Two-dimensional Distribution Function Research Articles

Modelling of water sorption hysteresis of cement-based materials based on pore microstructure

This paper presents a model for predicting water sorption isotherms of cement-based materials. In this model, hysteresis contributions of interlayer pores and gel/capillary pores are calculated separately. The hysteresis model of gel/capillary pores is achieved in four steps: (i) quantification of the pore network, (ii) determination of the criterion of saturation/desaturation of pores, (iii) derivation of the two-dimensional volumetric density distribution function, (iv) calculation of the real-time water content of gel/capillary pores. The hysteresis of interlayer pores is represented by an empirical model based on experiments. The reliability of the model is verified by comparing the model predictions and the experimental data in the literatures. Furthermore, three subjects were discussed: the influence of pore network on hysteresis, the hysteretic behavior of water in pores, the interaction of hysteresis mechanisms.

Establishment of fog droplet distribution model and study on canopy deposition uniformity

In plant protection operations, the distribution of droplets affects the atomization effect. To make the distribution of fog droplets more uniform in the air field, a fog droplet distribution model was established based on a three-dimensional motion model of droplets and the particle size distribution function, combined with a two-dimensional normal distribution function. The effects of the initial incidence angle and the additional wind speed on the distribution of fog droplets were analyzed. The fog droplet distribution was simulated to analyze the droplet distribution in the spatial layer, which was compared with the experimental results. To investigate the impacts of different factors on the atomization distribution, the Lagrangian interpolation method was employed, and the optimal initial incidence angle and external wind speed were found. When the initial angle of incidence was 17°, the slope of the fitted curve was the smallest, with a coefficient of determination of 0.9622 and a relative error of 3.12%. With an additional wind speed of 0.1 m/s, the coefficient of determination was 0.9782, with an average error of 4.61%. The simulation results were consistent with the experimental findings, and the accuracy of the fog droplet distribution model was verified. In summary, this research provides a novel method to improve the uniformity of the droplet distribution, which can provide a theoretical basis for determining the operating parameters.

High-resolution spectroscopy of LaAlO3-Pr3+ pseudo-cubic perovskite single crystals: Crystal-field parameters, hyperfine and deformation splittings

We report high-resolution measurements and analysis of the optical transmission and emission spectra of a concentration series of La(1-x)PrxAlO3 (x = 10−3, 9 ⋅ 10−3, and 2 ⋅ 10−2) single crystals in a wide frequency range ((2-27) ⋅ 103 cm−1) at temperatures 5–300 K, below the structural phase transition from the cubic Pm3‾m to the rhombohedral R3‾c phase. Pr3+ ions substitute for La3+ ions at sites with point symmetry D3. All recorded spectral lines are assigned to specific initial and final crystal-field (CF) energy levels, the scheme of CF levels is constructed and described by an appropriate set of CF parameters. The structural phase transition is accompanied by shear strains and the formation of ferroelastic twin domains of four types compressed along one of the four C3 axes in the parent cubic crystal lattice. Specific features of the measured spectra, namely, anomalous broadening of spectral lines and doublet structure of some lines corresponding to transitions between CF singlets and doublets, are considered as a result of interaction of 4f electrons with the field of random shear deformations competing at the boundaries of twin domains. Modeling of the observed line shapes was performed taking into account both hyperfine interactions and random lattice strains, as well as the effect of temperature. The width (6.6 ± 0.7)⋅10− 4 of the introduced two-dimensional distribution function of random strains was found from a comparison of simulated and measured profiles of the split spectral lines. The results of this work can be applied for quantitative assessment of crystal quality.

