Süleyman Murat Bağdatlı, Necla Togun, Burak Emre Yapanmış, Şevki Akkoca
Abstract This study investigates the nonlinear vibration motions of the Euler–Bernoulli microbeam on a nonlinear elastic foundation in a uniform magnetic field based on Modified Couple Stress Theory (MCST). The effect of size, foundation, and magnetic field on the nonlinear vibration motion of microbeam has been examined. The governing equations related to the nonlinear vibration motions of the microbeam are obtained by using Hamilton’s Principle, and the Multiple Time Scale Method was used to obtain the solutions for the governing equations. The linear natural frequencies of microbeam are presented in the table according to nonlinear parameters and boundary conditions. The linear and nonlinear natural frequency ratio graphs are shown. The present study results are also compared with previous work for validation. It is observed that length scale parameters and magnetic force have a more significant effect on the natural frequency of microbeams. It is seen that when the linear elastic foundation coefficient, the Pasternak foundation and the magnetic force effects increase, the ratio of nonlinear and linear natural frequency decreases.
{"title":"Nonlinear vibration of microbeams subjected to a uniform magnetic field and rested on nonlinear elastic foundation","authors":"Süleyman Murat Bağdatlı, Necla Togun, Burak Emre Yapanmış, Şevki Akkoca","doi":"10.1515/zna-2023-0225","DOIUrl":"https://doi.org/10.1515/zna-2023-0225","url":null,"abstract":"Abstract This study investigates the nonlinear vibration motions of the Euler–Bernoulli microbeam on a nonlinear elastic foundation in a uniform magnetic field based on Modified Couple Stress Theory (MCST). The effect of size, foundation, and magnetic field on the nonlinear vibration motion of microbeam has been examined. The governing equations related to the nonlinear vibration motions of the microbeam are obtained by using Hamilton’s Principle, and the Multiple Time Scale Method was used to obtain the solutions for the governing equations. The linear natural frequencies of microbeam are presented in the table according to nonlinear parameters and boundary conditions. The linear and nonlinear natural frequency ratio graphs are shown. The present study results are also compared with previous work for validation. It is observed that length scale parameters and magnetic force have a more significant effect on the natural frequency of microbeams. It is seen that when the linear elastic foundation coefficient, the Pasternak foundation and the magnetic force effects increase, the ratio of nonlinear and linear natural frequency decreases.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"7 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Serge Benjamin Mbam Mbam, Maurice Lamara, Noé Richard Makon, Elisabeth Ngo Nyobe, Elkana Pemha
Abstract The steady laminar flow of an incompressible Newtonian fluid in a porous annular duct with accelerated rotating walls is investigated. The flow is located in the polar plane and is driven by suction and injection at the walls. As required by conservation of mass with zero axial velocity, the fluid is injected into one of the cylinders, which becomes the upstream cylinder, and suctioned into the other, which represents the downstream cylinder. Only the case of the downstream cylinder at rest is examined. The duct gap ratio, the velocity ratio comparing the radial and azimuthal velocities, the Reynolds number, and the velocity coefficient that compares the fluid velocity at the upstream and downstream cylinders are the four parameters of the problem. The purpose of this research is to identify the prerequisites for the flow’s existence and determine how the aforementioned variables affect the flow velocity and pressure gradients at a fixed Reynolds number. The Navier–Stokes equations are replaced by the polar-plane vorticity equation, which is solved using the similarity-solutions method. The shooting technique, including the fourth-order Runge–Kutta algorithm, is used to produce numerical solutions. From the findings, physical understandings of the flow are derived. More specifically, we discover an unexpected interior zone where the fluid is perpetually at rest even while flow is present. The only solution found corresponds to the case of the inner cylinder upstream and rotating provided that the velocity ratio does not exceed the threshold of 0.1 with a velocity coefficient greater than 1.
