Abstract Low-temperature elementary conductivity formula in Fermi metals is reviewed starting from Ohm’s law. This provides the background needed to understand why and how the equations exploited are complicated due to effective mass effect and complex scattering rate even in the presence of small-angle electron-electron scattering at low temperatures. Using the mathematical conditions and physical arguments exploited to derive the Drude conductivity formula, we arrive at our main result—the analytic scattering rate formula at low temperatures that gives rise to the famous T 2 dependence without any ad hoc constants. Our derivation formally proves that the formula, 1/τ=(A/ℏ)(kBT)2/EF $1/tau =(A/hslash ){({k}_{text{B}}T)}^{2}/{E}_{text{F}}$ first guessed by Ashcroft and Mermin to be correct where A = N impurity /4 π 2 and N impurity is the number of impurities (or scattering centers) present in a given sample. We also highlight the discovery of a new fundamental physical constant, λArulsamy=3ℏ2(4πϵ0)2/mele4 ${lambda }_{text{Arulsamy}}=left[3{hslash }^{2}{(4pi {{epsilon}}_{0})}^{2}right]/left[{m}_{text{el}}{e}^{4}right]$ that associates quantum mechanical energy with that of thermal energy, and is also related to Rydberg constant.
摘要从欧姆定律出发，对费米金属中的低温元素电导率公式进行了评述。这为理解有效的质量效应和复杂的散射率(即使在低温下存在小角度电子-电子散射)所导致的方程为何以及如何复杂提供了必要的背景。利用推导德鲁德电导率公式的数学条件和物理参数，我们得到了我们的主要结果——低温下的解析散射率公式，它产生了著名的t2依赖关系，没有任何特别常数。我们的推导正式证明了公式1 / τ = (A / h) (k B T) 2 / E F $1/tau =(A/hslash ){({k}_{text{B}}T)}^{2}/{E}_{text{F}}$首先由Ashcroft和Mermin猜测是正确的，其中A = N杂质/4 π 2, N杂质是给定样品中存在的杂质(或散射中心)的数量。我们还强调了一个新的基本物理常数的发现，λ Arulsamy = 3 π 2 (4 π ε 0) 2 / m el e 4 ${lambda }_{text{Arulsamy}}=left[3{hslash }^{2}{(4pi {{epsilon}}_{0})}^{2}right]/left[{m}_{text{el}}{e}^{4}right]$，它将量子力学能与热能能联系起来，也与Rydberg常数有关。
{"title":"Low-temperature small-angle electron-electron scattering rate in Fermi metals","authors":"Andrew Das Arulsamy","doi":"10.1515/zna-2023-0099","DOIUrl":"https://doi.org/10.1515/zna-2023-0099","url":null,"abstract":"Abstract Low-temperature elementary conductivity formula in Fermi metals is reviewed starting from Ohm’s law. This provides the background needed to understand why and how the equations exploited are complicated due to effective mass effect and complex scattering rate even in the presence of small-angle electron-electron scattering at low temperatures. Using the mathematical conditions and physical arguments exploited to derive the Drude conductivity formula, we arrive at our main result—the analytic scattering rate formula at low temperatures that gives rise to the famous T 2 dependence without any ad hoc constants. Our derivation formally proves that the formula, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mi>τ</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>A</m:mi> <m:mo>/</m:mo> <m:mi>ℏ</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>k</m:mi> </m:mrow> <m:mrow> <m:mtext>B</m:mtext> </m:mrow> </m:msub> <m:mi>T</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo>/</m:mo> <m:msub> <m:mrow> <m:mi>E</m:mi> </m:mrow> <m:mrow> <m:mtext>F</m:mtext> </m:mrow> </m:msub> </m:math> $1/tau =(A/hslash ){({k}_{text{B}}T)}^{2}/{E}_{text{F}}$ first guessed by Ashcroft and Mermin to be correct where A = N impurity /4 π 2 and N impurity is the number of impurities (or scattering centers) present in a given sample. We also highlight the discovery of a new fundamental physical constant, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msub> <m:mrow> <m:mi>λ</m:mi> </m:mrow> <m:mrow> <m:mtext>Arulsamy</m:mtext> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mfenced close=\"]\" open=\"[\"> <m:mrow> <m:mn>3</m:mn> <m:msup> <m:mrow> <m:mi>ℏ</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mi>π</m:mi> <m:msub> <m:mrow> <m:mi>ϵ</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:mrow> </m:mfenced> <m:mo>/</m:mo> <m:mfenced close=\"]\" open=\"[\"> <m:mrow> <m:msub> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mtext>el</m:mtext> </m:mrow> </m:msub> <m:msup> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mn>4</m:mn> </m:mrow> </m:msup> </m:mrow> </m:mfenced> </m:math> ${lambda }_{text{Arulsamy}}=left[3{hslash }^{2}{(4pi {{epsilon}}_{0})}^{2}right]/left[{m}_{text{el}}{e}^{4}right]$ that associates quantum mechanical energy with that of thermal energy, and is also related to Rydberg constant.