, results showed the potential of using CHU, CSR, and VPD to describe and predict the growth indices of tomato clusters by mathematical models.

On the scaling behaviour and conformal properties of triangular Ising model with three-spin interactions at the critical point

The scaling behaviour and conformal properties of a triangular Ising model with three-spin interactions at the critical point are studied using extensive Monte Carlo simulations. We show that in the continuum limit the external perimeter of spin clusters are conformally invariant and statistically equivalent to Schramm–Loewner evolution (SLE κ ) curves with diffusivity κ = 4, indicating that the loop ensembles associated with the critical Ising model with three-spin interactions, belonging to the universality class of domain walls in the four-states Potts model. The left-passage probabilities, distribution of the winding angle, and the driving function distribution for the interfaces are consistent with each other. We also study many geometrical properties of the critical interfaces to characterize the fractal structure and the other scaling properties of conformal loop ensembles. To this end, the fractal dimension of contours, the scaling properties of length and areas distributions and Zipf’s laws, are demonstrated numerically. Our results are compatible with the hyper-scaling relation for spin models.

Low‐Temperature CO Oxidation over the Pt−TiN Interfacial Dual Sites

AbstractThe metal‐support interfacial synergistic catalysis allows the competitive reaction steps to occur in close proximity at different sites, thus decreasing the activation barrier and improving the catalytic efficiency. Combining the structural characterization, reactivity assessments and density functional theory (DFT) calculations, it is found that highly dispersed Pt clusters on TiN substrates favor the formation of Pt−TiN interfacial dual sites, which are highly reactive for the low‐temperature CO oxidation with an apparent activation energy as low as 38.7 kJ mol−1, much less than that on the traditional Pt/TiO2 or Pt/SiO2 catalysts. At low temperature, the surface sites of Pt are saturated with CO adsorption due to its high adsorption energy and the molecular O2 dissociatively adsorbs on the Ti sites to form the titanium oxynitride (TiNxOy) skin with a low barrier of 0.1 eV. The O atoms binding on Ti sites readily react with the adjacent CO molecules adsorbed on the perimeter of Pt clusters to attain a catalytic cycle with a reaction barrier of 0.5 eV. The interfacial synergistic effect between Pt and TiN is the origin of the low temperature CO oxidation activity on the metal‐nitride catalysts.

3D probabilistic cellular automation modeling of transition to fracture in rocks under loading

The three-dimensional model of the probabilistic cellular automaton, which has previously been constructed on the basis of the kinetic theory of strength, is studied in this paper. It describes the process of rock damage accumulation and formation of a damage cluster structure. Comparing the kinetic curves of damage accumulation and correlation functions of the model experiments, it is found that, depending on the sprouting probability of the damage cluster perimeter, which simulates the rate of material fracture under the action of local overstresses near the existing damage clusters, two qualitatively different modes of damage accumulation are observed in the 3D model. For the sprouting probabilities of the cluster perimeter higher than 0.2, the process of transition to irreversible fracture is significantly accelerated and becomes strongly correlated. Along with this, the best agreement of correlation functions in the model and in the physical experiments is observed for the sprouting perimeter probability values smaller than 0.2.

Morphological Differences between Liquid-Based Cytology and Conventional Preparation in Endometrial Endometrioid Carcinoma Grade 1 and Grade 3, and the Differentiation of Grades in Each Method

Introduction: Direct smearing preparation (conventional preparation [CP]) has been widely used for endometrial cytology in Japan. In CP, sampling and screening errors are problematic. In liquid-based cytology preparation (LBC), the problems of CP can be solved. But there is a problem that cytological findings of LBC are different from those of CP. The purpose of this study was to evaluate the differences of morphological findings of endometrial cytology between LBC and CP, and the usefulness of the endometrial LBC to differentiate endometrioid carcinoma grade 1 (G1) from grade 3 (G3). Methods: Thirteen cases of endometrioid carcinoma G1, and 5 cases of G3 collected by the Softcyte device and prepared by LBC and CP (split specimen) were used. We focused on the following items: (1) the number of clusters per cm², (2) the number of layers of clusters, (3) area of clusters, (4) perimeter of clusters, (5) roundness of clusters, (6) complexity of clusters, (7) area of nucleus, (8) perimeter of nucleus, (9) roundness of nucleus, (10) complexity of nucleus, (11) area of nucleolus, and (12) nucleolus-nucleus ratio (N/N). Results: Compared with CP, the number of clusters and layers of the clusters in LBC were significantly larger in G1. The area and perimeters of the clusters and the nucleus were significant smaller, and the N/N ratio was greater in LBC than that in CP in both G1 and G3. Regarding morphological differences between G1 and G3 in LBC and CP, the number of layers was significantly larger in G1 than in G3 in LBC and CP. The area of the clusters in LBC was significantly larger in G1 than in G3. The area and perimeters of the nucleus in CP and the area of the nucleolus and N/N ratio in LBC and CP were significantly smaller in G1 than in G3. Conclusion: In the endometrial cytology, it became clear that the cell image was different between LBC and CP and between G1 and G3. By microscopic examination understanding the characteristics of the cell image in LBC, endometrial LBC could be useful to diagnose endometrial carcinoma.

