Two-dimensional Model Research Articles

A Simple Approach to Simulate Logjams in Two-Dimensional Hydrodynamic Models

A Simple Approach to Simulate Logjams in Two-Dimensional Hydrodynamic Models

In Ukrainian

The contact wetting is one of the effective methods of studying the adsorption capacity of sorbents. The purpose of the work was to compare the experimentally obtained data on the adsorption capacity of shungite, obtained by the sessile drop method, and the results of modeling the behavior of liquid droplets on heterogeneous surfaces using the Boltzmann lattice method, and to show the suitability of the simplified version of the LBM method that we applied within the framework of a two-dimensional model for modeling complex cases of contact interaction between liquids and sorbent, when it cannot be carried out by the method of contact wetting. The adsorption properties of shungite with regard to the extraction of various impurities from water-alcohol solutions and the capability of the sorbent to recover were investigated by the method of contact wetting and analyzed by involving the data obtained by the methods of nitrogen adsorption, thermogravimetry and IR spectroscopy. It is shown that the adsorption properties of shungite are due to the presence on its surface of hydroxyl functional groups attached to carbon atoms in phenol or enol form, which give the surface hydrophilic characteristics. These groups play a key role in the adsorption of components from the liquid (aqueous) phase due to the formation of a hydrogen bond during the sorption of components from the liquid phase, and are restored after heating in the temperature range of 80–180 °C with the formation of carbon-containing gases and water. It has been found that silanol groups present in shungite do not participate in sorption. Compared to the original shungite sample, the sample after five cycles of adsorption is characterized by a noticeable effect of mass loss (1.8 %) in the temperature range of 80–180 °С. At the same time, the loss of mass is not significant at temperatures below 100 °С. This suggests that the sorbed substances are in the pores and not on the surface of shungite, and they begin to be removed only after heating above 100 °C. The LBM method was used to study fast-moving processes at the meso-level. A comparative analysis of the experimental data obtained by the method of contact wetting with the results of simulation by the Boltzmann lattice method within the framework of the two-dimensional model was carried out. 2D modeling by the LBM method turned out to be an effective means of studying capillary condensation in mesopores, anticipatory wetting of the solid phase, liquid penetration into a porous medium with different topologies, and the formation of anisotropic droplets and anisotropic bridges. The role of mesopores in the sorption process was analyzed by modeling the behavior of liquid droplets on heterogeneous surfaces and using data on the course of adsorption and capillary processes on the surface of a solid phase with different levels of porosity, roughness, and functional composition.

Accurate two-dimensional simulation model and experimental demonstration in ultraviolet picosecond laser scribing ablation

Laser patterning of copper thin films is essential for the electronics manufacturing industry. In this work, to efficiently and accurately describe the physics process of UV-ps laser ablating copper thin film, a two-temperature model (TTM) consisting of the electron-lattice system and phase explosion mechanism was proposed. The process of electron heating and electron-lattice heat transfer in single pulse ablation were revealed. The average relative errors (ARE) of simulated ablation depth and width were 6.24% and 4.82%, respectively. The process of laser scribing ablation presents the characteristics of repeated ablation in the overlapping ablation region and new ablation in the non-overlapping region. The physics essence of laser scribing is the multiple laser ablations with different energies on the cross-section. The laser scribing cross-section ablation was simulated on 2D TTM. Compared with 3D simulation, though the ARE of ablation depth and width of 2D simulation slightly increased from 15.81% and 5.69% to 18.96% and 8.76%, respectively, the average solving time decreased significantly, from 81960 s to 2140 s. This comprehensive study aims to offer some insights into the characteristics of UV-ps laser ablation of copper thin film.

Explanations for the positive storm surges on the left side of landfall typhoons in China

The coastal regions of Southeast China frequently experience unusual positive storm surges on the left side of landfalling typhoons, a phenomenon historically overlooked and inadequately explained by conventional circular wind field models. In this study, a high resolution, two-dimensional storm surge model based on ADCIRC along with tide gauge data were used to investigate the spatiotemporal distribution of these surges and proposes underlying mechanisms, informed by a comparative analysis of circular and ERA5 reanalysis wind fields during typical typhoon event 9711 Winnie. Analyzing tide gauge data spanning from 1986 to 2016, the study uncovers a distinct pattern of left-side positive storm surges along the southeastern coast, notably on the Fujian coast and within the Taiwan Strait, which are found to be comparable to those on the cyclone’s right side. The research also documents a significant escalation in both the frequency and intensity of these left-side surges over the past three decades. Simulation results highlights the inadequacies of circular wind field models in operational forecasting and emphasizes the necessity of accounting for topographic influences and the structural complexity of wind fields in storm surge predictions. This is particularly pertinent in semi-enclosed seas with intricate hydrodynamics, such as the Taiwan Strait. The insights gleaned from this study are pivotal for enhancing the real-time simulation and prediction of storm surges, which are vital for coastal safety and disaster prevention measures.

