Karamcheti Mallika, K. Vijaya Lakshmi, K. Lakshmi Sarada, S. Sreehari Sastry
In this paper, phase transition temperatures of nematic liquid crystals: 4-n alkoxy benzoic acid (nOBA, where n = 4 and 6) are determined from the Legendre moments of liquid crystal textures. Here, the image analysis technique in conjunction with polarizing optical microscope is used to compute the Legendre moments from the textures of liquid crystals. As a function of temperature, Liquid crystal textures are recorded from the arthroscopic mode of optical microscope. Changes in textural features of the sample with respect to temperature bring the variations in intensity values of liquid crystal textures. The brightness image that is generated from the liquid crystal textural patterns separates the information about fluctuations in intensity. In this approach, Legendre moments are computed from the brightness images of the liquid crystal textures and are plotted as a function of temperature. Significant variations in the brightness Legendre moment curve provide insight into the liquid crystal transition temperatures. Results obtained from the present methodology are compared with gray color textures data and the experimental technique of differential scanning calorimetry and are in good agreement with each other. This method is an objective and quantitative technique whereas POM method is qualitative and subjective.
{"title":"Computation Legendre moments using image analysis technique","authors":"Karamcheti Mallika, K. Vijaya Lakshmi, K. Lakshmi Sarada, S. Sreehari Sastry","doi":"10.1515/zna-2024-0116","DOIUrl":"https://doi.org/10.1515/zna-2024-0116","url":null,"abstract":"In this paper, phase transition temperatures of nematic liquid crystals: 4-<jats:italic>n</jats:italic> alkoxy benzoic acid (<jats:italic>n</jats:italic>OBA, where <jats:italic>n</jats:italic> = 4 and 6) are determined from the Legendre moments of liquid crystal textures. Here, the image analysis technique in conjunction with polarizing optical microscope is used to compute the Legendre moments from the textures of liquid crystals. As a function of temperature, Liquid crystal textures are recorded from the arthroscopic mode of optical microscope. Changes in textural features of the sample with respect to temperature bring the variations in intensity values of liquid crystal textures. The brightness image that is generated from the liquid crystal textural patterns separates the information about fluctuations in intensity. In this approach, Legendre moments are computed from the brightness images of the liquid crystal textures and are plotted as a function of temperature. Significant variations in the brightness Legendre moment curve provide insight into the liquid crystal transition temperatures. Results obtained from the present methodology are compared with gray color textures data and the experimental technique of differential scanning calorimetry and are in good agreement with each other. This method is an objective and quantitative technique whereas POM method is qualitative and subjective.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218947","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}
Ahmet Yildiz, Emre İbram, Onur Erol, Hande Güler Özgül
In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies.
{"title":"Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations","authors":"Ahmet Yildiz, Emre İbram, Onur Erol, Hande Güler Özgül","doi":"10.1515/zna-2024-0062","DOIUrl":"https://doi.org/10.1515/zna-2024-0062","url":null,"abstract":"In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218946","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 wireless optical communication, the optical signal passes through the atmospheric turbulence, resulting in the simultaneous distortion of the amplitude and phase of the optical signal at the receiving end. This article applies the idea of phase contrast method to simultaneously compensate the amplitude and phase of the optical signal at the receiving end, derives the mapping relationship between the compensated phase and light intensity, and obtains the required compensated phase for full-field compensation. Numerical calculations show that when the difference between zero-frequency phase compensation and nonzero-frequency phase compensation is ±π, the maximum light intensity compensation is obtained. Based on the Gerchberg Saxton algorithm, a new method is proposed to invert the compensated phase with the maximum light intensity after full-field compensation and perform full-field correction through the adaptive optical system. The numerical calculation and experiment show that the phase contrast Gerchberg Saxton algorithm can effectively compensate the distorted optical signals under different turbulence, and thus the received signals of optical wireless communication can be corrected in full field.