{"title":"Polar-plane flow in porous annular ducts with accelerated rotating walls. A region of stagnation inside the fluid","authors":"Serge Benjamin Mbam Mbam, Maurice Lamara, Noé Richard Makon, Elisabeth Ngo Nyobe, Elkana Pemha","doi":"10.1515/zna-2023-0197","DOIUrl":"https://doi.org/10.1515/zna-2023-0197","url":null,"abstract":"Abstract The steady laminar flow of an incompressible Newtonian fluid in a porous annular duct with accelerated rotating walls is investigated. The flow is located in the polar plane and is driven by suction and injection at the walls. As required by conservation of mass with zero axial velocity, the fluid is injected into one of the cylinders, which becomes the upstream cylinder, and suctioned into the other, which represents the downstream cylinder. Only the case of the downstream cylinder at rest is examined. The duct gap ratio, the velocity ratio comparing the radial and azimuthal velocities, the Reynolds number, and the velocity coefficient that compares the fluid velocity at the upstream and downstream cylinders are the four parameters of the problem. The purpose of this research is to identify the prerequisites for the flow’s existence and determine how the aforementioned variables affect the flow velocity and pressure gradients at a fixed Reynolds number. The Navier–Stokes equations are replaced by the polar-plane vorticity equation, which is solved using the similarity-solutions method. The shooting technique, including the fourth-order Runge–Kutta algorithm, is used to produce numerical solutions. From the findings, physical understandings of the flow are derived. More specifically, we discover an unexpected interior zone where the fluid is perpetually at rest even while flow is present. The only solution found corresponds to the case of the inner cylinder upstream and rotating provided that the velocity ratio does not exceed the threshold of 0.1 with a velocity coefficient greater than 1.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"57 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135091774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A mesoporous cobalt ferrite nanostructure was prepared by a green chemistry approach using Pimpinella anisum extract for Cd (II) ions elimination from an aqueous medium. The metal ions adsorption was explored under varying operating conditions, comprising of the pH, initial adsorbate concentration, and contact time. The synthesized sorbent was characterized by various techniques where the XRD data verified a ferrite structure of ≈25 nm crystallite size and the EDX elemental analysis affirmed the presence of the corresponding elements. The CoFe 2 O 4 established porosity characteristic of 10.8 m 2 g −1 BET-specific surface area and 0.023 cm 3 g −1 pore volume values. Batch mode experiments ascertained that the Cd (II) ions uptake was pH-dependent, with peak removal of 170 mg/g accomplished at pH = 5. The adsorption process of the metal ions onto the mesoporous nanomaterial surface fitted well with the Langmuir isotherm and pseudo-second-order kinetics models. The mechanistic aspects indicated the role of intra-particle and film diffusion in the adsorption process. The adsorbent could efficiently remove the pollutant up 74.3 % to four cycles of successful regeneration. This investigation endorsed that CoFe 2 O 4 might be potent candidate for heavy metals from aqueous systems.
摘要:采用绿色化学方法制备了介孔钴铁氧体纳米结构，并利用香草提取物去除水中的Cd (II)离子。考察了不同操作条件下(pH、初始吸附浓度和接触时间)对金属离子的吸附性能。通过各种技术对合成的吸附剂进行了表征，XRD数据证实其为铁氧体结构，晶粒尺寸约为25 nm, EDX元素分析证实了相应元素的存在。cofe2o4的孔隙度特征为10.8 m 2 g−1 bet比表面积和0.023 cm 3 g−1孔隙体积。批处理模式实验确定了Cd (II)离子的吸收与pH有关，在pH = 5时达到峰值170 mg/g。金属离子在介孔纳米材料表面的吸附过程符合Langmuir等温线和拟二级动力学模型。机理方面表明了颗粒内扩散和膜扩散在吸附过程中的作用。该吸附剂再生成功4次，对污染物的去除率高达74.3%。这项研究表明，CoFe 2o4可能是水中重金属的有力候选者。
{"title":"Green creation of CoFe<sub>2</sub>O<sub>4</sub> nanosorbent for superior toxic Cd ions elimination","authors":"Laila S. Alqarni","doi":"10.1515/zna-2023-0180","DOIUrl":"https://doi.org/10.1515/zna-2023-0180","url":null,"abstract":"Abstract A mesoporous cobalt ferrite nanostructure was prepared by a green chemistry approach using Pimpinella anisum extract for Cd (II) ions elimination from an aqueous medium. The metal ions adsorption was explored under varying operating conditions, comprising of the pH, initial adsorbate concentration, and contact time. The synthesized sorbent was characterized by various techniques where the XRD data verified a ferrite structure of ≈25 nm crystallite size and the EDX elemental analysis affirmed the presence of the corresponding elements. The CoFe 2 O 4 established porosity characteristic of 10.8 m 2 g −1 BET-specific surface area and 0.023 cm 3 g −1 pore volume values. Batch mode experiments ascertained that the Cd (II) ions uptake was pH-dependent, with peak removal of 170 mg/g accomplished at pH = 5. The adsorption process of the metal ions onto the mesoporous nanomaterial surface fitted well with the Langmuir isotherm and pseudo-second-order kinetics models. The mechanistic aspects indicated the role of intra-particle and film diffusion in the adsorption process. The adsorbent could efficiently remove the pollutant up 74.3 % to four cycles of successful regeneration. This investigation endorsed that CoFe 2 O 4 might be potent candidate for heavy metals from aqueous systems.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":" 35","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients zn/n! ${z}^{n}/sqrt{n!}$ of the canonical coherent states by the factorial xnγ!=x1γ.x2γ…xnγ ${x}_{n}^{gamma }!={x}_{1}^{gamma }.{x}_{2}^{gamma }dots {x}_{n}^{gamma }$ with x0γ=0 ${x}_{0}^{gamma }=0$ , where xnγ ${x}_{n}^{gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.