Natural scenes reveal diverse representations of 2D and 3D body pose in the human brain

Human pose, defined as the spatial relationships between body parts, carries instrumental information supporting the understanding of motion and action of a person. A substantial body of previous work has identified cortical areas responsive to images of bodies and different body parts. However, the neural basis underlying the visual perception of body part relationships has received less attention. To broaden our understanding of body perception, we analyzed high-resolution fMRI responses to a wide range of poses from over 4,000 complex natural scenes. Using ground-truth annotations and an application of three-dimensional (3D) pose reconstruction algorithms, we compared similarity patterns of cortical activity with similarity patterns built from human pose models with different levels of depth availability and viewpoint dependency. Targeting the challenge of explaining variance in complex natural image responses with interpretable models, we achieved statistically significant correlations between pose models and cortical activity patterns (though performance levels are substantially lower than the noise ceiling). We found that the 3D view-independent pose model, compared with two-dimensional models, better captures the activation from distinct cortical areas, including the right posterior superior temporal sulcus (pSTS). These areas, together with other pose-selective regions in the LOTC, form a broader, distributed cortical network with greater view-tolerance in more anterior patches. We interpret these findings in light of the computational complexity of natural body images, the wide range of visual tasks supported by pose structures, and possible shared principles for view-invariant processing between articulated objects and ordinary, rigid objects.

Existence of long-range magnetic order in Heisenberg spin nanoribbons with edge modification

Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature, although no spontaneous magnetization exists in a one- or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin–Wagner theorem. By use of the spin Green’s function method, we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature, whether the decorated edge spins of the system link together or separate from each other. When the width of the nanoribbon achieves infinite limit, the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon. The results reveal that the magnetism of a low-dimensional spin system is different from that of a three-dimensional spin system. When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally, various useful long-range magnetic orders of the system can be obtained. This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.

1,3-Dioxolane production via reactive distillation combined with vapor permeation: Experiments and modelling

To overcome the problem of difficult separation of the 1,3-dioxane (DOL)–H2O azeotrope in the production of DOL, a new process via reactive distillation (RD) combined with vapor permeation (VP) was established. The reliability of the RD model has been reported in the literature. The VP membrane used an Aspen Custom Modeler (ACM) self-built model, with the permeation parameters of H2O, DOL, and formaldehyde (FA) in the membrane flux equation fitted through the H2O-DOL-FA dehydration experiments by NaA zeolite membrane. The results showed that the relative error between the mass of H2O in a series of permeates in experiments and simulated by the VP model was mainly within 20%, and R2 is 0.94. For DOL and FA, which have very small permeation, the value was within 50%, implying the reliability of the VP model. On this basis, a two-dimensional VP model was established. Finally, a new RD-VP-D process for producing DOL was designed. The VP was used to overcome the azeotropic point of DOL and H2O by dehydration. Then 99.9 wt% DOL can be obtained at the bottom of the subsequent DOL purification column, with DOL- H2O azeotrope at the top recycled back to the VP membrane. The effects of the degree of VP dehydration and column pressure on membrane area, reboiler duty, and TAC were investigated, meanwhile introducing a new concept: logarithmic mean partial-pressure difference (LMPD). Under the optimal parameter, TAC was reduced by 20.0% compared with the process reported in the literature, and CO2 emissions were reduced by 35.8%.

Numerical investigation of the effect of operating conditions on performance of PV-PCM system

The photovoltaic module only manages to convert around 15% of the incoming light into usable electricity and the rest is lost as heat, reducing the module's overall efficiency. Hybrid photovoltaic thermal systems are therefore the best way to collect thermal and electrical energy. The cooling and heat storage benefits of PV cells are amplified using phase change materials (PCMs). In this article, a simple two-dimensional CFD model to forecast the temperature of the PV where it contacts the PCM. The findings of the numerical simulations show that PV systems equipped with PCM have been studied under a variety of situations. A contemporary thermodynamic study is performed to examine system behaviour under different operating settings by investigating the effect of some rather crucial aspects that have not been taken into account before. The research takes into account three instances, each with its own unique combination of wind speed, ambient temperature, and sun irradiation. It has been shown that the solar radiation is a key component for growth in the PV temperature. The findings show that an increase in PV temperature of 5–7°C is caused by an increase in solar irradiance of 1000 W/m2. The rise in wind velocity, heat dissipation rate increases resulting to the fall in the temperature of the PCM and glass, the decrease in PCM temperature leads to a further drop in glass temperature. More so than wind speed or solar irradiation, ambient temperature determines how quickly PV glass heats up. Furthermore, at an ambient temperature of 35°C, PCM is found to melt entirely in 435 min, whereas at an ambient temperature of 30°C, PCM melts up to a liquid fraction of 0.77 min. Therefore, the efficiency of the PV system improves dramatically as the outside temperature is lowered.