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135817806","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 hydrodynamic instability of variable density swirling flows under gravity between two infinite coaxial cylinders is investigated for axisymmetric disturbances. It is shown that the complex wave velocity of any arbitrary unstable axisymmetric mode must lie within the semi-elliptical region whose minor axis depends on the density stratification parameter J ( r ). The stabilizing effect of density stratification is shown by reducing the semi-circular instability region of [G. K. Batchelor and A. E. Gill, “Analysis of the stability of axisymmetric jets,” J. Fluid Mech., vol. 14, p. 529, 1962]. Furthermore, we have obtained two parabolic instability regions which intersect and reduce the semi-elliptical instability region for density-stratified flows. These parabolic instability regions are uniformly valid for both variable density and density homogeneous flows also.
考虑轴对称扰动，研究了重力作用下两个无限同轴圆柱间变密度旋流的水动力不稳定性。结果表明，任意不稳定轴对称模态的复波速必须位于半椭圆区域内，该区域的小轴取决于密度分层参数J (r)。密度分层的稳定作用通过减小[G.]的半圆不稳定区得到体现。J. Batchelor和A. E. Gill，“轴对称射流稳定性分析”，流体力学。(第14卷第529页，1962年)。此外，我们还得到了密度分层流的两个抛物型不稳定区域，它们相互相交并减少了半椭圆型不稳定区域。这些抛物线不稳定区域对于变密度流和密度均匀流都是一致有效的。
{"title":"On the limitations of the complex wave velocity for the heterogeneous swirling flows","authors":"Prakash Shanmugam","doi":"10.1515/zna-2023-0208","DOIUrl":"https://doi.org/10.1515/zna-2023-0208","url":null,"abstract":"Abstract The hydrodynamic instability of variable density swirling flows under gravity between two infinite coaxial cylinders is investigated for axisymmetric disturbances. It is shown that the complex wave velocity of any arbitrary unstable axisymmetric mode must lie within the semi-elliptical region whose minor axis depends on the density stratification parameter J ( r ). The stabilizing effect of density stratification is shown by reducing the semi-circular instability region of [G. K. Batchelor and A. E. Gill, “Analysis of the stability of axisymmetric jets,” J. Fluid Mech., vol. 14, p. 529, 1962]. Furthermore, we have obtained two parabolic instability regions which intersect and reduce the semi-elliptical instability region for density-stratified flows. These parabolic instability regions are uniformly valid for both variable density and density homogeneous flows also.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135815612","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}
Monira Galal Ghoniem, Mohamed Ali Ben Aissa, Fatima A. Adam, Walid M. Daoush, Mohamed Khairy
Abstract Manufacturing active and economical catalysts and using them in water treatment is one of the most important challenges facing researchers. Spent batteries signify a source of harmful materials when discarded without suitable treatment. In this work, a black paste as one of the main components of spent battery doped with different ratios of TiO 2 nanocomposites (0, 1, 3, 7, and 10 %) were manufactured using the sol–gel method. The characterization of the paste@TiO 2 nanocomposites has been investigated by SEM, XRD, DRS, FTIR, and BET analysis. The results show formation of anatase phase of TiO 2 in all doped samples. While the XRD of black paste indicates the presence of Mn 3 O 4 as a main phase. Photocatalytic properties of black paste@TiO 2 nanocomposites have been investigated using Congo red dye. The results showed that the presence of TiO 2 in the paste could increase the specific surface area and the composites’ photocatalytic efficiency. A higher percentage of TiO 2 (10 %) added to the black paste resulted in higher black paste@TiO 2 nanocomposite catalytic activity. The experimental photodegradation data were found to be consistent with the Lagergren kinetics model. The recyclability of the photocatalysts was examined for reuse in the industrial sector. Signifying that the black paste dopped with 10 % of TiO 2 (PTO4) photocatalyst in this study had high reusability.