通过替换系数z n / n的阶乘，构造了一类新的等压振荡器的非线性相干态。${z}^{n}/sqrt{n!}$正则相干态的阶乘x n γ != x1 γ。x2 γ…X n γ ${x}_{n}^{gamma }!={x}_{1}^{gamma }.{x}_{2}^{gamma }dots {x}_{n}^{gamma }$其中X 0 γ = 0 ${x}_{0}^{gamma }=0$，其中X n γ ${x}_{n}^{gamma }$是一个正数序列，γ是一个正实参数。这也导致了巴格曼型积分变换的构造，它将使我们能够找到正交多项式的一些积分变换。相干态的统计也将通过曼德尔参数的演算来考虑。并对挤压现象进行了讨论。
{"title":"Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator","authors":"Ghayth Ouirdani, Othmane El Moize","doi":"10.1515/zna-2023-0206","DOIUrl":"https://doi.org/10.1515/zna-2023-0206","url":null,"abstract":"Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msup> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>/</m:mo> <m:msqrt> <m:mrow> <m:mi>n</m:mi> <m:mo>!</m:mo> </m:mrow> </m:msqrt> </m:math> ${z}^{n}/sqrt{n!}$ of the canonical coherent states by the factorial <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>!</m:mo> <m:mo>=</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>.</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>…</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> </m:math> ${x}_{n}^{gamma }!={x}_{1}^{gamma }.{x}_{2}^{gamma }dots {x}_{n}^{gamma }$ with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:math> ${x}_{0}^{gamma }=0$ , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> </m:math> ${x}_{n}^{gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"25 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The geometrical structures, stabilities, electronic properties and nonlinear optical response of the halogen doped bimetallic Li n ClK ( n = 1–6) clusters were studied within the density functional theory. Based on the dissociation energy, second order energy difference and GH-L (HOMO-LUMO gap), the Li n ClK ( n = 2, 4, 6) clusters are more stable. According to their ionization energies, the clusters can be classified as a superalkali. From the NBO analysis, the clusters are excess electron systems. The obtained first static hyperpolarizability ( β o ) values are in the range of 1.56 × 10 4 − 4.33 × 10 4 au while the second static hyperpolarizability vary within 2.47 × 10 6 au to 13.9 × 10 6 au for the Li n ClK ( n = 1–6) superalkalis that are slightly higher than the nonlinear optical response of halogen doped monometallic clusters. More importantly, the Li 5 ClK is transparent in the deep UV region ( λ < 300 nm) among the superalkalis indicating that the Li 5 ClK superalkali can be a candidate structure as new member of NLO materials.
{"title":"Nonlinear optical response of Li<sub> <i>n</i> </sub>ClK (<i>n</i> = 1–6) superalkali clusters","authors":"Şükrü Şentürk, Yavuz Ekincioğlu, Ümit Doğan","doi":"10.1515/zna-2023-0177","DOIUrl":"https://doi.org/10.1515/zna-2023-0177","url":null,"abstract":"Abstract The geometrical structures, stabilities, electronic properties and nonlinear optical response of the halogen doped bimetallic Li n ClK ( n = 1–6) clusters were studied within the density functional theory. Based on the dissociation energy, second order energy difference and GH-L (HOMO-LUMO gap), the Li n ClK ( n = 2, 4, 6) clusters are more stable. According to their ionization energies, the clusters can be classified as a superalkali. From the NBO analysis, the clusters are excess electron systems. The obtained first static hyperpolarizability ( β o ) values are in the range of 1.56 × 10 4 − 4.33 × 10 4 au while the second static hyperpolarizability vary within 2.47 × 10 6 au to 13.9 × 10 6 au for the Li n ClK ( n = 1–6) superalkalis that are slightly higher than the nonlinear optical response of halogen doped monometallic clusters. More importantly, the Li 5 ClK is transparent in the deep UV region ( λ < 300 nm) among the superalkalis indicating that the Li 5 ClK superalkali can be a candidate structure as new member of NLO materials.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denoted Ŝ $hat{boldsymbol{S}}$ ; the corresponding matrix is the Ŝ -matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operator Ŝ $hat{boldsymbol{S}}$ The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s ( s = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via the Ŝ $hat{S}$ -matrix formalism.