Novel two-dimensional Wigner distribution and ambiguity function in the framework of the two-dimensional nonseparable linear canonical transform

Novel two-dimensional Wigner distribution and ambiguity function in the framework of the two-dimensional nonseparable linear canonical transform

Molecular simulation of bulk and confined (1,1,1,3,3-pentafluorobutane)

Here we present a computational study of the thermodynamic and structural properties of bulk and confined (1,1,1,3,3-pentafuorobutane). The DREIDING force field model has been used in the method of molecular dynamics. In order to study the effect of confinement we have placed (1,1,1,3,3-pentauorobutane) molecules between two graphene walls. In order to study the influence of pore loading on system behavior we have simulated systems of the same size, but with a different number of (1,1,1,3,3-pentauorobutane) molecules, from 200 to 2000. The equations of state at T = 300 K in a wide range of densities for all considered systems had a single peculiarity that is attributed to gas-liquid transition. From the two-dimensional radial distribution functions, density profile and angular distribution we have observed the systems split into layers with amorphization rather than crystallization in them.

Study on the plasma plume structures in a cylindrical Hall thruster

The structures of two typical plume modes (divergent and convergent plume) and their respective formation mechanisms in a cylindrical Hall thruster are investigated. The non-monotonic distribution of the two-dimensional ion energy distribution function map is obtained to segment the plume into 5 levels with different energy interval. The test results of the ion current fraction indicate that the ion beams in Level III and IV were the main components of the two plume modes. For Level IV (enhanced significantly in the convergent mode), these ions with focusing structure could only originate from the upstream E × B field due to their similar high potential and identical variation tendency in the mode transition, where the electric field converges towards the axis. This is mainly responsible for the formation of convergent mode. On the other hand, for Level III (dominating the divergent mode), these ions with hollow structure and less acceleration voltage are speculated to originate from the downstream magnetic mirror field, where the electric field manifests a defocusing characteristic along the diverging magnetic field lines. This is mainly responsible for the formation of divergent mode. Through the thrust equivalent calculation method, it is revealed that the upstream acceleration associated with the E × B field is the dominant contributor to the enhancement of thrust in the convergent mode. This study on the complex plume structure would facilitate the understanding of the CHT acceleration mechanism and provide useful ideas for the optimization of electric field structure and enhancement of plume efficiency.

Two-Dimensional Analytical Models for Cogging Torque Prediction in Interior Permanent Magnet Machine

Analytical prediction of cogging torque needs accurate flux density and relative permeance closed-form expressions. The accurate two-dimensional (2D) air gap flux density distribution function and the 2D permeance function are currently almost always applied to surface-mounted permanent magnet (SPM) machines, instead of interior permanent magnet (IPM) machines, due to complications from IPMs severe magnetic saturation and leakage flux. To address these issues, this paper proposes a set of new methods to derive the accurate closed-form 2D expressions of IPMs for both flux density and relative permeance. As for the flux density 2D model, a virtual equivalence model for IPM is introduced, so that Laplace’s equation and quasi-Poisson equation can be directly applied to IPM. As for permeance, the same virtual equivalence model also enables 2D models derivation for IPM. Subsequently, the resulting cogging torque analytical expression is obtained with the accurate relative permeance and air gap flux density models. The results from the proposed 2D analytical models showed similar accuracy to the finite element analysis (FEA). In addition, as demonstrated, the proposed 2D analytical models is a highly efficient tool set in the design process of cogging torque optimization, facilitating fast evaluation of different design factors.

Моделирование процесса приема собственного радиотеплового излучения земной поверхности

The receiving model of the own soil radiothermal radiation by a bipolarized microwave radiometer when remote sensing the soil moisture from an unmanned aerial vehicle on low altitude is considered. The simulation is carried out taking into account the receiving antenna pattern with side lobes. The height, speed of the carrier and the main lobe axis angle are taken into account. The main parameters of the microwave radiometer for remote determination of portraits of moistened soils are given. The Earth's surface is modeled by a two-dimensional distribution function of the soil permittivity on the thickness of the near-surface layer and a deeper layer with a different permittivity value. The two-dimensional permittivity distribution function represents as "checkerboard" with a periodic change in the permittivity of the soil by "cells". Both the proper radiothermal radiation of the soil and the relict sky radiation of the celestial sphere, re-reflected by the earth's surface, are taken into account. The perspective of using the simulation results to optimize the parameters of the radiometer and remote sensing system according to the criterion of maximum sensitivity of the system to variations in soil moisture content is analyzed.

