Two-dimensional Contour Plots Research Articles

Generalized extended (2+1)-dimensional Kadomtsev-Petviashvili equation in fluid dynamics: analytical solutions, sensitivity and stability analysis

This study discusses a new version of the (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensional Kadomtsev-Petviashvili equation. This equation is used to model the behavior of nonlinear waves in various fields like ferromagnetic media, ion-acoustic waves in plasma physics, and fluid dynamics. It is instrumental in modeling surface and internal waves in straits or channels. The main goal of the research is to determine the exact solutions for this equation and analyze their physical characteristics. We obtain exact solutions using two improved techniques, namely the modified extended tanh-function and the modified generalized Kudryashov methods. These techniques investigate various exact solutions, such as exponential, rational, hyperbolic, and trigonometric. Besides, the sensitivity and the stability analysis of the model are presented. Additionally, three- and two-dimensional contour plots are created to present the physical behavior of the exact solutions.

Removal of Congo red dye by electrochemical advanced oxidation process: optimization, degradation pathways, and mineralization

The degradation of Congo red dye has been studied by electrochemical advanced oxidation process based on the generation of powerful oxidizing agents especially hydroxyl radicals ·OH. In this study, the effect of several experimental parameters, such as pH, ferrous ion concentration, electrolyte support concentration and current intensity, on the process was investigated. The experimental design of Doehlert was applied to determine the optimum conditions of three factors, namely current intensity, initial Fe2+ concentration and electrolysis time for the Congo red removal. The relationship of response to experimental variables was represented graphically by the construction of the two-dimensional iso-response contour plots and those indicated that 360 mA, 19 mM Fe2+ and 30 min reaction time were optimal under 50 mM Na2SO4 at pH 3, leading to a total Congo red degradation. A quadratic polynomial model was determined and its statistical significance was verified through the variance analysis, which indicated that the proposed model was statistically meaningful and convenient for the results prediction. The mineralization of Congo red under the obtained optimum conditions was examined and the results showed a high TOC removal rate (81.1%) after 300 min of reaction time. Finally, a plausible degradation pathway was suggested.

The nonlinear wave dynamics of fractional foam drainage and Boussinesq equations with Atangana’s beta derivative through analytical solutions

The space–time fractional foam drainage and the Boussinesq equations are valuable mathematical models to describe different complex physical phenomena, including the drainage of soap films in bubbles and foams, the behavior of surface water waves in oceans and rivers, the propagation of long waves, etc. In this research, we explore several unrivaled and some existing analytical soliton solutions to the above-stated equations using an effective expansion scheme, known as the G′/(G′+G+A)-expansion scheme within the framework of Atangana’s beta derivative. A fractional composite transformation is used to interpret the considered equations into nonlinear equations of a single independent variable. The wave dynamics of the outcomes are illustrated through three- and two-dimensional graphical representations and contour plots. The solutions include kink, flat kink-shaped, the parabolic-shaped, the bell-shaped, and the compacton solitons. The study reveals that the fractional-order derivative in the projected equations influences the wave behavior, providing deeper insights into wave composition when the fractional derivative approaches larger. The comparison table demonstrates the effectiveness of the method across various fractional orders, with results approaching accuracy as the fractional-order approaches integer values. This study emphasizes the computational robustness and adaptability of the proposed method for investigating various phenomena across a wide range of physical science and engineering disciplines.

The traveling wave solution and dynamics analysis of the parabolic law nonlinear stochastic dispersive Schrödinger-Hirota equation with multiplicative white noise

This article investigates the traveling wave solution of the parabolic law nonlinear stochastic dispersive Schrödinger-Hirota equation with multiplicative white noise, and its conclusions can be applied to optical communication. Firstly, the equation is transformed into a nonlinear ordinary differential equation through traveling wave transformation, and its planar dynamic system is studied. The phase portraits of the equation in various cases are drawn by Maple software. Secondly, the traveling wave solutions of this equation are obtained by using the complete discriminant system theory of cubic polynomials. Finally, we draw two-dimensional graphics, three-dimensional graphics, density plots and contour plots for the module length of some solutions under specific parameters. In addition, the above research results can help readers have a more comprehensive and clear understanding of this equation and its application.