在量子散射理论中，物理系统的时间演化可以描述为一系列的酉变换。这个变换的算子表示为S´$hat{boldsymbol{S}}$;对应的矩阵为Ŝ -矩阵(散射矩阵)。最后一个对象包含与操作符S´$hat{boldsymbol{S}}$相关的广播过程的所有信息。一方面建立了局域电磁场存在下自旋为s (s = 0,1 /2)的相对论粒子散射矩阵的一维形式，另一方面利用s′$hat{s}$ -矩阵形式分析了自旋为s的相对论粒子与局域标量势相互作用下的散射态问题的解。
{"title":"Relativistic <i>Ŝ</i>-matrix formulation in one dimension for particles of spin-s (<i>s</i> = 0, 1/2)","authors":"Nahla Bourouis, Kamel Khounfais, Meheiddine Bouatrous","doi":"10.1515/zna-2023-0096","DOIUrl":"https://doi.org/10.1515/zna-2023-0096","url":null,"abstract":"Abstract In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denoted <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mover accent=\"true\"> <m:mi mathvariant=\"bold-italic\">S</m:mi> <m:mo stretchy=\"false\">̂</m:mo> </m:mover> </m:math> $hat{boldsymbol{S}}$ ; the corresponding matrix is the Ŝ -matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mover accent=\"true\"> <m:mi mathvariant=\"bold-italic\">S</m:mi> <m:mo stretchy=\"false\">̂</m:mo> </m:mover> </m:math> $hat{boldsymbol{S}}$ The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s ( s = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mrow> <m:mover accent=\"true\"> <m:mrow> <m:mi>S</m:mi> </m:mrow> <m:mo stretchy=\"false\">̂</m:mo> </m:mover> </m:mrow> </m:math> $hat{S}$ -matrix formalism.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"133 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article discusses the Riemann problem for the Chaplygin gas Euler equations that include the presence of two source terms. By means of variable substitution, two kinds of non-self-similar Riemann solutions involving delta-shock are constructed explicitly. For the delta-shock, the generalized Rankine–Hugoniot relations and the over-compressive entropy condition are clarified. Moreover, the position, propagation speed and strength of the delta-shock are given explicitly. It is discovered that the position of the delta-shock is a combination of an exponential function and a linear function, and the weight of the delta-shock is an exponential function of the time. Interestingly, even when the delta-shock is a straight line, the weight of the delta-shock is no longer a linear function of the time t . In addition, it is proved that the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations with friction as k drops to zero, and the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations as k and β tend to zero simultaneously. Furthermore, it is also shown that the limits of Riemann solutions are just the Riemann solutions to the transport equations with same source terms as the Chaplygin gas pressure falls to zero.
{"title":"Delta-shock for the Chaplygin gas Euler equations with source terms","authors":"Shiwei Li","doi":"10.1515/zna-2023-0181","DOIUrl":"https://doi.org/10.1515/zna-2023-0181","url":null,"abstract":"Abstract This article discusses the Riemann problem for the Chaplygin gas Euler equations that include the presence of two source terms. By means of variable substitution, two kinds of non-self-similar Riemann solutions involving delta-shock are constructed explicitly. For the delta-shock, the generalized Rankine–Hugoniot relations and the over-compressive entropy condition are clarified. Moreover, the position, propagation speed and strength of the delta-shock are given explicitly. It is discovered that the position of the delta-shock is a combination of an exponential function and a linear function, and the weight of the delta-shock is an exponential function of the time. Interestingly, even when the delta-shock is a straight line, the weight of the delta-shock is no longer a linear function of the time t . In addition, it is proved that the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations with friction as k drops to zero, and the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations as k and β tend to zero simultaneously. Furthermore, it is also shown that the limits of Riemann solutions are just the Riemann solutions to the transport equations with same source terms as the Chaplygin gas pressure falls to zero.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"20 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Iqra Abbas, Nadia Anwar, Muqarrab Ahmed, Muhammad Naeem, Ghazi Aman Nowsherwan, Shaheen Irfan, Rabia Khalid, Nazia Iram, Bushra Anwar, Muhammad Ahmad
Abstract This work reports the sol–gel synthesis of zirconia (ZrO 2 ) nanoparticles (NPs) in which the effect of varying molarities of zirconium oxychloride salt (such as 0.025 M, 0.050 M, 0.075 M, 0.100 M, and 0.125 M) has been investigated on the structural, mechanical, and optical characteristics by maintaining a basic pH at 9. All experimental conditions were conducted using basic media, with XRD, SEM, hardness, and optical analysis performed. Structural analysis, which was performed by using an X-ray diffractometer, reveals the formation of mixed phase zirconia (tetragonal and monoclinic) under as-synthesized conditions. Optical analysis shows that transmission increases as the molarity grows. The refractive index and extinction coefficient conform to the normal dispersion behavior, while the refractive index is observed to increase as the molarity becomes large. A high value of the refractive index of about 1.65 and lowest value of band gap 3.96 eV have been observed at a molarity of 0.075 M in the UV region. The hardness is observed to be continuously increased as the molarity grows, wherein the maximum hardness of 1167 HV is observed at a molarity of 0.075 M within the considered molarities (0.025 M, 0.050 M, 0.075 M, 0.100 M, and 0.125 M).