Computing Individual Area per Head Group Reveals Lipid Bilayer Dynamics.

Lipid bilayers express a range of phases from solid-like to gel-like to liquid-like as a function of temperature and lipid surface concentration. The area occupied per lipid head group serves as one useful indicator of the bilayer phase, in conjunction with the two-dimensional radial distribution function (i.e., structure factor) within the bilayer. Typically, the area per head group is determined by dividing the bilayer area equally among all head groups. Such an approach is less satisfactory for a multicomponent set of diverse lipids. In this work, area determination is performed on a lipid-by-lipid basis by attributing to a lipid the volume that surrounds each atom. Voronoi tessellation provides this division of the interfacial region on a per-atom basis. The method is applied to a multicomponent system of water, NaCl, and 19 phospholipid types that was devised recently [Langmuir2022, 38, 9481-9499] as a computational representation of the Gram-positive Staphylococcus aureus phospholipid bilayer. Results demonstrate that lipids and water molecules occupy similar extents of area within the interfacial region; ascribing area only to head groups implicitly incorporates assumptions about head group hydration. Results further show that lipid tails provide non-negligible contributions to area on the membrane side of the bilayer-water interface. Results for minimum and maximum area of individual lipids reveal that spontaneous fluctuations displace head groups more than 10 Å from the interfacial region during an NPT simulation at 310 K, leading to a zero contribution to total area at some times. Total area fluctuations and fluctuations per individual lipid relax with a correlation time of ∼10 ns. The method complements density profile as an approach to quantify the structure and dynamics of computational lipid bilayers.

Molecular dynamics simulations of the human ocular lens with age and cataract

The human ocular lens consists primarily of elongated, static fibers characterized by high stability and low turnover, which differ dramatically in their composition and properties from other biological membranes. Cholesterol (Chol) and sphingolipids (SL) are present at high concentrations, including saturated SLs, such as dihyrosphingomyelin (DHSM). Past molecular dynamics simulations demonstrated that the presence of DHSM and high Chol concentration contributes to higher order in lipid membranes. This current study simulated more complex models of human lens membranes. Models were developed representing physiological compositions in cataractous lenses aged 74 ± 6 years and in healthy lenses aged 22 ± 4, 41 ± 6, and 69 ± 3 years. With older age, Chol and ceramide concentrations increase and glycerophospholipid concentration decreases. With cataract, ceramide concentration increases and Chol and glycerophospholipid concentrations decrease. Surface area per lipid, deuterium order parameters (SCD), sterol tilt angle, electron density profiles, bilayer thickness, chain interdigitation, two-dimensional radial distribution functions (2D-RDF), lipid clustering, and hydrogen bonding were calculated for all simulations. All systems exhibited low surface area per lipid and high bilayer thickness, indicative of strong vertical packing. SCD parameters suggest similarly, with saturated tails in the hydrophobic core of the membrane having elevated order. Vertical packing and acyl tail order increased with both age and cataract condition. Lateral diffusion decreased with age and cataracts, with the older and cataractous models demonstrating increased long-range structure by the 2D-RDF analysis. In future work examining the membrane proteins of the lens, these models can serve as a physiologically accurate representation of the lens lipidome.