{"title":"Research on adaptive optics technology based on phase contrast Gerchberg Saxton algorithm","authors":"Rui Wang, Xizheng Ke, Jingyuan Lang, JiaLi Wu","doi":"10.1515/zna-2024-0058","DOIUrl":"https://doi.org/10.1515/zna-2024-0058","url":null,"abstract":"In wireless optical communication, the optical signal passes through the atmospheric turbulence, resulting in the simultaneous distortion of the amplitude and phase of the optical signal at the receiving end. This article applies the idea of phase contrast method to simultaneously compensate the amplitude and phase of the optical signal at the receiving end, derives the mapping relationship between the compensated phase and light intensity, and obtains the required compensated phase for full-field compensation. Numerical calculations show that when the difference between zero-frequency phase compensation and nonzero-frequency phase compensation is ±π, the maximum light intensity compensation is obtained. Based on the Gerchberg Saxton algorithm, a new method is proposed to invert the compensated phase with the maximum light intensity after full-field compensation and perform full-field correction through the adaptive optical system. The numerical calculation and experiment show that the phase contrast Gerchberg Saxton algorithm can effectively compensate the distorted optical signals under different turbulence, and thus the received signals of optical wireless communication can be corrected in full field.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218945","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}
We present calculations of interferograms (interference patterns) of one or multiple spiral phase plates that would be observed with a perfect crystal neutron interferometer of Mach–Zehnder type. A spiral phase plate (SPP) in one of the two coherent beam paths produces a twist in the phase front and thus a vortex beam with intrinsic angular momentum, which in the case of neutrons should be observed as a characteristic interference pattern that appears complementary to each other in both detectors behind the interferometer. Adding additional SPPs in one beam path of the interferometer yield interference patterns similar to that of a single SPP but only due to the cumulative step height. All simulated interferograms have been calculated on the basis of dynamical neutron diffraction without any assumption of a neutron orbital angular momentum and show very convincing agreement with experimental results from the literature, see e.g. (C. W. Clark, R. Barankov, M. G. Huber, M. Arif, D. G. Cory, and D. A. Pushin, “Controlling neutron orbital angular momentum,” Nature, vol. 525, pp. 504–506, 2015). In particular, this clarifies, that the cited experiments do not give evidence of the quantization of interactions caused by a twist of the phase front of a neutron wave in the interferometer and thus no evidence for the effect of a neutron orbital angular momentum.
我们介绍了对一个或多个螺旋相板干涉图（干涉图案）的计算，这些干涉图可以通过马赫-泽恩德（Mach-Zehnder）型完美晶体中子干涉仪观测到。两个相干光束路径中的一个螺旋相位板（SPP）会在相位前沿产生扭曲，从而产生具有固有角动量的涡旋光束。在干涉仪的一条光束路径上添加额外的 SPP 会产生与单个 SPP 相似的干涉图，但这只是由于累积的阶跃高度所致。所有模拟干涉图都是在动态中子衍射的基础上计算得出的，没有任何中子轨道角动量的假设，并且与文献中的实验结果显示出非常令人信服的一致性，例如参见（C. W. Clark、R. Barankov、M. G. Huber、M. Arif、D. G. Cory 和 D. A. Pushin，"控制中子轨道角动量"，《自然》，第 525 卷，第 504-506 页，2015 年）。这尤其说明，所引用的实验并不能证明干涉仪中的中子波相位前沿扭曲所导致的相互作用量子化，因此也就不能证明中子轨道角动量的影响。
{"title":"Computerized simulation of 2-dimensional phase contrast images using spiral phase plates in neutron interferometry","authors":"Wolfgang Treimer, Frank Haußer, Martin Suda","doi":"10.1515/zna-2024-0142","DOIUrl":"https://doi.org/10.1515/zna-2024-0142","url":null,"abstract":"We present calculations of interferograms (interference patterns) of one or multiple spiral phase plates that would be observed with a perfect crystal neutron interferometer of Mach–Zehnder type. A spiral phase plate (SPP) in one of the two coherent beam paths produces a twist in the phase front and thus a vortex beam with intrinsic angular momentum, which in the case of neutrons should be observed as a characteristic interference pattern that appears complementary to each other in both detectors behind the interferometer. Adding additional SPPs in one beam path of the interferometer yield interference patterns similar to that of a single SPP but only due to the cumulative step height. All simulated interferograms have been calculated on the basis of dynamical neutron diffraction without any assumption of a neutron orbital angular momentum and show very convincing agreement with experimental results from the literature, see e.g. (C. W. Clark, R. Barankov, M. G. Huber, M. Arif, D. G. Cory, and D. A. Pushin, “Controlling neutron orbital angular momentum,” <jats:italic>Nature</jats:italic>, vol. 525, pp. 504–506, 2015). In particular, this clarifies, that the cited experiments do not give evidence of the quantization of interactions caused by a twist of the phase front of a neutron wave in the interferometer and thus no evidence for the effect of a neutron orbital angular momentum.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227431","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}
Naseem Abbas, Akhtar Hussain, Muhammad Waseem Akram, Shah Muhammad, Mohammad Shuaib
This present study is concerned with the group-invariant solutions of the (3 + 1)-dimensional Martinez Alonso–Shabat equation by using the Lie symmetry method. The Lie transformation technique is used to deduce the infinitesimals, Lie symmetry operators, commutation relations, and symmetry reductions. The optimal system for the obtained Lie symmetry algebra is obtained by using the concept of the adjoint map. As for now, the considered model equation is converted into nonlinear ordinary differential equations (ODEs) in two cases in the symmetry reductions. The exact closed-form solutions are obtained by applying constraint conditions on the symmetry generators. Due to the presence of arbitrary functional parameters, these group-invariant solutions are displayed based on suitable numerical simulations. The conservation laws are obtained by using the multiplier method. The conclusion is accounted for toward the end.