CLASSIM: A relational database driven crop model interface

Crop models are valuable tools for examining the interactions of cultivar characteristics, environment, and management practices, and how they affect crop growth and development. The difficulty in finding all the data needed to set up a simulation can often deter potential users from utilizing a crop model. Model interfaces are necessary to make these complex tools accessible to end-users who may lack the expertise needed to work with the models directly, but who would benefit from the information generated by the models. As crop models vary in terms of input and output structures, there is no one universally compatible interface, so different crop model suites require their own interface. CLASSIM is a graphical user interface (GUI) for a suite of models developed by USDA-ARS. The interface provides a simplified tool to assemble input data for a model simulation. Web access to online databases for soil and weather data simplifies finding site-related data. The user is guided step by step to build the necessary input files. A database structure facilitates data entry, storage, and retrieval. The use of Structured Query Language (SQL) for data retrieval allows for advanced analysis and visualization outside of the interface. We describe the features of the GUI and provide examples of various operations. Model outputs are provided in tables and graphs to allow for visualization and analysis. Two-dimensional contour plots of soil processes are provided to visualize output from the two-dimensional finite element soil model. CLASSIM also allows users to set up single- and multiple-season runs for maize, cotton, soybean, potato, and fallow treatments, and is expected to be expanded to more crops in the future. A user-friendly GUI is essential for making simulation tools accessible to the broad range of researchers and practitioners working to solve the agricultural system challenges.

Dynamics and optical soliton solutions in birefringent fibers for the coupled Kaup–Newell equation via planar dynamical system analysis method

In this paper, the dynamical behavior and optical soliton of the coupled Kaup–Newell equation are studied. Firstly, the phase portraits of the coupled Kaup–Newell equation are drawn by using Maple software. Secondly, the optical soliton solutions of the coupled Kaup–Newell equation are construct by the bifurcation theory of planar dynamical system together with the “three-step method” of Professor Li’s method. Finally, in order to better explain the wave propagation in birefringent fiber, the three-dimensional graphic, the two-dimensional graphic, contour plot and polar plot of some optical soliton solutions are drawn.

Importance of surface morphology on secondary electron emission: a case study of Cu covered with carbon, carbon pairs, or graphitic-like layers

Understanding the relationship between surface adsorbates and secondary electronic emission is critical for a variety of technologies, since the secondary electrons can have deleterious effects on the operation of devices. The mitigation of such phenomena is desirable. Here, using the collective efforts of first-principles, molecular dynamics, and Monte Carlo simulations, we studied the effects of a variety of carbon adsorbates on the secondary electron emission of Cu (110). It was demonstrated that the adsorption of atomic C and C_2 pair layers can both reduce and increase the number of secondary electrons depending on the adsorbate coverage. It was shown that under electron irradiation, the C–Cu bonds can be dissociated and reformed into C_2 pairs and graphitic-like layers, in agreement with experimental observation. It was verified that the lowest secondary electron emission was due to the formation of the graphitic-like layer. To understand the physical reason for changes in number of secondary electrons for different systems from an electronic structure perspective, two-dimensional potential energy surfaces and charge density contour plots were calculated and analyzed. It was shown that the changes are strongly influenced by the Cu surface morphology and depends highly on the nature of the interactions between the surface Cu and C atoms.

Structure, energetics, and spectroscopy of the K2+(X2Σ+g) interacting with the noble gas atoms Ar, Kr and Xe

The structure, energetic, and spectroscopy properties of the ionic system K2+(X2Σ+g) interacting with the noble gas atoms Argon, Krypton and Xenon are studied. The computations are done by an accurate ab initio approach based on the pseudo-potential technique, Gaussian basis sets, parameterized l-dependent polarization potentials and an analytic potential form for the K+Ar, K+Kr and K+Xe interactions. These interactions are added via the CCSD(T) potential taken from literature and fitted applying the analytical expression of Tang and Toennies. The application of the pseudo-potential approach reduces the number of active electrons of each complex to only one electron. The potential energy surfaces are analyzed on a large range of the Jacobi coordinates, R and θ. By the general interpolation outline based on the RKHS (Reproducing Kernel Hilbert Space) procedure, we have reproduced for each complex from our ab initio results the two-dimensional contour plots of an analytical potential. To evaluate the stability of each complex, we have determined from the potential energy surfaces the equilibrium distance (Re), the well depth (De), the quantum energy (D0), the zero-point-energy (ZPE) and the ZPE%. The results showed that the linear configurations, where the noble gas atom connected to the K2+(X2Σ+g) system, are the more stable.

Degenerate lump chain solutions of (4+1)-dimensional Fokas equation

This paper takes (4+1)-dimensional Fokas equation as an example to introduce an ingenious limit approach to generate degenerate solutions in detail. Under this technique, we start with solutions describing lump chains and obtain degenerate solutions from coupled lump chains quickly and easily. The complex dynamics of these degenerate solutions are shown in both three-dimensional plots and two-dimensional contour plots. Additionally, we find the central area of the degenerate solutions is a very good approximation of corresponding rogue wave solutions which can be used to formulate the rogue waves in a optical system.

