The biharmonic equation is one of the important equations of mathematical physics, describing the behaviour of harmonic functions in higher-dimensional spaces. The main purpose of this study was to construct a finite-dimensional perturbation for the Dirichlet boundary value problem associated with the biharmonic equation. The methodological basis for this study was an integrated approach that includes mathematical analysis, algebraic methods, operator theory, and the theorem on the existence and uniqueness of a solution for a boundary value. The main tool is a finite-dimensional perturbation, which allows for examining the properties and behaviour of boundary value problems in as much detail as possible. In the study, descriptions of correctly solvable internal boundary value problems for a biharmonic equation in non-simply connected domains were considered in detail. The study is also devoted to the search for solutions and the analytical representation of resolvents of boundary value problems for a biharmonic equation in multi-connected domains. Within the framework of the study, theorems and their consequences were proved, and a finite-dimensional perturbation was constructed for the Dirichlet boundary value problem. Analytical representations of resolvents of boundary value problems for a biharmonic equation in multi-connected domains were also obtained. The examination of a finite-dimensional perturbation of the Dirichlet boundary value problem for a biharmonic equation has expanded the understanding of the properties of this equation in various contexts.
{"title":"Finite-dimensional perturbation of the Dirichlet boundary value problem for the biharmonic equation","authors":"Gulnaz Berikkhanova","doi":"10.1515/zna-2024-0020","DOIUrl":"https://doi.org/10.1515/zna-2024-0020","url":null,"abstract":"The biharmonic equation is one of the important equations of mathematical physics, describing the behaviour of harmonic functions in higher-dimensional spaces. The main purpose of this study was to construct a finite-dimensional perturbation for the Dirichlet boundary value problem associated with the biharmonic equation. The methodological basis for this study was an integrated approach that includes mathematical analysis, algebraic methods, operator theory, and the theorem on the existence and uniqueness of a solution for a boundary value. The main tool is a finite-dimensional perturbation, which allows for examining the properties and behaviour of boundary value problems in as much detail as possible. In the study, descriptions of correctly solvable internal boundary value problems for a biharmonic equation in non-simply connected domains were considered in detail. The study is also devoted to the search for solutions and the analytical representation of resolvents of boundary value problems for a biharmonic equation in multi-connected domains. Within the framework of the study, theorems and their consequences were proved, and a finite-dimensional perturbation was constructed for the Dirichlet boundary value problem. Analytical representations of resolvents of boundary value problems for a biharmonic equation in multi-connected domains were also obtained. The examination of a finite-dimensional perturbation of the Dirichlet boundary value problem for a biharmonic equation has expanded the understanding of the properties of this equation in various contexts.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Globally, enhanced oil recovery (EOR) has become a pressing issue as the demand for crude oil continues to increase. This study investigates the flow and thermal-fluid–solid coupling of crude oil in a rod pump during hot water recovery and obtains the maximum recovery of crude oil in a vertical pipeline through numerical analysis. The pressure gradient in the pump barrel was first developed and deduced based on the ideal gas state equation and Bernoulli’s equation. According to the rheological experiment results, it was proven that the light crude oil conforms to the Newtonian constitutive equation. Subsequently, the momentum equation of crude oil flowing in the pipeline and fluid–solid coupling heat transfer equations were established and solved using the finite difference method. The effects of the thermal recovery temperature Tw, wall thickness c, and stroke time n of the rod pump on flow Q are discussed. In particular, the flow Q within 1 min first increases and then slows down with the increase in stroke time n and reaches its maximum value at n = 7 r/min. Furthermore, flow Q decreases with an increase in c but increases as Tw increases; c = 1.2 cm, Tw = 363 K is the best oil recovery scheme.