Theoretical prediction of soft-forming micro-hemispherical shells from fused silica substrates in reclining mold

A reclining mold can support the soft forming of fused silica substrates into micro-hemispherical shells with the same height, which makes the processing of micro-hemispherical shells attractive. Currently, it is difficult to determine the optimal process parameters for machining micro-hemispherical shells, and several iterations of experiments are required. This process wastes large amounts of substrate material, experimental consumables, and machining time, and increases the cost of the experiments. In this paper, we report a reflow process for soft-forming micro-hemispherical shells from fused silica substrates supported by a reclining mold. The shapes of the shells formed from the fused silica substrates in reclining and non-reclining molds were analysed by building a two-dimensional model. Moreover, we predicted the effects of varying the process parameters on the shell-forming time and geometrical parameters, as well as the stresses and deformations of the shells after cooling. The effect of the eccentricity of the central support column of the mold on the symmetry of micro-hemispherical shells was also investigated, and the influence of the mold and substrate heating inhomogeneity on micro-hemispherical shell formation was analysed. Additionally, the heat uniformity of the substrate in the rotating state was examined. Finally, we investigated the temperature field and thickness distribution during the shell-forming process through 3D modelling to verify the 2D modelling results. Analysing and predicting the parameters helps to reduce the number of trial-and-error processes in experiments, and we expect this work to provide a theoretical parametric basis for micro-hemispherical shell machining.

Numerical Study of Heat Transfer and Fluid Flow Characteristics of a Hydrogen Pulsating Heat Pipe with Medium Filling Ratio

Benefiting from its high thermal conductivity, simple structure, and light weight, the pulsating heat pipe (PHP) can meet the requirements for high efficiency, flexibility, and low cost in industrial heat transfer applications such as aerospace detector cooling and vehicle thermal management. Compared to a PHP working at room temperature, the mechanism of a PHP with hydrogen as the working fluid differs significantly due to the unique thermal properties of hydrogen. In this paper, a two-dimensional model of a hydrogen PHP with a filling ratio of 51% was established to study the flow characteristics and thermal performance. The volume of fluid (VOF) method was used to capture the phase distribution and interface dynamics, and the Lee model was employed to account for phase change. To validate the model, a comparison was conducted between the simulation results and experimental data obtained in our laboratory. The simulation results show that the pressure and temperature errors were within 25% and 5%, respectively. Throughout a pressure oscillation cycle, the occurrence of uniform flow velocity, acceleration, and flow reversal can be attributed to the changes in the vapor–liquid phase distribution resulting from the effect of condensation and evaporation. In addition, when the fluid velocity was greater than 0.6 m/s, dynamic contact angle hysteresis was observed in the condenser. The results contribute to a deeper understanding of the flow and heat transfer mechanism of the hydrogen PHPs, which have not been yet achieved through visualization experiments.

The effects of non-local observations on the adjoint estimation of local model parameters: An example of Manning’s n coefficient in a tidal model over the Bohai, Yellow, and East China Seas

Accurate parameter estimation is a key issue for enhancing the performance of hydrological models. With the rapid development of satellite technology, integrating satellite data and numerical modelling for parameter estimation has gained more prominence. The limited spatial coverage of altimeters necessitates areas without direct local observations to rely only on information from nearby non-local observations. However, the relation is far from clear between non-local observations and the estimation of local model parameters. In this study, a two-dimensional adjoint tidal model over the Bohai, Yellow, and East China Seas (BYECS) is developed, assimilating observations from TOPEX/Poseidon, Jason-1, and Jason-2 altimeters in conjunction with tide-gauge stations. In twin experiments, the feasibility and reliability of utilizing non-local observations are emphasized by varying synthetic observations. The experiments also reveal how the number and distance of non-local observations affect the ill-posedness of local parameter estimation. The estimation errors can be reduced by increasing observations within a ‘critical distance’, beyond which the accuracy does not improve further. Subsequently, the robustness of ‘critical distance’ is discussed under different prescribed parameter distributions, sizes of predefined optimized area, and random observational errors, indicating that the ‘critical distance’ is approximately 1.0°-2.0°. These results provide a positive reference for practical experiment. In BYECS, the order of Manning’s n coefficient ranges from 10-4 to 10-1, with an average value of 0.0246 in shallow waters. The spatial distribution reveals 9 high-value areas, primarily modulated by a concurrence of sandy sediment and weak tidal currents. This study offers valuable insights into refining the adjoint model for physical parameter estimation, particularly in anticipation of the expanded spatial coverage of SWOT. Compared to only assimilating T/P series altimeters, incorporating SWOT reduces discrepancies by over 38%. Additionally, the spatial Manning’s n coefficient provides guidance for enhancing tidal simulation in other models.