Bayesian Optimization of photonic curing process for flexible perovskite photovoltaic devices

Photonic curing is a thin-film processing technique that can enable high-throughput perovskite solar cell (PSC) manufacturing. However, photonic curing has many variables that can affect the processing outcome, making optimization challenging. Here, we introduce Bayesian Optimization (BO), a machine-learning framework, to optimize the power conversion efficiency (PCE) of photonically cured MAPbI3 PSCs on ITO-coated Willow Glass. We apply BO with four input variables—MAPbI3 concentration, additive CH2I2 volume, pulse voltage, and pulse length. These input variables were dynamically adjusted in response to the new data, an example of a human-machine partnership. With the limited experimental budget of 48 conditions, we achieved a champion PCE of 11.42% and predicted 14 new conditions resulting in >10% PCE. Beyond simple optimization, we examined the relationships between pairs of inputs with two-dimensional contour plots and investigated the relative importance of each input to gain insight into photonic curing. We demonstrate that BO is a powerful tool in process optimization and can be adapted to other PSC manufacturing cases.

In silico screening of off-line comprehensive two-dimensional counter-current chromatography with liquid chromatography for four saponins isolation.

Being restrained by the limited peak capacity, one-dimensional chromatography usually leads to an unsatisfactory separation with low purity of compounds in a complex mixture. To obtain more highly pure targets for standard reference and to discover new substances for structural elucidation, two-dimensional chromatography is more and more prevalent in many fields. As few metrics on assessment of the preparative capability of two-dimensional chromatographic separations are reported, a methodology of in silico screening of various two-dimensional chromatographic separations with a minimal number of experiments was demonstrated in this work, which was based on three descriptors including the occupation rate of peaks and system homogeneity of a two-dimensional separation space, and the minimal distance of all nearest-neighbor distances of peaks. Combining the advantages of counter-current chromatography and liquid chromatography, we elaborated the methodology by employing off-line comprehensive two-dimensional counter-current chromatography with liquid chromatography to be in silico screened for separation of four saponins from Panax notoginseng at an analytical scale to simulate the case of preparative scale transfer. The predictive results were presented by two-dimensional contour plots and verified by experiments. The result showed that the experimental results were in general accord with the predictive results.

FEM solution to quadratic convective and radiative flow of Ag-MgO/H2O hybrid nanofluid over a rotating cone with Hall current: Optimization using Response Surface Methodology

The nonlinear buoyancy-induced (quadratic convection) flow of water conveying hybrid nanoparticles (25 nm Ag and 40 nm MgO) around a revolving cone surface subjected to quadratic radiative heat transfer is studied, taking into deliberation of Hall current, and thermal jump condition. The quadratic form of Boussinesq approximation (QBA) with quadratic Rosseland thermal radiation (QRTR) is employed to model the problem. Esfe models for thermal conductivity and dynamic viscosity with a volumetric fraction of nanoparticles (50% MgO and 50% Ag) are used. The effective medium correlations for heat capacitance, thermal expansion factor, and density of Ag-MgO/water hybrid nanofluid are used. The governing equations are solved by using the Finite element method (FEM). The effects of parameters on the shear stress and heat transport of the system are scrutinized using the friction factors and Nusselt number through two-dimensional contour and three-dimensional surface plots. The friction factor and the heat transport rate are optimized using the Response Surface Method (RSM) and the optimal level of intensity of the magnetic field, radiation, and thermal slip is determined. Because of the influence of hybrid nanoparticles, the heat transport rate is observed to be the highest. When compared to Linear Rosseland Thermal Radiation (LRTR), the Nusselt number for QRTR is found to be the highest. Furthermore, at a low level of Ts and a high level of Ha and Rd, maximum heat transport (2.42951) and minimum shear stress (1.07598) are achieved with a desirability of 0.797.