Detection of Standing Dead Trees after Pine Wilt Disease Outbreak with Airborne Remote Sensing Imagery by Multi-Scale Spatial Attention Deep Learning and Gaussian Kernel Approach

The continuous and extensive pinewood nematode disease has seriously threatened the sustainable development of forestry in China. At present, many studies have used high-resolution remote sensing images combined with a deep semantic segmentation algorithm to identify standing dead trees in the red attack period. However, due to the complex background, closely distributed detection scenes, and unbalanced training samples, it is difficult to detect standing dead trees (SDTs) in a variety of complex scenes by using conventional segmentation models. In order to further solve the above problems and improve the recognition accuracy, we proposed a new detection method called multi-scale spatial supervision convolutional network (MSSCN) to identify SDTs in a wide range of complex scenes based on airborne remote sensing imagery. In the method, a Gaussian kernel approach was used to generate a confidence map from SDTs marked as points for training samples, and a multi-scale spatial attention block was added into fully convolutional neural networks to reduce the loss of spatial information. Further, an augmentation strategy called copy–pasting was used to overcome the lack of efficient samples in this research area. Validation at four different forest areas belonging to two forest types and two diseased outbreak intensities showed that (1) the copy–pasting method helps to augment training samples and can improve the detecting accuracy with a suitable oversampling rate, and the best oversampling rate should be carefully determined by the input training samples and image data. (2) Based on the two-dimensional spatial Gaussian kernel distribution function and the multi-scale spatial attention structure, the MSSCN model can effectively find the dead tree extent in a confidence map, and by following this with maximum location searching we can easily locate the individual dead trees. The averaged precision, recall, and F1-score across different forest types and disease-outbreak-intensity areas can achieve 0.94, 0.84, and 0.89, respectively, which is the best performance among FCN8s and U-Net. (3) In terms of forest type and outbreak intensity, the MSSCN performs best in pure pine forest type and low-outbreak-intensity areas. Compared with FCN8s and U-Net, the MSSCN can achieve the best recall accuracy in all forest types and outbreak-intensity areas. Meanwhile, the precision metric is also maintained at a high level, which means that the proposed method provides a trade-off between the precision and recall in detection accuracy.

Assessing the benefits of Imaging Infrared Radiometer observations for the CALIOP version 4 cloud and aerosol discrimination algorithm

Abstract. The features detected in monolayer atmospheric columns sounded by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and classified as cloud or aerosol layers by the CALIOP version 4 (V4) cloud and aerosol discrimination (CAD) algorithm are reassessed using perfectly collocated brightness temperatures measured by the Imaging Infrared Radiometer (IIR) aboard the same satellite. Using the IIR's three wavelength measurements of layers that are confidently classified by the CALIOP CAD algorithm, we calculate two-dimensional (2-D) probability distribution functions (PDFs) of IIR brightness temperature differences (BTDs) for different cloud and aerosol types. We then compare these PDFs with 1-D radiative transfer simulations for ice and water clouds and dust and marine aerosols. Using these IIR 2-D BTD signature PDFs, we develop and deploy a new IIR-based CAD algorithm and compare the classifications obtained to the results reported by the CALIOP-only V4 CAD algorithm. IIR observations are shown to be able to identify clouds with a good accuracy. The IIR cloud identifications agree very well with layers classified as confident clouds by the V4 CAD algorithm (88 %). More importantly, simultaneous use of IIR information reduces the ambiguity in a notable fraction of “not confident” V4 cloud classifications. 28 % and 14 % of the ambiguous V4 cloud classifications are reclassified more appropriately as confident cloud layers through the use of the IIR observations in the tropics and in the midlatitudes, respectively. IIR observations are of relatively little help in deriving high-confidence classifications for most aerosols, as the low altitudes and small optical depths of aerosol layers yield IIR signatures that are similar to those of clear skies. However, misclassifications of aerosol layers, such as dense dust or elevated smoke layers, by the V4 CAD algorithm can be corrected to cloud layer classification by including IIR information. 10 %, 16 %, and 6 % of the ambiguous V4 dust, polluted dust, and tropospheric elevated smoke, respectively, are found to be misclassified cloud layers by the IIR measurements.

Microstructure of the fluid particles around the rigid body at the shear-thickening state toward understanding of the fluid mechanics

We studied the shear-thickening behavior of systems containing rigid spherical bodies immersed in smaller particles using non-equilibrium molecular dynamics simulations. We generated shear-thickening states through particle mass modulation of the systems. From the microstructures, i.e., two-dimensional pair distribution functions, we found anisotropic structures resulting from shear thickening, that are explained by the difference between the velocities of rigid bodies and fluid particles. The increasing viscosity in our system originated from collisions between fluid particles and rigid bodies. The lubrication forces defined in macroscale physics are then briefly discussed.