Study of Graphene-like Indium Phosphide

The semiconductor compounds in a state of graphene-like structure are the interesting object for both fundamental studies and technology. The two-dimensional material have unique electronic, structural, chemical and physical properties that plays a significant role for technology of new devices. Therefore the obtaining of various properties of that graphene-like materials and the understanding of the nature of chemical interaction with various species are important. In this work for the geometry optimisation graphene-like structure of indium phosphide the GAMESS program package [1] have been used. The electronic properties of g-InP has been obtained by ABINIT program package [2].Such species as hydrogen, oxygen and carbon are a part of many natural compositions of the environment. In this work the preferred adsorption sites for the H, O and C adatoms have been defined through the potential-energy profiles of its interacting with g-InP sheet.All ab initio calculations reported in this work were carried out using the Hartree-Fock method of GAMESS program package. The GAMESS was run on computers cluster of V.M.Glushkov Institute of Cybernetics of NAS of Ukraine [3]. Both STO-3G and 3-21G Pople style basis sets were used for C, H and O atoms. The g-InP sheet has been presented by cluster model with 48 In-atoms and 48 P-atoms in the hexagonal cells and 24 hydrogen atoms on the cluster perimeter. In the atomic-force probe technique the atom-probe (H, O or C) is moving above the surface of sheet on fixed distance without any optimization of its geometry. As a result the potential-energy (PE) profiles of interaction of the various atoms-probe with g-InP sheet have been obtained.[1] Gordon M.S., Schmidt M.W. // in "Theory and Applications of Computational Chemistry: the first forty years" by ed. C.E.Dykstra. - Elsevier, Amsterdam, 2005, p.1167-1189.[2] https://docs.abinit.org/topics/features/[3] http://www.icyb.kiev.ua/s/189/ua/klaster_ik.html Figure 1

Properties of Cracking Patterns of Multi-Walled Carbon Nanotube-Reinforced Cement Matrix.

The research presented in this paper presents a quantitative analysis of cracking patterns on the surface of cement paste, which has been modified by the addition of the multi-wall carbon nanotubes (MWCNTs). The cracking patterns analyzed were created as a result of increased temperature load. MWCNTs were used as an aqueous dispersion in the presence of a surfactant, sodium dodecyl sulfate (SDS). Four series of the cement paste were tested, and the samples differed in the water/cement (w/c) ratio, cement class, and the presence of MWCNTs. Image analysis tools were used to quantify the cracking patterns and it was proposed to measure parameters, such as the average cluster area, average cluster perimeter, average crack width, and crack density. In order to facilitate the image analysis process, the sample surface was subjected to preparation and using statistical analysis tools it was assessed whether the method of surface preparation affects the way the sample is cracked. The paper also presents the analysis of the relationships that occur between parameters describing the cracking patterns, and also with the physico-mechanical properties of the cement pastes. It was attempted to explain the dependencies using elements of fractal theory and the theory of dispersion systems.

Tree clusters in savannas result from islands of soil moisture

Tree clusters in savannas are commonly found in sizes that follow power laws with well-established exponents. We show that their size distributions could result from the space-time probabilistic structure of soil moisture, estimated over the range of rainfall observed in semiarid savannas; patterns of soil moisture display islands whose size, for moisture thresholds above the mean, follows power laws. These islands are the regions where trees are expected to exist and they have a fractal structure whose perimeter-area relationship is the same as observed in field data for the clustering of trees. When the impact of fire and herbivores is accounted for, as acting through the perimeter of the tree clusters, the power law of the soil moisture islands is transformed into a power law with the same exponents observed in the tree cluster data.

Valence bonds in planar and quasi-planar boron disks.