Optimization and Characterization of Self Nano Emulsifying Drug Delivery System loaded with 18- β Glycerrhetinic acid

The purpose of this study was to prepare, optimize and evaluate self nano emulsifying drug delivery system (SNEDDS) containing 18- β glycerrhetinic acid which enhances the dissolution profile or bioavailability of the drug in comparison to pure suspension of 18- β glycerrhetinic acid.18- β glycerrhetinic acid loaded SNEDDS having geranium oil as oil phase, tween 80 as a surfactant, and dimethyl sulfoxide (DMSO) as co-surfactant were prepared using pseudo ternary phase diagram and Box-Behnken experimental design was used to optimize the different formulations. Optimized formulations were characterized for self-emulsifying time, globule size, zeta potential, and drug release. The mean droplet size and PDI of the optimized formulation were found to be in a variation of 93.42 nm and 0.401 respectively. FTIR data showed no physicochemical interaction between excipients and drug. The encapsulation efficiency of optimised 18- β glycerrhetinic acid SNEDDS was found 80.12±1.52% , % transmittance was found 99.34±0.134% and the viscosity of all the formulations was found 0.8872 cp. Three-dimensional response surface plots and two-dimensional contour plots of the responses across the selected factors were constructed that explained the relationship between the independent and dependent variables. Release kinetics was calculated by using KinetDS3.0. It was concluded that prepared formulations were formulated with approximately desired mean droplet size confirmed by Box- Behnken experimental design as well as properly optimized and characterized.

On-top description of the effect of excitation on electron correlation with quasiparticles

A spectrum of $\mathrm{\ensuremath{\Delta}}$-correlon quasiparticles is proposed to describe the excitation effect on electron correlation. The proposed quasiparticle description is based on the comparison of the pair-correlation functions of the excited and ground states at the special coalescence points of the configurational space. The complex form of the $\mathrm{\ensuremath{\Delta}}$-correlon wave function allows us to naturally separate regions with the excitation suppression of correlation (ESC $\mathrm{\ensuremath{\Delta}}$-correlon), where correlation is stronger in the ground state, from those with the excitation enhancement of correlation (EEC $\mathrm{\ensuremath{\Delta}}$-correlon), where correlation is stronger in the excited state. The proposed $\mathrm{\ensuremath{\Delta}}$-correlon approach is applied to characterize the important single excitations with the competition of ``anticorrelation squeezing'' and ``enhanced-correlation spreading'' of the two-electron distribution. The former feature characterizes single valence excitations of the ionic nature and this leads to the prevailing of the ESC effect in this type of excitations. In turn, the enhanced-correlation spreading characterizes single Rydberg excitations, which leads to the prevailing of the EEC effect in this type of excitations. The proposed $\mathrm{\ensuremath{\Delta}}$-correlon quasiparticles are studied both analytically and numerically. The analytical expressions for the on-top correlation functions are obtained with the two-determinantal two-electron model of the active site of an excitation. The two-dimensional contour plots of the ESC and EEC $\mathrm{\ensuremath{\Delta}}$-correlons obtained for the lowest vertical valence ionic and Rydberg excitations in the prototype molecules ${\mathrm{H}}_{2}, {\mathrm{N}}_{2}$, and ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ from the highly correlated wave functions confirm, in general, the trends in the relative correlation strength deduced from the model.

A test method for analyzing the deformation of landslide model

In order to study the overall deformation of geotechnical model conveniently, the worksite of landslide bridge foundation reinforced by the front and rear row anti-slide piles in Chenglan railway was taken as an example. On the basis of shaking tabe test of a 1/40 reduced scale model, the landslide deformation caused by vibration waves was monitored through burying self-made phosphor bronze strips in soil. Combined with the horizontal and vertical coordinates of the bending strain points on the phosphor bronze strips, the digital matrix was converted by applying Renka Cline random matrix generation method, and the two-dimensional contour plots were drawn based on it. The results showed that the two-dimensional contour plots reflected the basic law of landslide deformation reasonably, and it revealed the evolution process of landslide deformation and failure. The research conclusions were consistent with the test phenomenon, which met the basic requirements of overall deformation analysis of landslide model. This proposed method can monitor multiple cross sections and was practical for model test.

Dry Sliding Wear Behavior of Magnesium Nanocomposites Using Response Surface Methodology

Abstract In this study, a pure magnesium material reinforced with 0.5, 1, 1.5, and 2 w% of CaO was prepared through disintegrated melt deposition technique (DMD process). Nanocomposites were investigated for their sliding wear behavior in dry condition at room temperature. The amount of CaO, load, sliding distance, and sliding velocity were selected as input design parameters at their five level in central composite design using minitab 18.1 statistical software. The influence of design parameters on wear loss is reported through the response surface methodology (RSM). Analysis of variance (ANOVA) was used to confirm the soundness of the developed regression equation. The results indicate the contribution of linear, quadratic, and interaction terms of design parameters on response. Three-dimensional response surface and two-dimensional contour plots indicate the interaction effect. The result shows that an increase in the sliding velocity contributes to a decrease in the wear loss of the composites because of the emergence of protective oxidative layer at the surfaces of the pins, which is confirmed through field emission scanning electron microscope and energy dispersive X-ray analysis analyses of the pin surfaces. Wear loss of the material decreased as the amount of CaO increased. The ANOVA analysis concluded that the sliding distance and load contribute significantly to wear loss of the composites, and their percentage of contribution is 64.02% and 3.69%.