Algorithm for assessing changes in the functional state of muscles of the maxillofacial area of athletes using individual relaxation occlusal splints or mouth guards

The paper proposes an algorithm for assessing changes in the functional state of bilaterally located muscles. The proposed algorithm is based on the analysis of two-dimensional distribution function and two-dimensional probability density of the amplitude of electromyograms of the muscles under study. The paper proposes criteria for assessing the symmetry and asymmetry of muscle activity, presents the results of the study of changes in the functional state of the temporalis muscles and the masseter muscles for a group of athletes. During sports competitions and preparing to them, athletes are exposed to high physical and emotional stress which leads to a premature decrease in the functional activity of the muscles causing changes in the biomechanics of movements. The reasons that lead to a decrease in the functional activity of the muscles are as follows: occlusal disharmony; changes in bite and / or interalveolar distance, hypertonicity of the muscles of the maxillofacial region. Ultimately, these reasons lead to a deterioration in sports performance. The group of the athletes under study involved 10 males aged 23 to 24 years, who are engaged in combat sports at a professional level. Each athlete underwent a clinical examination, palpation and isometric tests of the muscles of the maxillofacial region (MR) and temporomandibular joints (TMJ), auscultation of the TMJ, control of occlusion (using copy paper and T-scan apparatus), cone-beam computed tomography (CBCT) of the dentoalveolar system (DAS) and electromyography (EMG) of the muscles of the maxillofacial region. At this stage of the research, each athlete received individual relaxation occlusal splints or mouthguards of two types: 2.0 mm thick soft one and 3.0 mm thick semi-rigid one. It was recommended to the athletes that they should wear the splints for 1–2 months in the following manner: to wear 2.0 mm thick soft splint on an ongoing basis, excluding food intakes and the training process, whereas 3.0 mm thick semi-rigid splints should be used during the training process and other types of physical activity, as well as at competitions.

New Two-Dimensional Wigner Distribution and Ambiguity Function Associated with the Two-Dimensional Nonseparable Linear Canonical Transform

New Two-Dimensional Wigner Distribution and Ambiguity Function Associated with the Two-Dimensional Nonseparable Linear Canonical Transform

Recovery of the Two-Dimensional Ion Distribution Function in a Magnetic Mirror from Measurements of Collective Thomson Scattering Spectra

A method is proposed for tomography of the distribution function of energetic ions that are adiabatically trapped in an open magnetic trap, according to the diagnostic data by the method of collective Thomson scattering. This method is based on measurements of the scattering spectra from successive plasma cross sections corresponding to different values of the magnetic-field strength along a single line of force. It is shown that the problem of restoring the ion distribution function in the velocity space from the measurement data in this situation is reduced to an integral equation of the first kind that allows an analytical solution. Several ways to construct exact and approximate solutions of the resulting integral equation are considered.

Molecular Simulations of Ocular Lens Membranes at Various Stages of Age and Cataract