New hybrid thermal energy storage unit using dual hydrides with cascaded PCMs: Application to CSP plants

Thermal energy storage is necessary for concentrated solar power (CSP) plants; it's a useful technique for reducing fluctuations in the energy supply and aids in peak demand management. Therefore, in the present paper, a novel Hybrid Cascaded Thermal Energy Storage (Hyb-CTES) unit is proposed for use in solar-driven Rankine steam power plant. The concept of the heat storage hybridization examined in this study is to couple metal hydride-based thermochemical heat storage system with cascaded phase change materials-based latent heat storage. To assess the dynamic behavior of the Hyb-CTES unit, a two-dimensional transient model is established, and a computational code is developed. The mathematical model has been validated successfully by comparing it with experimental data and by verifying both the mass and energy balance. To choose the appropriate PCM's melting temperature, four approaches are proposed and tested. Numerical simulations were performed with the help of the developed computer code, and the findings demonstrated that the supplied hydrogen pressure and the temperatures of the metal hydride beds are the crucial parameters for determining the PCM melting temperature. In addition, it is found that the proposed cascaded PCMs configuration enhances the heat storage unit's thermal performance and can reduce the heat charge/discharge cycle duration by 19 %. Also, the results indicate that the new Hyb-CTES unit is a promising alternative for thermal storage for CSP plants.

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Influence of radio frequency wave driving frequency on capacitively coupled plasma discharge

A two-dimensional symmetric fluid model is established to study the influence of radio frequency (RF) wave driving frequency on the capacitively coupled plasma discharge. The relationship between the driving frequency and electron density is obtained by solving the electron energy balance equation. The calculation results show that the average electron density first increases rapidly with the increase in driving frequency and then gradually tends to saturation at a threshold frequency. A fluid simulation is also carried out, which provides similar results. Physical studies on this phenomenon are conducted, revealing that the essence of this phenomenon is due to the inability of electrons to quickly respond to potential changes within the boundary sheath when the driving frequency of RF exceeds the plasma frequency. In addition, it is also found that increasing gas pressure can enhance the electron density and the type of gas can also affect the electron density.

Chaos and bifurcations of a two-dimensional hepatitis C virus model with hepatocyte homeostasis.

In this paper, we delve into the intricate local dynamics at equilibria within a two-dimensional model of hepatitis C virus (HCV) alongside hepatocyte homeostasis. The study investigates the existence of bifurcation sets and conducts a comprehensive bifurcation analysis to elucidate the system's behavior under varying conditions. A significant focus lies on understanding how changes in parameters can lead to bifurcations, which are pivotal points where the qualitative behavior of the system undergoes fundamental transformations. Moreover, the paper introduces and employs hybrid control feedback and Ott-Grebogi-Yorke strategies as tools to manage and mitigate chaos inherent within the HCV model. This chaos arises due to the presence of flip and Neimark-Sacker bifurcations, which can induce erratic behavior in the system. Through the implementation of these control strategies, the study aims to stabilize the system and restore it to a more manageable and predictable state. Furthermore, to validate the theoretical findings and the efficacy of the proposed control strategies, extensive numerical simulations are conducted. These simulations serve as a means of confirming the theoretical predictions and provide insight into the practical implications of the proposed control methodologies. By combining theoretical analysis with computational simulations, the paper offers a comprehensive understanding of the dynamics of the HCV model and provides valuable insights into potential strategies for controlling and managing chaos in such complex biological systems.

A two-dimensional chaotic model and its application in image encryption

In this paper, we propose a rule that follows a time-varying delay construction method and construct a time-varying delay scheme based on it. This construction scheme is also combined with a polynomial to obtain a novel two-dimensional chaotic model. Both mathematical analysis and experimental results show that the model satisfies the chaos condition. Good experimental results have been achieved in complexity analysis, information entropy analysis, and Auto-correlation analysis, and have certain competitiveness. The obtained chaotic model is also applied to the image encryption algorithm. The experimental results show that the encryption algorithm has high security and can effectively resist noise attacks, shear attacks, differential attacks.