{"title":"Invariant analysis of the multidimensional Martinez Alonso–Shabat equation","authors":"Naseem Abbas, Akhtar Hussain, Muhammad Waseem Akram, Shah Muhammad, Mohammad Shuaib","doi":"10.1515/zna-2024-0115","DOIUrl":"https://doi.org/10.1515/zna-2024-0115","url":null,"abstract":"This present study is concerned with the group-invariant solutions of the (3 + 1)-dimensional Martinez Alonso–Shabat equation by using the Lie symmetry method. The Lie transformation technique is used to deduce the infinitesimals, Lie symmetry operators, commutation relations, and symmetry reductions. The optimal system for the obtained Lie symmetry algebra is obtained by using the concept of the adjoint map. As for now, the considered model equation is converted into nonlinear ordinary differential equations (ODEs) in two cases in the symmetry reductions. The exact closed-form solutions are obtained by applying constraint conditions on the symmetry generators. Due to the presence of arbitrary functional parameters, these group-invariant solutions are displayed based on suitable numerical simulations. The conservation laws are obtained by using the multiplier method. The conclusion is accounted for toward the end.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218953","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}
This study focuses on the investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative by the implementation of the generalized projective Riccati equations technique. The proposed method uses symbolic computations to provide a dynamic and powerful mathematical tool for addressing the governing model and yielding significant results. Numerous analytical solutions of the governing model, including bell-shaped soliton solutions, anti-kink soliton solutions, periodic solitary wave solutions and other solutions, have been constructed effectively utilizing this effective technique. The findings acquired from the governing model utilizing the suggested technique demonstrate that all results are novel and presented for the first time in this study. Solitons are of immense significance in the domain of nonlinear optics due to their inherent ability to preserve their shape and velocity during propagation. The study of the propagation and the dynamical behaviour of the derived results have been explored by representing them graphically through 3D, density, and contour plots with different selections of arbitrary parameter values. The solitons acquired from the proposed model can provide significant advantages in the field of fiber-optic transmission technology. The obtained results demonstrate that the suggested approach is extremely promising, straightforward, and efficient. Furthermore, this approach may be effectively used in numerous emerging nonlinear models found in the fields of applied sciences and engineering.