{"title":"Photocatalytic decomposition of Congo red dye by black paste@TiO<sub>2</sub> as an efficient recyclable photocatalyst","authors":"Monira Galal Ghoniem, Mohamed Ali Ben Aissa, Fatima A. Adam, Walid M. Daoush, Mohamed Khairy","doi":"10.1515/zna-2023-0142","DOIUrl":"https://doi.org/10.1515/zna-2023-0142","url":null,"abstract":"Abstract Manufacturing active and economical catalysts and using them in water treatment is one of the most important challenges facing researchers. Spent batteries signify a source of harmful materials when discarded without suitable treatment. In this work, a black paste as one of the main components of spent battery doped with different ratios of TiO 2 nanocomposites (0, 1, 3, 7, and 10 %) were manufactured using the sol–gel method. The characterization of the paste@TiO 2 nanocomposites has been investigated by SEM, XRD, DRS, FTIR, and BET analysis. The results show formation of anatase phase of TiO 2 in all doped samples. While the XRD of black paste indicates the presence of Mn 3 O 4 as a main phase. Photocatalytic properties of black paste@TiO 2 nanocomposites have been investigated using Congo red dye. The results showed that the presence of TiO 2 in the paste could increase the specific surface area and the composites’ photocatalytic efficiency. A higher percentage of TiO 2 (10 %) added to the black paste resulted in higher black paste@TiO 2 nanocomposite catalytic activity. The experimental photodegradation data were found to be consistent with the Lagergren kinetics model. The recyclability of the photocatalysts was examined for reuse in the industrial sector. Signifying that the black paste dopped with 10 % of TiO 2 (PTO4) photocatalyst in this study had high reusability.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"196 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010153","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 theoretical assessment of mechanical and elastic properties is used to analyze the distinctive properties of high entropy alloys (HEAs) at room temperature. Using Lennard–Jones potential model, the second order elastic constants (SOECs) and third order elastic constants (TOECs) have been determined for the HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25− x Al x ( x ≤ 15 %) in their hexagonal close-packed (hcp) phases. SOECs have been used to calculate mechanical constants, Poisson’s ratio, Pugh’s ratio, Kleinman’s parameter. In order to determine the anisotropic behaviour of the selected HEAs, the elastic anisotropy has also been computed at room temperature. All the HEAs under consideration have anisotropy parameters that are not equal to one, indicating anisotropic behaviour. Later, the Grüneisen parameters were estimated for the chosen HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25− x Al x ( x ≤ 15 %) along longitudinal and shear modes of wave propagation. Analysis of the research results reveals the inherent properties of HEAs.