Molecular Dynamics Simulation of Atomic Interactions in the Vancomycin Binding Site.

Vancomycin is a glycopeptide antibiotic produced by Amycolaptopsis orientalis used to treat serious infections by Gram-positive pathogens including methicillin-resistant Staphylococcus aureus. Vancomycin inhibits cell wall biosynthesis by targeting lipid II, which is the membrane-bound peptidoglycan precursor. The heptapeptide aglycon structure of vancomycin binds to the d-Ala-d-Ala of the pentapeptide stem structure in lipid II. The third residue of vancomycin aglycon is asparagine, which is not directly involved in the dipeptide binding. Nonetheless, asparagine plays a crucial role in substrate recognition, as the vancomycin analogue with asparagine substituted by aspartic acid (VD) shows a reduction in antibacterial activities. To characterize the function of asparagine, binding of vancomycin and its aspartic-acid-substituted analogue VD to l-Lys-d-Ala-d-Ala and l-Lys-d-Ala-d-Lac was investigated using molecular dynamic simulations. Binding interactions were analyzed using root-mean-square deviation (RMSD), two-dimensional (2D) contour plots, hydrogen bond analysis, and free energy calculations of the complexes. The analysis shows that the aspartate substitution introduced a negative charge to the binding cleft of VD, which altered the aglycon conformation that minimized the repulsive lone pair interaction in the binding of a depsipeptide. Our findings provide new insight for the development of novel glycopeptide antibiotics against the emerging vancomycin-resistant pathogens by chemical modification at the third residue in vancomycin to improve its binding affinity to the d-Ala-d-Lac-terminated peptidoglycan in lipid II found in vancomycin-resistant enterococci and vancomycin-resistant S. aureus.

Interactive tools to assist convenient group-type identification and comparison of low-temperature coal tar using GC × GC–MS

Coal tar is considered a valuable product obtained from coal pyrolysis. An accurate and convenient analytical study on its composition would be of great significance for its further processing and utilization. This work focused on the group-type identification and comparison of low-temperature coal tar by using comprehensive two-dimensional gas chromatography-mass spectrometry (GC × GC–MS). In this work, three low-temperature coal tar samples, diluted in dichloromethane, were analyzed by GC × GC–MS. It was observed that aliphatic hydrocarbons, benzene series, phenolic compounds, benzenediol compounds, naphthol compounds, naphthalene series, anthracene series, indene series and other different types of compounds in coal tar exhibited zonal distribution in the two-dimensional contour plot. The classification of different groups can be achieved by construction of spatial polygons. The classification results showed good reliability confirmed by manually identifying each compound contained in each group. The application of computer language for identifying compounds (CLIC) based on mass fragment characteristics and retention time assisted greatly in the identification of different chemical groups. Five major chemical groups including aliphatics, aromatics, oxygen-containing compounds, nitrogen-containing compounds and sulfur-containing compounds were retrieved from the two-dimensional contour plot by automated pattern recognition using CLIC expressions. The relative content of different chemical groups between a series of contour plots can be conveniently compared by comprehensive implementation of CLIC expressions and an interactive feature template matching function.

Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation

In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

Reduction in the $$\mathbf {(4+1)}$$-dimensional Fokas equation and their solutions

An integrable extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations is investigated in this paper. We will refer to this integrable extension as the $$(4+1)$$-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the $$(4+1)$$-dimensional Fokas equation are constructed based on the Hirota’s bilinear method and the KP hierarchy reduction method. The complex dynamics of these new exact solutions are shown in both three-dimensional plots and two-dimensional contour plots. Interestingly, the patterns of obtained high-order lumps are similar to those of rogue waves in the $$(1+1)$$-dimensions by choosing different values of the free parameters of the model. Furthermore, three kinds of new semi-rational solutions are presented and the classification of lump fission and fusion processes is also discussed. Additionally, we give a new way to obtain rational and semi-rational solutions of $$(3+1)$$-dimensional KP equation by reducing the solutions of the $$(4+1)$$-dimensional Fokas equation. All these results show that the $$(4+1)$$-dimensional Fokas equation is a meaningful multidimensional extension of the KP and DS equations. The obtained results might be useful in diverse fields such as hydrodynamics, nonlinear optics, and photonics, ion-acoustic waves in plasmas, matter waves in Bose–Einstein condensates, and sound waves in ferromagnetic media.