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Table of Content
03 January 2023 Volume 41 Issue 11
Analytical solution of pseudo-Landau levels in graphene under an inhomogeneous uniaxial strain
SUN Jun-song, MA Nv-sen, GUO Huai-ming
College Physics. 2022, 41(11): 1. doi:
10.16854/j.cnki.1000-0712.210602
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525
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Graphene is a cutting-edge research topic in condensed matter physics. This paper introduces the analytical solution of the pseudo-Landau energy level of graphene under a pseudo-magnetic field generated by the non-uniform uniaxial strain. We show in detail the derivation of the low-energy effective Hamiltonian under strain and the solution of related differential equations. The solution of the pseudo-Landau energy level, comprehensively using the basic knowledge of mathematics and physics learned by college students, is of great reference value for related theoretical courses
Application of tensor analysis in deriving geometric equations and equilibrium differential equations of elasticity in cylindrical coordinates and spherical coordinates
ZHOU Zheng-feng
College Physics. 2022, 41(11): 4. doi:
10.16854 /j.cnki.1000-0712.220043
Abstract
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2169
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First, using the relations of the unit vectors between orthogonal curvilinear coordinates and Cartesian coordinates, and the invariability of the unit vectors in Cartesian coordinates, the gradient operator in both coordinates, and the partial derivative of the unit vectors to the coordinates are derived from the perspective of the transformation of the unit vectors. Then, using the fundamentals of the theorems of tensor field, the gradient of displacement vector and the divergence of stress tensor are derived by derivation. Last, the geometric equations of strain and the differential equations of equilibrium are derived in details in cylindrical coordinates and spherical coordinates from their forms expressed by tensor.
Derivation of heat balanced condition in black body cavity
College Physics. 2022, 41(11): 9. doi:
10.16854/j.cnki.1000-0712.220018
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430
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We derive the heat balanced condition from the fact that the lost energy of an atomic oscillator in its radiation damping in black body cavity is equal to its acquired energy from electromagnetic wave．
Cause analysis of rolling friction
ZHANG Ma-yue, CHEN Si-bo, SANG Zhi-fang
College Physics. 2022, 41(11): 11. doi:
10.16854 /j.cnki.1000-0712.220047
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560
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438
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Rolling friction is very common in our real life, but most students lack a correct understanding of the cause of rolling friction. In this paper, the cause of rolling friction is analyzed in two cases: a rigid body on a horizontal soft underlay and a soft body on a horizontal rigid underlay. It is found that rolling friction is a kind of effect caused by the asymmetric distribution of the force applied to the rolling body that hinders rolling when one object is rolling on another object or has a rolling tendency. The concepts of rolling friction and the force of rolling friction are also explained.
An analysis of the energy of longitudinal wave
ZHOU Yue, ZHANG Guo-feng
College Physics. 2022, 41(11): 15. doi:
10.16854 /j.cnki.1000-0712.220045
Abstract
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369
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186
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The energy density and energy flow of a harmonic longitudinal wave in elastic medium are calculated and the relevant formulas in general physics textbook are further discussed, the composition and origin of the energy flow are analyzed.
Moving images of a bugcrawling on a plane motion rigid body
GU Zhi-qin, LIANG Pei-pei
College Physics. 2022, 41(11): 18. doi:
10.16854 /j.cnki.1000-0712.220072
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308
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232
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The problem of a bug crawling on a plane motion rigid body is studied by the law of conservation of momentum and the law of conservation of angular momentum. By which, the differential relation between the rotation angle of the rigid body and angular coordinates of the bug in the rotating coordinate system is derived. Moreover, the formula of the rotation angle is obtained as the trajectory of the bug on the rigid body is straight, and the application of the formula is presented by given typical example.
Principle of noise measurement with lock-in amplifiers and teaching design for laboratory courses
HE Zhen-hui
College Physics. 2022, 41(11): 22. doi:
10.16854/j.cnki.1000-0712.220063
Abstract
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246
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278
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The teaching method of obtaining Boltzmann constant by measuring the thermal noise of a resistor with a lock-in amplifier is easy for students to understand in physics, and its smooth implementation requires technical support of high precision measurement and students’ clear understandings of the measurement principle and the meanings of instrument parameters of the lock-in amplifier. To meet the peculiarity and the requirements of physics specialty, especially that of precision measurement physics, it is tried to avoid as much as possible involving in knowledge of electronics, but focus on mathematical description of noise measurement with a lock-in amplifier, including the derivations of thermal noise of a resistor, the noise processing process of a lock-in amplifier, and the equivalent noise bandwidth. The experimental design of Boltzmann constant measurement is optimized based on error analysis. Finally, the preliminary teaching practice is briefly introduced.