{"title":"Zirconia nanoparticles unveiled: multifaceted insights into structural, mechanical, and optical properties","authors":"Iqra Abbas, Nadia Anwar, Muqarrab Ahmed, Muhammad Naeem, Ghazi Aman Nowsherwan, Shaheen Irfan, Rabia Khalid, Nazia Iram, Bushra Anwar, Muhammad Ahmad","doi":"10.1515/zna-2023-0169","DOIUrl":"https://doi.org/10.1515/zna-2023-0169","url":null,"abstract":"Abstract This work reports the sol–gel synthesis of zirconia (ZrO 2 ) nanoparticles (NPs) in which the effect of varying molarities of zirconium oxychloride salt (such as 0.025 M, 0.050 M, 0.075 M, 0.100 M, and 0.125 M) has been investigated on the structural, mechanical, and optical characteristics by maintaining a basic pH at 9. All experimental conditions were conducted using basic media, with XRD, SEM, hardness, and optical analysis performed. Structural analysis, which was performed by using an X-ray diffractometer, reveals the formation of mixed phase zirconia (tetragonal and monoclinic) under as-synthesized conditions. Optical analysis shows that transmission increases as the molarity grows. The refractive index and extinction coefficient conform to the normal dispersion behavior, while the refractive index is observed to increase as the molarity becomes large. A high value of the refractive index of about 1.65 and lowest value of band gap 3.96 eV have been observed at a molarity of 0.075 M in the UV region. The hardness is observed to be continuously increased as the molarity grows, wherein the maximum hardness of 1167 HV is observed at a molarity of 0.075 M within the considered molarities (0.025 M, 0.050 M, 0.075 M, 0.100 M, and 0.125 M).","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"55 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136376166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work, we report an effective approach based on an artificial intelligence technique to investigate the secondary ions mass spectroscopy (SIMS) profiles of boron, phosphorus and arsenic ions. Those dopant ions were implanted into n- and p-type (100) Silicon substrate using the ion implantation technique with energy of 100 and 180 keV. Annealing treatment was conducted at various temperatures ranging from 900 to 1030 °C for 30 min. The doping profile parameters such as the activation energy, diffusion coefficient, junction depth, implant dose, projected range and standard deviation were determined using particle swarm optimization (PSO) algorithm. The efficiency of this strategy was experimentally verified by the fitting between both real measured SIMS profile and predicted ones. In addition, a set of simulated doping profiles was generated for different annealing time to prove the ability of this approach to accurately estimate the above parameters even when changing the experimental conditions.
{"title":"Artificial intelligence approach to analyze SIMS profiles of <sup>11</sup>B, <sup>31</sup>P and <sup>75</sup>As in n- and p-type silicon substrates: experimental investigation","authors":"Walid Filali, Mohamed Boubaaya, Elyes Garoudja, Fouaz Lekoui, Ibrahime Abdellaoui, Rachid Amrani, Slimane Oussalah, Nouredine Sengouga","doi":"10.1515/zna-2023-0200","DOIUrl":"https://doi.org/10.1515/zna-2023-0200","url":null,"abstract":"Abstract In this work, we report an effective approach based on an artificial intelligence technique to investigate the secondary ions mass spectroscopy (SIMS) profiles of boron, phosphorus and arsenic ions. Those dopant ions were implanted into n- and p-type (100) Silicon substrate using the ion implantation technique with energy of 100 and 180 keV. Annealing treatment was conducted at various temperatures ranging from 900 to 1030 °C for 30 min. The doping profile parameters such as the activation energy, diffusion coefficient, junction depth, implant dose, projected range and standard deviation were determined using particle swarm optimization (PSO) algorithm. The efficiency of this strategy was experimentally verified by the fitting between both real measured SIMS profile and predicted ones. In addition, a set of simulated doping profiles was generated for different annealing time to prove the ability of this approach to accurately estimate the above parameters even when changing the experimental conditions.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"58 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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