在全球范围内，随着原油需求的持续增长，提高石油采收率（EOR）已成为一个紧迫的问题。本研究通过数值分析，研究了热水采油过程中原油在有杆泵中的流动和热-流-固耦合，并获得了垂直管道中原油的最大采收率。首先根据理想气体状态方程和伯努利方程建立并推导了泵筒内的压力梯度。根据流变实验结果，证明轻质原油符合牛顿构成方程。随后，建立了原油在管道中流动的动量方程和流固耦合传热方程，并采用有限差分法进行了求解。讨论了有杆泵的热回收温度 T w、壁厚 c 和冲程时间 n 对流量 Q 的影响。其中，随着冲程时间 n 的增加，1 分钟内的流量 Q 值先增大后减小，并在 n = 7 r/min 时达到最大值。此外，流量 Q 随 c 的增大而减小，但随 T w 的增大而增大；c = 1.2 cm，T w = 363 K 是最佳采油方案。
{"title":"Analysis of the flow and thermal-fluid–solid coupling of crude oil in circular pipe caused by variable pressure gradient","authors":"Jinxia Jiang, Mengqi Liu, Yan Zhang, Zhen Huang","doi":"10.1515/zna-2023-0293","DOIUrl":"https://doi.org/10.1515/zna-2023-0293","url":null,"abstract":"Globally, enhanced oil recovery (EOR) has become a pressing issue as the demand for crude oil continues to increase. This study investigates the flow and thermal-fluid–solid coupling of crude oil in a rod pump during hot water recovery and obtains the maximum recovery of crude oil in a vertical pipeline through numerical analysis. The pressure gradient in the pump barrel was first developed and deduced based on the ideal gas state equation and Bernoulli’s equation. According to the rheological experiment results, it was proven that the light crude oil conforms to the Newtonian constitutive equation. Subsequently, the momentum equation of crude oil flowing in the pipeline and fluid–solid coupling heat transfer equations were established and solved using the finite difference method. The effects of the thermal recovery temperature <jats:italic>T</jats:italic> <jats:sub> <jats:italic>w</jats:italic> </jats:sub>, wall thickness <jats:italic>c</jats:italic>, and stroke time <jats:italic>n</jats:italic> of the rod pump on flow <jats:italic>Q</jats:italic> are discussed. In particular, the flow <jats:italic>Q</jats:italic> within 1 min first increases and then slows down with the increase in stroke time <jats:italic>n</jats:italic> and reaches its maximum value at <jats:italic>n</jats:italic> = 7 r/min. Furthermore, flow <jats:italic>Q</jats:italic> decreases with an increase in <jats:italic>c</jats:italic> but increases as <jats:italic>T</jats:italic> <jats:sub> <jats:italic>w</jats:italic> </jats:sub> increases; <jats:italic>c</jats:italic> = 1.2 cm, <jats:italic>T</jats:italic> <jats:sub> <jats:italic>w</jats:italic> </jats:sub> = 363 K is the best oil recovery scheme.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohamed Abd-Elzaher, Kottakkaran S. Nisar, Abdel-Haleem Abdel-Aty, Pralay K. Karmakar, Ahmed Atteya
Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.
在双流体量子磁流体力学模型的范围内，对自旋为 1/2 的电子-离子磁等离子体中的磁声冲击波和孤波进行了研究。使用还原扰动方法对等离子体系统进行非线性研究时，会产生 Korteweg de Vries-Burgers (KdVB) 方程。萨格迪夫势能产生，揭示了孤解的存在。然而，当包含耗散项时，就能得到耐人寻味的物理解。利用平面动力系统的相平面理论进一步研究了 KdVB 方程，证明了周期波和孤波解的存在。由于存在各种相位轨道，预测几类行波解是有利的，它们表现为孤子冲击波和振荡冲击波。磁场的存在、电子和离子的密度以及运动粘度会显著改变磁声孤子波和冲击波的特性。此外，还发现了电场。这里获得的成果可用于研究在紧凑的天体物理环境中观测到的磁声波的性质，在这种环境中量子自旋现象的影响仍然很大，也可用于受控实验室等离子体实验。
{"title":"Magnetoacoustic waves in spin-1/2 dense quantum degenerate plasma: nonlinear dynamics and dissipative effects","authors":"Mohamed Abd-Elzaher, Kottakkaran S. Nisar, Abdel-Haleem Abdel-Aty, Pralay K. Karmakar, Ahmed Atteya","doi":"10.1515/zna-2023-0322","DOIUrl":"https://doi.org/10.1515/zna-2023-0322","url":null,"abstract":"Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.