The human ocular lens consists primarily of elongated, static fibers characterized by high stability and low turnover, which differ dramatically in their composition and properties from other biological membranes. Cholesterol (Chol) and sphingolipids (SL) are present at high concentrations, including saturated SLs, such as dihyrosphingomyelin. Past molecular dynamics (MD) simulations demonstrated that the presence of DHSM and high Chol concentration contributes to higher order in lipid membranes. Using the CHARMM36 all-atom force field, this study simulated more complex models of human lens membranes with the inclusion of lysolipids and plasmanyl lipids. Models were developed representing physiological compositions in cataractous lenses aged 74±6 years and in healthy lenses aged 22±4, 41±6, and 69±3 years. With older age, Chol and ceramide concentrations increase and glycerophospholipid concentration decreases. With cataract, ceramide concentration increases and Chol and glycerophospholipid concentrations decrease. Surface area per lipid, deuterium order parameters (SCD), sterol tilt angle, electron density profiles (EDP), bilayer thickness, chain interdigitation, two-dimensional radial distribution functions (2D-RDF), mean-square displacement, lipid clustering, and hydrogen bonding were calculated for all simulations. All systems exhibited low surface area per lipid and high bilayer thickness, indicative of strong vertical packing. SCD parameters suggest similarly, with saturated tails in the hydrophobic core of the membrane having order parameter exceeding 0.4. Vertical packing and acyl tail order increased with both age and cataract. Lateral diffusion decreased with age and cataracts, with the older and cataractous models demonstrating increased long-range structure by the 2D-RDF analysis. Experimental results have found crystallization of Chol in older lenses, which similarly indicates increased order. In future work examining the membrane proteins of the lens, these models can serve as physiologically accurate representations of the lens lipidome.

Method for determining the two-dimensional current density distribution function over the radiating structure based on chiral metamaterials

The article is devoted to the development of a method of electrodynamic analysis and a two-dimensional mathematical model of strip radiating structures based on the apparatus of hypersingular equations in order to ensure the correct calculation of their characteristics when using relatively small computational resources. A system of hypersingular integral equations with respect to the unknown transverse and longitudinal components of the current density distribution functions is obtained. This system of hypersingular equations was solved using the collocation method, where Gaussian nodes (zeros of Legendre polynomials) were used as collocation points. This approach allows for faster convergence compared to uniform partitioning. Numerical results of calculations of current density distribution functions for various parameters of the radiating structure based on chiral metamaterials are obtained. It is shown that in the case of wide emitters, it is necessary to take into account both components of the current density distribution function. The advantage of this method in comparison with universal analogues is the ability to accurately calculate the characteristics of radiating structures based on chiral metamaterials with wide emitters.

Investigation of iron carbide (Fe3C) corrosion in water and acidic solution using ReaxFF molecular dynamics

The corrosion of iron carbide was investigated in the water at 298 K and 500 K as a weak electrolyte and a solution of hydrochloric acid at 298 K, using the reactive force field molecular dynamics. The thickness of the passive film, the formed species, and two-dimensional radial distribution function were investigated. The species FeO5H10, FeO4H8, and FeO3H6 were recognized as the products of corrosion reaction in the water at 500 K and FeO5H10, FeO4H8, and FeO5H9 in acidic solution at 298 K. The quantum mechanics calculations have shown that the more stable products in water and acidic solution are FeO4H8 and FeO5H9, respectively.

Transport of hydrated nitrate and nitrite ions through graphene nanopores in aqueous medium.

Nitrate ( ) and nitrite ( ) ions are naturally occurring inorganic ions that are part of the nitrogen cycle. High doses of these ions in drinking water impose a potential risk to public health. In this work, molecular dynamics simulations are carried out to study the passage of nitrate and nitrite ions from water through graphene nanosheets (GNS) with hydrogen-functionalized narrow pores in presence of an external electric field. The passage of ions through the pores is investigated through calculations of ion flux, and the results are analyzed through calculations of various structural and thermodynamic properties such as the density of ions and water, ion-water radial distribution functions, two-dimensional density distribution functions, and the potentials of mean force of the ions. Current simulations show that the nitrite ions can pass more in numbers than the nitrate ions in a given time through GNS hydrogen-functionalized pore of different geometry. It is found that the nitrite ions can permeate faster than the nitrate ions despite the former having higher hydration energy in the bulk. This can be explained in terms of the competition between the number density of the ions along the pore axis and the free energy barrier calculated from the potential of mean force. Also, an externally applied electric field is found to be important for faster permeation of the nitrite over the nitrate ions. The current study suggests that graphene nanosheets with carefully created pores can be effective in achieving selective passage of ions from aqueous solutions.