{"title":"Dynamical investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative","authors":"Nilkanta Das, S. Saha Ray","doi":"10.1515/zna-2024-0112","DOIUrl":"https://doi.org/10.1515/zna-2024-0112","url":null,"abstract":"This study focuses on the investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative by the implementation of the generalized projective Riccati equations technique. The proposed method uses symbolic computations to provide a dynamic and powerful mathematical tool for addressing the governing model and yielding significant results. Numerous analytical solutions of the governing model, including bell-shaped soliton solutions, anti-kink soliton solutions, periodic solitary wave solutions and other solutions, have been constructed effectively utilizing this effective technique. The findings acquired from the governing model utilizing the suggested technique demonstrate that all results are novel and presented for the first time in this study. Solitons are of immense significance in the domain of nonlinear optics due to their inherent ability to preserve their shape and velocity during propagation. The study of the propagation and the dynamical behaviour of the derived results have been explored by representing them graphically through 3D, density, and contour plots with different selections of arbitrary parameter values. The solitons acquired from the proposed model can provide significant advantages in the field of fiber-optic transmission technology. The obtained results demonstrate that the suggested approach is extremely promising, straightforward, and efficient. Furthermore, this approach may be effectively used in numerous emerging nonlinear models found in the fields of applied sciences and engineering.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218954","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}
We investigate the flow dynamics within an elastic tube transporting a power-law fluid, where the tube is subject to a specified external forcing in the form of a progressive traveling wave. The oesophagus is cylindrical in shape and exhibits linear elastic properties. The flow is creeping, and the long wavelength and low Reynolds number approximations are employed for a solution. The relationship between the pressure distribution within the oesophagus and the radial variation of the tube characterizes the behavior of the tube. Findings reveal that the elasticity and the variations in the applied dilating forcing amplitude substantially impact pressure resulting from sinusoidal wave forcing. Notably, even a nominal increase in the inward radial force amplitude for dilatant fluid results in significant pressure changes compared with Newtonian fluid. We also observe a notable distinction between time-averaged volume flow rate and velocity in pseudo-plastic and dilatant forms. Our study also identifies that the radial velocity experiences either attenuation or enhancement due to the fluid’s shear thickening and thinning characteristics. Moreover, our research uncovers a novel dimension by highlighting that in shifting from pseudo-plasticity to dilatancy, the fluid requires higher pressure to propel the bolus toward the hiatus. This observation has important implications, suggesting that feeding a more dilatant fluid to patients with pre-diagnosed swallowing disorders, such as sliding hiatus hernia, is not advisable, fearing increased pressure.
{"title":"Impact of dilating forcing amplitudes on a peristaltically driven non-Newtonian fluid in an elastic tube: application to swallowing disorders","authors":"Sanjay K. Pandey, Anupam K. Pandey","doi":"10.1515/zna-2024-0063","DOIUrl":"https://doi.org/10.1515/zna-2024-0063","url":null,"abstract":"We investigate the flow dynamics within an elastic tube transporting a power-law fluid, where the tube is subject to a specified external forcing in the form of a progressive traveling wave. The oesophagus is cylindrical in shape and exhibits linear elastic properties. The flow is creeping, and the long wavelength and low Reynolds number approximations are employed for a solution. The relationship between the pressure distribution within the oesophagus and the radial variation of the tube characterizes the behavior of the tube. Findings reveal that the elasticity and the variations in the applied dilating forcing amplitude substantially impact pressure resulting from sinusoidal wave forcing. Notably, even a nominal increase in the inward radial force amplitude for dilatant fluid results in significant pressure changes compared with Newtonian fluid. We also observe a notable distinction between time-averaged volume flow rate and velocity in pseudo-plastic and dilatant forms. Our study also identifies that the radial velocity experiences either attenuation or enhancement due to the fluid’s shear thickening and thinning characteristics. Moreover, our research uncovers a novel dimension by highlighting that in shifting from pseudo-plasticity to dilatancy, the fluid requires higher pressure to propel the bolus toward the hiatus. This observation has important implications, suggesting that feeding a more dilatant fluid to patients with pre-diagnosed swallowing disorders, such as sliding hiatus hernia, is not advisable, fearing increased pressure.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933031","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}
Nicolas Mam Bakalack, Valjacques Nyemb Nsoga, Gérémino Ella Eny, Martin N. Azese, Jacques Hona
The Navier–Stokes equations and the energy equation are used to investigate a fluid flow between two stretching rectangular surfaces subjected to a temperature difference that affects the dynamic viscosity and thermal conductivity of the fluid. The wall stretching process enhances the momentum boundary layer thickness which slows the axial motion of the fluid away from the flow boundaries. When the stretching parameter γ is equal to 1, that is the case corresponding to symmetric stretching, the minimum of the axial velocity is located at the midplane of the channel y = 0.5 if the viscosity variational parameter α equals 0. This minimum moves towards the region 0.5 < y < 1 for α > 0, but migrates towards the region 0 < y < 0.5 for α < 0. Moreover, in the case of symmetric stretching corresponding to γ = 1, the growth in Reynolds number Re tends to increase the axial velocity around the middle of the channel for α ≥ 0 in the attempt to counteract the effects of enhancing the momentum boundary layer thickness leading to the flattening of axial velocity profiles for Re ≥ 100. While the conductivity variational parameter β does not influence enough the fluid dynamics and heat transfer, the Reynolds number Re and the Péclet number Pé can increase or decrease the temperature distribution inside the channel depending on the sign of the parameter α. Practical applications related to the present study include lubrification, food manufacturing, paint industries, extrusion processes in plastic and metal industries.