研究了非均质、有界、圆柱形尘埃等离子体中的尘埃磁声波，该等离子体包含对立极化的尘埃粒子。考虑到极化力，研究了在沿 z 轴的不均匀外部磁场作用下，r - θ 平面上的尘埃动力学。在平衡状态下，尘埃等离子体成分应遵循高斯密度分布。利用还原扰动法（RPM），推导出了可变系数圆柱卡多姆采夫-彼得维亚什维利（VCCKP）方程。对于微弱的方位角扰动，选择了 Zhang（"Exp-function method via Exp-function method, Exact solutions of a kdv equation with variable coefficients," Nonlinear Dynam.发现尘埃磁声波的相速度受密度不均匀性、极化力、尘埃电荷状态比和离子电子温度比的影响。还注意到尘埃数量密度的时空演变。在所选的尘埃等离子体参数范围内，数值观测到了压缩电磁孤波的存在。此外，还讨论了不均匀性、极化力、尘埃电荷状态比和离子-电子温度比对尘埃磁声波相对振幅的影响。
{"title":"Dust magnetoacoustic waves in an inhomogeneous cylindrical four-component dusty plasma in the presence of polarization force","authors":"Sarit Maitra, Chitrita Dasgupta","doi":"10.1515/zna-2024-0047","DOIUrl":"https://doi.org/10.1515/zna-2024-0047","url":null,"abstract":"Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in <jats:italic>r</jats:italic> − <jats:italic>θ</jats:italic> plane is studied in the presence of inhomogeneous external magnetic field along <jats:italic>z</jats:italic> axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” <jats:italic>Nonlinear Dynam.</jats:italic>, vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maryam Ayaz, Hilal Khan, Hessa A. Alsalmah, Muhammad Yunas, Ghulam Murtaza
The subject of given project is to highlight the basic elastic, electronic and optical reflectivity of ALi2B (A = Cu, Ag; B = Ge, Sn, Pb). For the calculation of these properties, we used the full potential linearized augmented plane wave (FP-LAPW) procedures carry through Wien2k package. Specifically, the Perdew, Burke and Ernzerhof’s generalized gradient approximation (PBE-GGA) and Wu and Cohen generalized gradient approximation (WC-GGA) have been used. The obtained results fit well with existing experimental data. Different elastic parameters, such as constant of elasticity, elastic moduli, Poisson’s ratio, anisotropy factor and Cauchy pressure, are calculated for the first time for the compounds. The elastic properties clearly summarized the compound’s elastically stability and brittleness in both zinc blend phase. The band structure results for ALi2B shows that the compounds are metallic having overlapping bands across the electron chemical potential. The valance band highest energy state is composed from combination of Cu-d and Sn-p state, disclosed through these compound’s total (DOS) plots, whereas the conduction band primarily constitution is from Li-p, Sn-s Cu-s and Sn-p states. The intraband transitions play vital rule in the description of the optical reflectivity of the ALi2B compounds.
{"title":"Structural, band profiles and optical reflectivity studies of ALi2B (A = Cu, Ag; B = Ge, Sn, Pb) compounds","authors":"Maryam Ayaz, Hilal Khan, Hessa A. Alsalmah, Muhammad Yunas, Ghulam Murtaza","doi":"10.1515/zna-2023-0268","DOIUrl":"https://doi.org/10.1515/zna-2023-0268","url":null,"abstract":"The subject of given project is to highlight the basic elastic, electronic and optical reflectivity of ALi<jats:sub>2</jats:sub>B (A = Cu, Ag; B = Ge, Sn, Pb). For the calculation of these properties, we used the full potential linearized augmented plane wave (FP-LAPW) procedures carry through Wien2k package. Specifically, the Perdew, Burke and Ernzerhof’s generalized gradient approximation (PBE-GGA) and Wu and Cohen generalized gradient approximation (WC-GGA) have been used. The obtained results fit well with existing experimental data. Different elastic parameters, such as constant of elasticity, elastic moduli, Poisson’s ratio, anisotropy factor and Cauchy pressure, are calculated for the first time for the compounds. The elastic properties clearly summarized the compound’s elastically stability and brittleness in both zinc blend phase. The band structure results for ALi<jats:sub>2</jats:sub>B shows that the compounds are metallic having overlapping bands across the electron chemical potential. The valance band highest energy state is composed from combination of Cu-<jats:italic>d</jats:italic> and Sn-<jats:italic>p</jats:italic> state, disclosed through these compound’s total (DOS) plots, whereas the conduction band primarily constitution is from Li-<jats:italic>p</jats:italic>, Sn-<jats:italic>s</jats:italic> Cu-<jats:italic>s</jats:italic> and Sn-<jats:italic>p</jats:italic> states. The intraband transitions play vital rule in the description of the optical reflectivity of the ALi<jats:sub>2</jats:sub>B compounds.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.