Taking Pixie-Net digitizer in teaching experiments of nuclear physics
WEI Kang, HU Han-rui, LOU Jian-ling, XU Jin-yan
College Physics. 2022, 41(11): 28. doi:
10.16854/j.cnki.1000-0712.220026
Abstract
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333
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123
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With the development of nuclear physics experiment technology, the acquisition system using traditional analog electronics has been gradually replaced by the digital acquisition system. Many sets of Pixie-Net digitizers have been introduced into the teaching laboratory of nuclear physics and nuclear technology at Peking University. We tried to use them in teaching experiments instead of the traditional acquisition system. Taking the NaI(Tl) detector as an example, the advantages of pixie-net digitizer (compared with traditional electronics) and the principle of its energy measurement are reported. The influence of various parameters in setting file on the energy resolution of NaI(Tl) detector is tested carefully. The energy resolution of NaI(Tl) detector when using Pixie-Net digitizer with the best parameters is better than that using the traditional electronics.
Discussion on treatment of random error
ZHANG Zhi-ming
College Physics. 2022, 41(11): 39. doi:
10.16854/j.cnki.1000-0712.220204
Abstract
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397
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376
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Some concepts (including the variance and the standard deviation) about random error in textbooks on physics experiments are discussed. Some related equations (including Bessel equation and the equation for standard deviation of arithmetic mean value) are proved, and some non-self-consistent descriptions for normal distribution are corrected.
The gravity potential of varied-density sphere and its spherical harmonic expansion
FAN Guang-xue, ZHONG Zhen
College Physics. 2022, 41(11): 43. doi:
10.16854/j.cnki.1000-0712.220153
Abstract
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334
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201
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The varied-density in the interior of a celestial body, generally results in an anisotropic gravity potential outside of the celestial. The general numerical integration method needs too much time in the potential determination to be efficiently applied in a large-scaled gravity inversion as well as the forward case. To deal with this problem, this paper proposes an updated model of spherical harmonic expansion, which is based on the generalized Fourier Transformation. Results indicate that the spherical harmonic expanded coefficients of the gravity potential can be directly estimated according to the expanded coefficients of density. Our method simplifies the potential calculation in the case of density varied in a celestial body. By applying our algorithm to the actual case, the potential from our approach shows a similar distribution with the general method, but our method spents less time in the computation than its counterpart. To the issue of lunar crustal density varied, the estimated gravity potential from our method shows the same behavior with the varied-density. Our method is validated and can be applied in the gravity inversion as well as its forward problem.
Substantialization of physical pictures in Fourier series
LIU Yi
College Physics. 2022, 41(11): 48. doi:
10.16854/j.cnki.1000-0712.220119
Abstract
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343
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276
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The first half of the course of methods of mathematical physics, complex functions, is mainly mathematical background technically needed for the second half. Students tend to take it as abstract and irrelevant with physics. Using Fourier series as a demo, it is shown how they directly treat problems in everyday life and physics. Presenting it in physical scenarios, i.e., substantializing the physics related, helps students essentially understand it. More importantly, this will directly connect the Fourier transform with major physics, and give students command of mathematics via physical pictures, which favors flexible applications of them in subsequential courses.
Application of Laplace transform in accurate solution of two body damped oscillation model#br#
LIU Jia-xian, WANG Wen-jia, MA Jia-xin, LI Xi-bin
College Physics. 2022, 41(11): 52. doi:
10.16854 /j.cnki.1000-0712.220080
Abstract
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348
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239
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Damped oscillating system is an extremely important topic in the study of molecular dynamics and classical dynamics, so the analytical result is the key problem on this system. But the exact expressions are always to obtain in many-body system. Motivated to get the two-bodys analytic expressions, Laplace transform, residual theory and Cardano formula are applied to the calculation. Accurate computations show that this system could be distinguished into three situations: critical damping oscillation, overdamped oscillation and underdamped oscillation, which is quite analogous to simple damped harmonic oscillator. Similarly, the three modes are also classified via the discriminant Δ. Finally, this study sheds some light into the topics on more complicated systems.