本文采用纳维-斯托克斯方程和能量方程来研究两个拉伸矩形表面之间的流体流动，该流动受到影响流体动态粘度和热导率的温差的作用。壁面拉伸过程增加了动量边界层厚度，从而减缓了流体远离流动边界的轴向运动。当拉伸参数 γ 等于 1 时，即对应于对称拉伸的情况，如果粘度变化参数 α 等于 0，则轴向速度的最小值位于通道的中平面 y = 0.5；当 α > 0 时，该最小值向 0.5 < y < 1 区域移动，但当 α < 0 时，该最小值向 0 < y < 0.此外，在相当于 γ = 1 的对称拉伸情况下，雷诺数 Re 的增长倾向于在 α ≥ 0 时提高通道中部周围的轴向速度，以抵消动量边界层厚度增加导致 Re ≥ 100 时轴向速度曲线变平的影响。虽然传导性可变参数 β 对流体动力学和传热影响不大，但雷诺数 Re 和贝克莱特数 Pé 可根据参数 α 的符号增减通道内的温度分布。 与本研究相关的实际应用包括润滑、食品制造、涂料工业、塑料和金属工业的挤压过程。
{"title":"Laminar flow with temperature-dependent fluid properties between two stretching rectangular surfaces","authors":"Nicolas Mam Bakalack, Valjacques Nyemb Nsoga, Gérémino Ella Eny, Martin N. Azese, Jacques Hona","doi":"10.1515/zna-2024-0101","DOIUrl":"https://doi.org/10.1515/zna-2024-0101","url":null,"abstract":"The Navier–Stokes equations and the energy equation are used to investigate a fluid flow between two stretching rectangular surfaces subjected to a temperature difference that affects the dynamic viscosity and thermal conductivity of the fluid. The wall stretching process enhances the momentum boundary layer thickness which slows the axial motion of the fluid away from the flow boundaries. When the stretching parameter <jats:italic>γ</jats:italic> is equal to 1, that is the case corresponding to symmetric stretching, the minimum of the axial velocity is located at the midplane of the channel <jats:italic>y</jats:italic> = 0.5 if the viscosity variational parameter <jats:italic>α</jats:italic> equals 0. This minimum moves towards the region 0.5 < <jats:italic>y</jats:italic> < 1 for <jats:italic>α</jats:italic> > 0, but migrates towards the region 0 < <jats:italic>y</jats:italic> < 0.5 for <jats:italic>α</jats:italic> < 0. Moreover, in the case of symmetric stretching corresponding to <jats:italic>γ</jats:italic> = 1, the growth in Reynolds number Re tends to increase the axial velocity around the middle of the channel for <jats:italic>α</jats:italic> ≥ 0 in the attempt to counteract the effects of enhancing the momentum boundary layer thickness leading to the flattening of axial velocity profiles for Re ≥ 100. While the conductivity variational parameter <jats:italic>β</jats:italic> does not influence enough the fluid dynamics and heat transfer, the Reynolds number Re and the Péclet number <jats:italic>Pé</jats:italic> can increase or decrease the temperature distribution inside the channel depending on the sign of the parameter <jats:italic>α</jats:italic>. Practical applications related to the present study include lubrification, food manufacturing, paint industries, extrusion processes in plastic and metal industries.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776030","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 main work of this paper is to construct the Wronskian solution and investigate the integrability characteristics of the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation. Firstly, the Wronskian technique is used to acquire a sufficient condition of the Wronskian solution. According to the Wronskian form, the soliton solution is obtained by selecting the elements in the determinant that satisfy the linear partial differential systems. Secondly, the bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are derived directly via the Hirota bilinear method and the Bell polynomial theory, respectively. Finally, Painlevé analysis proves that this equation possesses the Painlevé property, and a Painlevé-typed Bäcklund transformation is constructed to solve a family of exact solutions by selecting appropriate seed solution. It shows that the Wronskian technique, Bäcklund transformation, Bell polynomial and Painlevé analysis are applicable to obtain the exact solutions of the nonlinear evolution equations, e.g., soliton solution, single-wave solution and two-wave solution.