Planar and quasi-planar boron clusters with a disk-like shape are investigated in search of common bonding characteristics. Methods used involve molecular orbital calculations based on Density Functional Theory (DFT), and valence bond partitioning using Adaptive Natural Density Partitioning (AdNDP) analysis. For high-symmetry cases the proposed bonding schemes are confirmed using the group-theoretical induction method. The focus is on the electron occupation of delocalized in-plane 3-center and 4-center bonds. For disks consisting of concentric rings this inner electron count is found to be equal to a multiple of the vertex count of the inner polygon. For two concentric rings the multiplying factor is four, for three concentric rings it is eight. The appropriate bonding schemes are presented which explain these results. Some giant clusters with two hexagonal holes are also discussed.

Three-dimensional cellular automaton model for the destruction of brittle heterogeneous materials

The article investigates the evolution modes of cluster damage structure in brittle heterogeneous materials by using a three-dimensional probabilistic cellular automaton. By comparing the data of computer and physical experiments, there was established the essential role of the model parameter, which describes the intensity of the material destruction process under the influence of local overstress near the existing damage clusters - the probability of perimeter germination. The comparison of kinetic curves of damage accumulation and correlation functions showed that, depending on the probability value for damage cluster perimeter germination, two qualitatively different modes of evolution of damage accumulation process are observed. In this case, the best correspondence of correlation functions in model and physical experiment on pulsed electromagnetic emission is observed for perimeter germination probability values smaller than 0.2.

Ising ferromagnets in Ising-percolation square lattices, an example of Ising-Ising coupling

In this paper we consider the Ising model (called the dynamical Ising model with dynamical temperature $T$) on the Ising-correlated percolation lattice. To construct this lattice, another Ising model (which is called the quenched Ising model with quench artificial temperature ${T}_{q}$) is employed to model the correlations between imperfections. We argue that for each quenched temperature, there is a particular dynamical temperature ${T}_{c}({T}_{q})$ for which the dynamical Ising model becomes critical. We present some finite-size arguments (based on the moments of the magnetism and the energy as well as the spanning cluster probability) to extract the critical points and also show that they are compatible with the finite-size scaling of the singular point of the magnetic susceptibility. The model is thoroughly characterized in and out of these points. We find that the critical behaviors of the model change significantly with respect to the regular Ising model as well as the Ising model on the uncorrelated percolation lattice. It is shown that for the critical lattice, ${T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}}\ensuremath{\approx}2.269$, the critical temperature for the dynamical Ising model in the thermodynamic limit is ${T}_{c}({T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}})=1.94\ifmmode\pm\else\textpm\fi{}0.005$, and the fractal dimension of the exterior perimeter of geometrical spin clusters is ${D}_{f}^{T={T}_{c}({T}_{q}=2.269)}=1.408\ifmmode\pm\else\textpm\fi{}0.002$. Many quantities, such as the dynamical critical temperatures, all local and global critical exponents, and the fractal dimension of loops ${D}_{f}$, scale with the quench temperature in a power-law fashion, with some critical exponents that are reported. Significantly we see that ${D}_{f}^{T={T}_{c}({T}_{q})}\ensuremath{-}{D}_{f}^{T={T}_{c}({T}_{q}=2.269)}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\zeta}({T}_{q})}}$ in which $\ensuremath{\zeta}({T}_{q})$ is the correlation length of the quenched Ising model at temperature ${T}_{q}$.

Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We show numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H ∈ [−1, 0] is statistically equivalent to SLE curves. Our results suggest that the external perimeter also retains the Markovian properties, confirmed by the absence of time correlations in the driving function and the fact that the latter is Gaussian distributed for any specific time. We also confirm that for all H the variance of the winding angle grows logarithmically with size.

Analysis of the development of cluster cracks in the cement paste modified by microsilica

Article describes the course of research on the possibility of the application of the computer-based image analysis techniques to evaluate the structure of cluster cracks on the surface of modified cement paste. Four sets of specimens were performed, based on two Portland cements (CEM I 42,5R and CEM I 52,5R). In addition, the two series include microsilica as a substitute for 10% of cement. Cracks of samples were obtained by the sudden temperature load at the value of 250°C. Image of the cracked surface was obtained by scanning at a resolution of 2400DPI, and to digital processing and measurements ImageJ v. 1.46r software was used. To describe the structure of the cracks two stereological parameters were proposed: average cluster area (A) and average cluster perimeter (L). The aim of the work is to reference obtained results from the image analysis to the compressive and tensile strength of tested specimens. In addition, considering the structure of cement paste as a dispersion system the process of the cluster structures formation was described, which under external loads transform and affect the final properties of the composite material.