Application of COMSOL simulation to acoustic resonant tube experiment
LI Chun-yi, HU An-qi, ZHANG Ge-ge, BAI Zai-qiao, YU Xiao-chong
College Physics. 2022, 41(11): 58. doi:
10.16854/j.cnki.1000-0712.220159
Abstract
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915
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229
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In this paper, COMSOL Multiphysics simulation is applied to acoustic resonant tube experiment. First the sound pressure distribution in the vicinity of tube end is calculated and the departure from the picture given by one-dimensional wave appxoimation is visulized. Then, the shift of resonant frequency is investigated due to the existence of sound detector (microphone). The result shows that the shift, which may be positive as well as negative,depends on the size and position of sound detactor. Finally, the resonant frequency of a tube with partly closed end is calculated and find that the numerical results agree with the mearsured values quite well. The stduy shows that numerical simulations can be applied to undergraduate physics laboratory to help students achieving a better understanding of experiments and endow them with a powerful tool to tackle practical problems.
Study of electrostatic field between intersecting planes in electrodynamics
SHI Huan-yu, MIAO Rong-xin
College Physics. 2022, 41(11): 65. doi:
10.16854/j.cnki.1000-0712.220175
Abstract
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729
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429
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It is an interesting problem to investigate the electrostatic field between two intersecting planes with given opening angle and charge distribution. For simplicity, we focus on the case that the source is a point charge. First, the potential distribution of some special opening angles is analyzed by using the method of image. Furthermore, the general case is solved by applying the separation of variables. The equivalence of the two results is verified by mathematical derivations. Finally, the discussion is generalized to Neumann and mixed boundary conditions, where the general solutions of electric potential and a series of identities for the second kind of Legendre function are obtained.
High precision electromagnetic gun system based on multi-mode switching
CHEN Nan, LIU Jia-wei, ZHENG Li-jia, YANG Yu-hui, CAI Wen-cong, PENG-li,
College Physics. 2022, 41(11): 72. doi:
10.16854/j.cnki.1000-0712.220058
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440
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(1. School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, Guangdong 510006, China;
2. Qingyuan Institute of Science and Technology Innovation Co. Ltd., South China Normal University, Qingyuan,
Guangdong 511517, China)Abstract: As a hot topic in modern science and technology, electromagnetic gun has a wide range of military applications. In this experiment, the magnetic field is generated by the electric coil, and the magnetic force accelerates the conductor ball in the coil to obtain the velocity of exit. The 3D rotation of the device system is realized by the 2D servo turret system. STM32 microcontroller is used to control the 2D steering engine turret and openMV4H7 camera, so that the electromagnetic gun can meet the target color recognition and accurate target coordinates, and meet the requirements of the emerging military technology for the electromagnetic gun’s automaticity and autonomy. The device has the advantages of easy implementation, high degree of automation and high precision of hitting.
Key words: electromagnetic gun system; color recognition; fixed point coordinate strike; multimodal
Optical image encryption and decryption based on 4f system
SHENG Tian-shuang, CAI Le-yu, XU nuo, PAN Yong-hua, DING Jian-ping
College Physics. 2022, 41(11): 77. doi:
10.16854 /j.cnki.1000-0712.220017
Abstract
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476
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96
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Using Abbe
,
s imaging principle and symmetric-asymmetric hybrid encryption scheme, the optical image encryption and decryption based on 4f optical system are realized. First, the Lees detour phase encoding method is used to make the phase mask corresponding to the encryption function as the key, and the frequency domain encryption of optical image is completed by spatial filtering method. Secondly, the computer decryption is realized with the program developed by the authors, which gets rid of the difficulty of precise alignment of phase mask during optical image decryption, and greatly improves the efficiency and quality of decryption. Finally, the experiment reveals that the encryption method has high security level, and it also proves this experimental method possesses good robustness under mild noise influence.
An improved method of light speed measurement and its application in teaching practice#br#
GUO Nai-quan, MA Chao, ZHENG Liang, WU Juan
College Physics. 2022, 41(11): 82.
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668
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245
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The traditional light speed measurement in college physics experiment course suffers from multiple uncertainties for comparing the light-beat signals in two different pathways. In this paper, an optimized method is developed by utilizing the cursor function of oscilloscope to measure the phase variation of only one light-beat signal, which achieves much better accuracy in a more operative way and can be easily applied to teaching practice of this experiment. It is found that the instructional design which incorporates this improved method will become more pedagogical to illustrate the essence of this measurement and help students develop critical thinking and spirits of exploration in scientific research.
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