Spatial diffusion of potentially toxic elements in soils around non-ferrous metal mines

This study focuses on the diffusion patterns of principal ore-forming elements (Pb and Zn) and associated elements (Cd, Cu, Cr, and As) in lead-zinc ore. Sampling points in upwind and downwind directions of lead-zinc ore areas at various densities (1 N/km2 – 4 N/km2) were categorized. This study analyzed the statistical relationship between the content of PTEs in the soil around lead-zinc ore and the source strength and dominant wind direction, constructed one-dimensional and two-dimensional diffusion model, and simulated the EER scope caused by PTEs. The findings indicate that: (1) concerning source strength, the content of PTEs in soils of high-density ore aggregation areas is significantly higher than in low-density ore aggregation areas. However, the impact of source strength decreases with decreasing ore grade, with a difference in Pb content of 1.71 times among principal ore-forming elements and almost consistent Cd content among associated elements. (2) Regarding the transport pathways, for most PTEs, the inverse proportion coefficients downwind are higher than upwind, approximately 1.18–3.63 times, indicating greater migration distances of PTEs downwind due to atmospheric dispersion. (3) By establishing a two-dimensional risk diffusion model, the study simulates the maximum radius of risk diffusion (r = 5.7 km), the 50% probability radius (r = 3.1 km), and the minimum radius (r = 0.8 km) based on the maximum, median, and minimum values statistically obtained from the EER. This study provides a scientific basis for implementing preventive measures for PTEs accumulation in soil within different pollution ranges. Different risk prevention and control measures should be adopted for PTEs accumulation in soil within the three ranges after cutting off pollution sources. Subsequent research should further investigate the impact and contribution of atmospheric transmission and surface runoff on the diffusion of PTEs in areas with high risk near lead-zinc ore.

Modeling arboreal vegetation-induced friction and its influence on river flooding using a two-dimensional model

Modeling arboreal vegetation-induced friction and its influence on river flooding using a two-dimensional model

A dynamical system framework for a mathematical model of atherosclerosis

Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the inner artery wall. In atherosclerotic plaque formation monocytes and macrophages play a significant role in controlling the disease dynamics. In the present article, the entire biochemical process of atherosclerotic plaque formation is presented in terms of an autonomous system of nonlinear ordinary differential equations involving concentrations of oxidized low-density lipoprotein (LDL), monocytes, macrophages, and foam cells as the key dependent variables. To observe the capacity of monocytes and macrophages the model has been reduced to a two-dimensional temporal model using quasi steady state approximation theory. Linear stability analysis of the two-dimensional ordinary differential equations (ODEs) model has revealed the stability of the equilibrium points in the system. We have considered both one- and two-parameter bifurcation analysis with respect to parameters associated to the rate at which macrophages phagocytose oxidized LDL and the rate at which LDL enters into the intima. The bifurcation diagrams reveal the oscillating nature of the curves representing concentration of monocytes and macrophages with respect to significant model parameters. We are able to find the threshold values at which the plaque accumulation accelerates in an uncontrollable way. Further to observe the impact of diffusion, a spatiotemporal model has been developed. Numerical investigation of the partial differential equations (PDEs) model reveals the existence of travelling wave in the system which ensures the fact that the development of atherosclerotic plaque formation follows reaction–diffusion wave.

Copper(II) salts and complexes of 2-amino-5-nitropyridine*

Four new copper compounds of 2-amino-5-nitropyridine/pyridinium (5NAP/5NAPH) have been prepared and characterized: (5NAPH)2[CuBr4], 2; (d2-5NAPD)2[CuBr4], 2a; (5NAP)2CuCl2, 3; (5NAP)2CuBr2, 4. Compounds 2 and 2a are isomorphous and crystallize in the triclinic space group P-1. Packing is stabilized by hydrogen/deuterium bonds. Short Br…Br contacts provide potential magnetic superexchange pathways, but only very weak antiferromagnetic exchange is observed (J/kB∼-2 K). Compounds 3 and 4 are also isomorphous and crystallize in the monoclinic space group P21/c. The molecules are linked into chains by bihalide bridges, and the chains linked into rectangular/square layers by short X…X. contacts. Variable temperature magnetic data were best fit by the S = ½ antiferromagnetic rectangular model for 3 (C = 0.429(1) emu-K/mol-Oe, J/kB = −9.38(6) K, J’/kB = −5.91(4) K). Variable temperature magnetic susceptibility data for 4 were best fit by the two-dimensional antiferromagnetic square lattice model (C = 0.43(1) emu-K/mol-Oe, J/kB = −36.5(2) K).