A two-stage method for microcalcification cluster segmentation in mammography by deformable models.

Segmentation of microcalcification (MC) clusters in x-ray mammography is a difficult task for radiologists. Accurate segmentation is prerequisite for quantitative image analysis of MC clusters and subsequent feature extraction and classification in computer-aided diagnosis schemes. In this study, a two-stage semiautomated segmentation method of MC clusters is investigated. The first stage is targeted to accurate and time efficient segmentation of the majority of the particles of a MC cluster, by means of a level set method. The second stage is targeted to shape refinement of selected individual MCs, by means of an active contour model. Both methods are applied in the framework of a rich scale-space representation, provided by the wavelet transform at integer scales. Segmentation reliability of the proposed method in terms of inter and intraobserver agreements was evaluated in a case sample of 80 MC clusters originating from the digital database for screening mammography, corresponding to 4 morphology types (punctate: 22, fine linear branching: 16, pleomorphic: 18, and amorphous: 24) of MC clusters, assessing radiologists' segmentations quantitatively by two distance metrics (Hausdorff distance-HDISTcluster, average of minimum distance-AMINDISTcluster) and the area overlap measure (AOMcluster). The effect of the proposed segmentation method on MC cluster characterization accuracy was evaluated in a case sample of 162 pleomorphic MC clusters (72 malignant and 90 benign). Ten MC cluster features, targeted to capture morphologic properties of individual MCs in a cluster (area, major length, perimeter, compactness, and spread), were extracted and a correlation-based feature selection method yielded a feature subset to feed in a support vector machine classifier. Classification performance of the MC cluster features was estimated by means of the area under receiver operating characteristic curve (Az ± Standard Error) utilizing tenfold cross-validation methodology. A previously developed B-spline active rays segmentation method was also considered for comparison purposes. Interobserver and intraobserver segmentation agreements (median and [25%, 75%] quartile range) were substantial with respect to the distance metrics HDISTcluster (2.3 [1.8, 2.9] and 2.5 [2.1, 3.2] pixels) and AMINDISTcluster (0.8 [0.6, 1.0] and 1.0 [0.8, 1.2] pixels), while moderate with respect to AOMcluster (0.64 [0.55, 0.71] and 0.59 [0.52, 0.66]). The proposed segmentation method outperformed (0.80 ± 0.04) statistically significantly (Mann-Whitney U-test, p < 0.05) the B-spline active rays segmentation method (0.69 ± 0.04), suggesting the significance of the proposed semiautomated method. Results indicate a reliable semiautomated segmentation method for MC clusters offered by deformable models, which could be utilized in MC cluster quantitative image analysis.

An Atomic‐Scale View of CO and H2 Oxidation on a Pt/Fe3O4 Model Catalyst

AbstractMetal–support interactions are frequently invoked to explain the enhanced catalytic activity of metal nanoparticles dispersed over reducible metal oxide supports, yet the atomic‐scale mechanisms are rarely known. In this report, scanning tunneling microscopy was used to study a Pt1‐6/Fe3O4 model catalyst exposed to CO, H2, O2, and mixtures thereof at 550 K. CO extracts lattice oxygen atoms at the cluster perimeter to form CO2, creating large holes in the metal oxide surface. H2 and O2 dissociate on the metal clusters and spill over onto the support. The former creates surface hydroxy groups, which react with the support, ultimately leading to the desorption of water, while oxygen atoms react with Fe from the bulk to create new Fe3O4(001) islands. The presence of the Pt is crucial because it catalyzes reactions that already occur on the bare iron oxide surface, but only at higher temperatures.

An Atomic-Scale View of CO and H2 Oxidation on a Pt/Fe3 O4 Model Catalyst.

Metal-support interactions are frequently invoked to explain the enhanced catalytic activity of metal nanoparticles dispersed over reducible metal oxide supports, yet the atomic-scale mechanisms are rarely known. In this report, scanning tunneling microscopy was used to study a Pt1-6/Fe3O4 model catalyst exposed to CO, H2, O2, and mixtures thereof at 550 K. CO extracts lattice oxygen atoms at the cluster perimeter to form CO2, creating large holes in the metal oxide surface. H2 and O2 dissociate on the metal clusters and spill over onto the support. The former creates surface hydroxy groups, which react with the support, ultimately leading to the desorption of water, while oxygen atoms react with Fe from the bulk to create new Fe3O4(001) islands. The presence of the Pt is crucial because it catalyzes reactions that already occur on the bare iron oxide surface, but only at higher temperatures.