{"title":"On the stability analysis of a restrained FG nanobeam in an elastic matrix with neutral axis effects","authors":"Ömer Civalek, Büşra Uzun, Mustafa Özgür Yaylı","doi":"10.1515/zna-2023-0361","DOIUrl":"https://doi.org/10.1515/zna-2023-0361","url":null,"abstract":"In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
What the motivation of this paper is to provide chirped optical solitons for the complex Ginzburg–Landau equation with Hamiltonian perturbations and Kerr law nonlinearity. We get 19 exact chirped solutions by utilizing trial equation method and the complete discriminant system for polynomial method, which are richer than the solutions acquired in existing papers. We draw the two-dimensional graphs of amplitudes and corresponding chirps in order to verify the existence of the solutions and discuss the dynamical properties of the solutions. To our knowledge, this is the first time that comprehensive set of exact chirped solutions of the governing equation in the paper are obtained. The model and the results obtained in this paper may help explain some nonlinear problems.
{"title":"Chirped optical solitons for the complex Ginzburg–Landau equation with Hamiltonian perturbations and Kerr law nonlinearity","authors":"Ming-Yue Tang, Tong-Yu Meng","doi":"10.1515/zna-2023-0356","DOIUrl":"https://doi.org/10.1515/zna-2023-0356","url":null,"abstract":"What the motivation of this paper is to provide chirped optical solitons for the complex Ginzburg–Landau equation with Hamiltonian perturbations and Kerr law nonlinearity. We get 19 exact chirped solutions by utilizing trial equation method and the complete discriminant system for polynomial method, which are richer than the solutions acquired in existing papers. We draw the two-dimensional graphs of amplitudes and corresponding chirps in order to verify the existence of the solutions and discuss the dynamical properties of the solutions. To our knowledge, this is the first time that comprehensive set of exact chirped solutions of the governing equation in the paper are obtained. The model and the results obtained in this paper may help explain some nonlinear problems.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140595957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The electrothermoconvection in a rotating dielectric fluid layer heated from below (or above) is studied analytically using linear stability theory. First, we derive the necessary conditions for oscillatory motion when the fluid layer is heated from below and from above. Then as a consequence, sufficient conditions for the validity of the exchange principle are derived for the two configurations in terms of the parameters of the systems alone. The results hold for free boundaries for all wave numbers and for rigid boundaries with some restrictions. Further, the results for electrothermoconvection without rotation, rotatory Rayleigh–Bénard convection and Rayleigh–Bénard convection are also obtained as special cases which validate the existing results. To the best of author’s knowledge such results are not reported in the literature as far as the domain of electrothermoconvection studies is concerned.
{"title":"On the validity of the exchange principle in rotatory electrothermoconvection","authors":"Chitresh Kumari, Jitender Kumar, Jyoti Prakash","doi":"10.1515/zna-2023-0330","DOIUrl":"https://doi.org/10.1515/zna-2023-0330","url":null,"abstract":"The electrothermoconvection in a rotating dielectric fluid layer heated from below (or above) is studied analytically using linear stability theory. First, we derive the necessary conditions for oscillatory motion when the fluid layer is heated from below and from above. Then as a consequence, sufficient conditions for the validity of the exchange principle are derived for the two configurations in terms of the parameters of the systems alone. The results hold for free boundaries for all wave numbers and for rigid boundaries with some restrictions. Further, the results for electrothermoconvection without rotation, rotatory Rayleigh–Bénard convection and Rayleigh–Bénard convection are also obtained as special cases which validate the existing results. To the best of author’s knowledge such results are not reported in the literature as far as the domain of electrothermoconvection studies is concerned.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140595952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reem K. Alhefthi, Kalim U. Tariq, Ahmet Bekir, Arslan Ahmed
In this article, the modified Kudryashov and extended simple equation methods are employed to obtain analytical solutions for the Zhiber–Shabat problem. The outcomes of this study clearly indicate that the provided methodologies are appropriate techniques for generating some new exact solutions for nonlinear evolution equations. Furthermore, the nature of the solutions would be presented in three dimensions for various parameters applying the most advanced scientific instruments. The physical behavior of the solutions are graphically displayed, and it is established that the acquired solutions are newly constructed in the form of bright, dark, optical, singular, and bell-shaped periodic soliton wave structures. The properties of the nonlinear model have been illustrated using 3D, 2D, and contour plots by selecting an appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. To the best of our knowledge, the current work presents a novel case study that has not been previously studied in order to generate several new solutions to the governing model appearing in diverse disciplines. The results show that the strategies that have been employed are more effective and capable than the traditional methods found in previous research.