摘要:采用力学性能和弹性性能的理论评价方法，分析了高熵合金在室温下的特殊性能。利用Lennard-Jones势模型，测定了HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25−x Al x (x≤15%)在六方密排相中的二阶弹性常数(SOECs)和三阶弹性常数(TOECs)。soec已被用于计算力学常数、泊松比、皮尤比、克莱曼参数。为了确定所选HEAs的各向异性行为，还计算了室温下的弹性各向异性。所考虑的HEAs各向异性参数都不等于1，表明其各向异性行为。然后，估计了所选HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25−x Al x (x≤15%)沿波传播的纵向和剪切模式的grisen参数。对研究结果的分析揭示了高等教育机构的内在属性。
{"title":"Theoretical investigation on the elastic and mechanical properties of high-entropy alloys with partial replacement of Sc in Hf<sub>0.25</sub>Ti<sub>0.25</sub>Zr<sub>0.25</sub>Sc<sub>0.25−<i>x</i> </sub>Al<sub> <i>x</i> </sub> (<i>x</i> ≤ 15 %)","authors":"Ajit Kumar Maddheshiya, Shakti Pratap Singh, Devraj Singh, Phool Singh Yadav, Raja Ram Yadav, Thakur Prasad Yadav","doi":"10.1515/zna-2023-0160","DOIUrl":"https://doi.org/10.1515/zna-2023-0160","url":null,"abstract":"Abstract The theoretical assessment of mechanical and elastic properties is used to analyze the distinctive properties of high entropy alloys (HEAs) at room temperature. Using Lennard–Jones potential model, the second order elastic constants (SOECs) and third order elastic constants (TOECs) have been determined for the HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25− x Al x ( x ≤ 15 %) in their hexagonal close-packed (hcp) phases. SOECs have been used to calculate mechanical constants, Poisson’s ratio, Pugh’s ratio, Kleinman’s parameter. In order to determine the anisotropic behaviour of the selected HEAs, the elastic anisotropy has also been computed at room temperature. All the HEAs under consideration have anisotropy parameters that are not equal to one, indicating anisotropic behaviour. Later, the Grüneisen parameters were estimated for the chosen HEAs Hf 0.25 Ti 0.25 Zr 0.25 Sc 0.25− x Al x ( x ≤ 15 %) along longitudinal and shear modes of wave propagation. Analysis of the research results reveals the inherent properties of HEAs.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"151 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911307","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 group invariance technique is used to investigate the similarity solution of one-dimensional, unsteady motion of cylindrically symmetric shock waves propagating in a rotating, axisymmetric perfect gas permeated with an azimuthal or axial magnetic field, under the effect of monochromatic radiation, with or without self-gravitational effects. The density is considered to be varying with radiation flux moving through the gas. Considering the absorption coefficient to be variable and choosing different values for the arbitrary constants appearing in infinitesimal generators, all possible cases of similarity solutions with shock paths following the power law and exponential law are discussed in detail, and numerical solutions for both the power law and exponential law path is obtained. The effect of changes in the Alfven–Mach number, density exponent, adiabatic index, gravitational, and rotational parameters on shock formation and shock strength has been obtained for both the power law and the exponential law. Further, the effect of all these parameters on the behaviour of flow variables behind the shock is investigated in detail and the results are depicted graphically via figures. It has been found during the study that, the strength of the shock reduces considerably with an increase in the Alfven–Mach number, rotational parameter and adiabatic index, and it increases with increase in density index and gravitational parameter. Various computations involved in this article are carried out by using the MATLAB software.
{"title":"Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method","authors":"Vidit K. Vats, Dheerendra B. Singh, Danish Amin","doi":"10.1515/zna-2023-0050","DOIUrl":"https://doi.org/10.1515/zna-2023-0050","url":null,"abstract":"Abstract The group invariance technique is used to investigate the similarity solution of one-dimensional, unsteady motion of cylindrically symmetric shock waves propagating in a rotating, axisymmetric perfect gas permeated with an azimuthal or axial magnetic field, under the effect of monochromatic radiation, with or without self-gravitational effects. The density is considered to be varying with radiation flux moving through the gas. Considering the absorption coefficient to be variable and choosing different values for the arbitrary constants appearing in infinitesimal generators, all possible cases of similarity solutions with shock paths following the power law and exponential law are discussed in detail, and numerical solutions for both the power law and exponential law path is obtained. The effect of changes in the Alfven–Mach number, density exponent, adiabatic index, gravitational, and rotational parameters on shock formation and shock strength has been obtained for both the power law and the exponential law. Further, the effect of all these parameters on the behaviour of flow variables behind the shock is investigated in detail and the results are depicted graphically via figures. It has been found during the study that, the strength of the shock reduces considerably with an increase in the Alfven–Mach number, rotational parameter and adiabatic index, and it increases with increase in density index and gravitational parameter. Various computations involved in this article are carried out by using the MATLAB software.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134992205","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：