{"title":"Wronskian solution, Bäcklund transformation and Painlevé analysis to a (2 + 1)-dimensional Konopelchenko–Dubrovsky equation","authors":"Di Gao, Wen-Xiu Ma, Xing Lü","doi":"10.1515/zna-2024-0016","DOIUrl":"https://doi.org/10.1515/zna-2024-0016","url":null,"abstract":"The main work of this paper is to construct the Wronskian solution and investigate the integrability characteristics of the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation. Firstly, the Wronskian technique is used to acquire a sufficient condition of the Wronskian solution. According to the Wronskian form, the soliton solution is obtained by selecting the elements in the determinant that satisfy the linear partial differential systems. Secondly, the bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are derived directly via the Hirota bilinear method and the Bell polynomial theory, respectively. Finally, Painlevé analysis proves that this equation possesses the Painlevé property, and a Painlevé-typed Bäcklund transformation is constructed to solve a family of exact solutions by selecting appropriate seed solution. It shows that the Wronskian technique, Bäcklund transformation, Bell polynomial and Painlevé analysis are applicable to obtain the exact solutions of the nonlinear evolution equations, e.g., soliton solution, single-wave solution and two-wave solution.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745291","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}
This work is concerned with the relativistic quantum dynamics of a self-interacting neutron in the presence of an external ultra-strong electromagnetic (EM) field in a cylindrical inertial frame. We first regard the Dirac–Pauli (DP) Lagrangian to study the planar dynamics of a neutron polarized along the z-axis subjected to a confining external static EM field composed of a homogeneous magnetic field in the z-direction and a linear radial electric field in the polar plane. The corresponding discrete Landau energy levels are found. As a nonlinear (NL) example model, we introduce a 1-flavor Nambu Jona–Lasinio (NJL) mass term into the DP Lagrangian. The continuous ground-state Landau levels are determined. We readily obtain modified Maxwell’s equations associated with these levels. We consider a simple application of the model related to the dynamics of neutrons in the presence of strong-QED fields inside the surface of aligned neutron stars. We briefly comment on possible classical solitonic solutions of the model.
这项研究关注的是在圆柱惯性框架中，自相互作用中子在外部超强电磁场作用下的相对论量子动力学。我们首先利用狄拉克-保利（DP）拉格朗日来研究沿 z 轴极化的中子的平面动力学，该中子受到由 z 方向上的均匀磁场和极面上的线性径向电场组成的约束性外部静态电磁场的作用。我们找到了相应的离散朗道能级。作为非线性（NL）示例模型，我们在 DP 拉格朗日中引入了单味 Nambu Jona-Lasinio （NJL）质量项。我们确定了连续基态朗道能级。我们很容易得到与这些水平相关的修正麦克斯韦方程。我们考虑了该模型的一个简单应用，即在排列整齐的中子星表面内存在强 QED 场时的中子动力学。我们简要评述了该模型可能的经典孤子解。
{"title":"Neutron dynamics in ultra-strong electromagnetic fields: an example model","authors":"Stanley A. Bruce","doi":"10.1515/zna-2024-0070","DOIUrl":"https://doi.org/10.1515/zna-2024-0070","url":null,"abstract":"\u0000 This work is concerned with the relativistic quantum dynamics of a self-interacting neutron in the presence of an external ultra-strong electromagnetic (EM) field in a cylindrical inertial frame. We first regard the Dirac–Pauli (DP) Lagrangian to study the planar dynamics of a neutron polarized along the z-axis subjected to a confining external static EM field composed of a homogeneous magnetic field in the z-direction and a linear radial electric field in the polar plane. The corresponding discrete Landau energy levels are found. As a nonlinear (NL) example model, we introduce a 1-flavor Nambu Jona–Lasinio (NJL) mass term into the DP Lagrangian. The continuous ground-state Landau levels are determined. We readily obtain modified Maxwell’s equations associated with these levels. We consider a simple application of the model related to the dynamics of neutrons in the presence of strong-QED fields inside the surface of aligned neutron stars. We briefly comment on possible classical solitonic solutions of the model.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"7 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642372","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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