{"title":"On some novel solitonic structures for the Zhiber–Shabat model in modern physics","authors":"Reem K. Alhefthi, Kalim U. Tariq, Ahmet Bekir, Arslan Ahmed","doi":"10.1515/zna-2024-0010","DOIUrl":"https://doi.org/10.1515/zna-2024-0010","url":null,"abstract":"In this article, the modified Kudryashov and extended simple equation methods are employed to obtain analytical solutions for the Zhiber–Shabat problem. The outcomes of this study clearly indicate that the provided methodologies are appropriate techniques for generating some new exact solutions for nonlinear evolution equations. Furthermore, the nature of the solutions would be presented in three dimensions for various parameters applying the most advanced scientific instruments. The physical behavior of the solutions are graphically displayed, and it is established that the acquired solutions are newly constructed in the form of bright, dark, optical, singular, and bell-shaped periodic soliton wave structures. The properties of the nonlinear model have been illustrated using 3D, 2D, and contour plots by selecting an appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. To the best of our knowledge, the current work presents a novel case study that has not been previously studied in order to generate several new solutions to the governing model appearing in diverse disciplines. The results show that the strategies that have been employed are more effective and capable than the traditional methods found in previous research.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The electrospinning process allows the production of nanofibers from polymer solutions, making them suitable for various applications such as sensors, electronic devices, conductive materials, and advanced composites for high-temperature environments. In this research, polyaniline (PANI) was doped with camphor sulfonic camphor sulfonic acid (HCSA). HCSA dopant is used to modify the electrical and structural properties of polyaniline. To introduce reduced graphene oxide as a nanofiller to enhance the electrical properties of the polymer. Both the HCSA-doped PANI and HCSA-doped PANI with rGO nanofibers were electro-spun separately to create individual nanofibers. Fourier-transform infrared spectroscopy was used to investigate the chemical composition and functional groups present in the nanofibers. Field emission scanning electron microscopy was employed to study the nanofibers’ morphology, structure, and surface characteristics. Thermogravimetric analysis was used to assess the thermal stability of the nanofibers and to approximate the content of rGO. These results indicate that the addition of reduced graphene oxide (rGO) led to improvements in the nanofibers’ electrical conductivity and thermal stability.
电纺丝工艺可从聚合物溶液中生产出纳米纤维，使其适用于各种应用，如传感器、电子设备、导电材料和高温环境下的先进复合材料。在这项研究中，聚苯胺（PANI）掺杂了樟脑磺酸（HCSA）。HCSA 掺杂剂用于改变聚苯胺的电气和结构特性。引入还原氧化石墨烯作为纳米填料，以增强聚合物的电气性能。分别电纺掺杂了 HCSA 的 PANI 和掺杂了 HCSA 的 PANI 与 rGO 纳米纤维，以生成单独的纳米纤维。傅立叶变换红外光谱法用于研究纳米纤维中的化学成分和官能团。场发射扫描电子显微镜用于研究纳米纤维的形态、结构和表面特征。热重分析用于评估纳米纤维的热稳定性和 rGO 的大致含量。这些结果表明，添加还原氧化石墨烯（rGO）可提高纳米纤维的导电性和热稳定性。
{"title":"Tailoring reduced graphene oxide into nanofibrous architectures: fabrication, characterization, and functional insights","authors":"Jawaria Rehman, Nadia Anwar, Muqarrab Ahmed, Shaheen Irfan, Ghazi Aman Nowsherwan, Abdul Waheed Anwar, Nazia Iram, Javeria Arshad, Nosheen Mushahid, Ayesha Saleem","doi":"10.1515/zna-2023-0310","DOIUrl":"https://doi.org/10.1515/zna-2023-0310","url":null,"abstract":"The electrospinning process allows the production of nanofibers from polymer solutions, making them suitable for various applications such as sensors, electronic devices, conductive materials, and advanced composites for high-temperature environments. In this research, polyaniline (PANI) was doped with camphor sulfonic camphor sulfonic acid (HCSA). HCSA dopant is used to modify the electrical and structural properties of polyaniline. To introduce reduced graphene oxide as a nanofiller to enhance the electrical properties of the polymer. Both the HCSA-doped PANI and HCSA-doped PANI with rGO nanofibers were electro-spun separately to create individual nanofibers. Fourier-transform infrared spectroscopy was used to investigate the chemical composition and functional groups present in the nanofibers. Field emission scanning electron microscopy was employed to study the nanofibers’ morphology, structure, and surface characteristics. Thermogravimetric analysis was used to assess the thermal stability of the nanofibers and to approximate the content of rGO. These results indicate that the addition of reduced graphene oxide (rGO) led to improvements in the nanofibers’ electrical conductivity and thermal stability.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"2018 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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