Armchair （n, n） single walled boron nitride nanotubes with n = 2-17 are studied by the density functional theory at the B3LYP/3-21G（d） level combined with the periodic boundary conditions for simulating the ultra ...Armchair （n, n） single walled boron nitride nanotubes with n = 2-17 are studied by the density functional theory at the B3LYP/3-21G（d） level combined with the periodic boundary conditions for simulating the ultra long model. The results show that the structure parameters and the formation energies bear a strong relationship to n. The fitted analytical equations are developed with correlation coefficients larger than 0.999. The energy gaps of （2, 2） and （3, 3） tubes are indirect gaps, and the larger tubes （n = 4-17） have direct energy gaps. Results show that the armchair boron nitride nanotubes （n = 2-17） are insulators with wide energy gaps of between 5.93 eV and 6.23 eV.展开更多
The main objective of this study is to numerically investigate the characteristics of ultimate compressive strength of stiffened panels with opening and also to fit the design-oriented formulae. For this purpose, thre...The main objective of this study is to numerically investigate the characteristics of ultimate compressive strength of stiffened panels with opening and also to fit the design-oriented formulae. For this purpose, three series of well executed experimental data on longitudinally stiffened steel plates with and without opening subjected to the uniform axial in-pane load which is carried out to study the buckling and post-buckling up to the final failure are chosen. Also, a nonlinear finite element method capable of efficiently analyzing the large elasto-plastic deflection behavior of stiffened panels is developed and used for simulation. The feasibility of the present simulation process is confirmed by a good agreement with the experimental results. More case studies are developed employing the simulation process to analyze the influence of various design variables on the reduction rate of ultimate strength of stiffened panel induced by opening. Based on the computed results, two design formulae are fitted and the accuracy of design formulae is studied. Furthermore, the viability of the design formulae for practical engineering is proved.展开更多
Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, ...Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.展开更多
A total of 58 years self-recording rainfall records at Guilin National Weather Station from January 1957 to December 1957 were used. Using the annual maximum sampling method,11 short-duration maximum rainfall records ...A total of 58 years self-recording rainfall records at Guilin National Weather Station from January 1957 to December 1957 were used. Using the annual maximum sampling method,11 short-duration maximum rainfall records in every year were selected,and statistical samples of rainstorm intensity formula were obtained. Fitting of statistical samples was conducted by using three kinds of frequency distribution curves: Pearson-Ⅲdistribution,Gumbel distribution and exponential distribution. The formula of rainstorm intensity was derived by the least square method and Gauss Newton method,and then the accuracy of results was inspected. The results showed that the fitting effect based on the Pearson-Ⅲdistribution and Gumbel distribution was better than that of the exponential distribution;the accuracy of rainstorm intensity formula based on Pearson-Ⅲdistribution was better than that of Gumbel distribution and exponential distribution;the accuracy of rainstorm intensity formula derived by the least square method was better than that of Gauss Newton method;the accuracy of interval parameter formula of rainstorm intensity was better than that of rainstorm intensity formula.展开更多
In this work, new cross section formulae for (n, p) and (n, d) reactions of He-3 have been investigated as a function of incident neutron energy. The new Empirical formulae were produced by using the least squares met...In this work, new cross section formulae for (n, p) and (n, d) reactions of He-3 have been investigated as a function of incident neutron energy. The new Empirical formulae were produced by using the least squares method to the experimental cross sections data, which were taken from Experimental Nuclear Reaction Data EXFOR Database Version of 2021. Several functions were examined to choose the best one that fits the data. Statistical hypothesis testing was used to insure how well the suggested equations fit the set of data. Two statistical indicators were used for each case for goodness-of-fit. Very high compatibility was found between the empirical values and the experimental data for both reactions.展开更多
The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved...The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved to be very complicated, and various trials were published between the 1900s and 2000s. The development of indentation instruments and the wish to make the application in numerous steps easier, led in 1992 to trials with iterations by using relative values instead of absolute ones. Excessive iterations of computers with 3 + 8 free parameters of the loading and unloading curves became possible and were implemented into the instruments and worldwide standards. The physical formula for hardness was defined as force over area. For the conical, pyramidal, and spherical indenters, one simply took the projected area for the calculation of the indentation depth from the projected area, adjusted it later by the iterations with respect to fused quartz or aluminium as standard materials, and called it “contact height”. Continuously measured indentation loading curves were formulated as loading force over depth square. The unloading curves after release of the indenter used the initial steepness of the pressure relief for the calculation of what was (and is) incorrectly called “Young’s modulus”. But it is not unidirectional. And for the spherical indentations’ loading curve, they defined the indentation force over depth raised to 3/2 (but without R/h correction). They till now (2025) violate the energy law, because they use all applied force for the indenter depth and ignore the obvious sidewise force upon indentation (cf. e.g. the wood cleaving). The various refinements led to more and more complicated formulas that could not be reasonably calculated with them. One decided to use 3 + 8 free-parameter iterations for fitting to the (poor) standards of fused quartz or aluminium. The mechanical values of these were considered to be “true”. This is till now the worldwide standard of DIN-ISO-ASTM-14577, avoiding overcomplicated formulas with their complexity. Some of these are shown in the Introduction Section. By doing so, one avoided the understanding of indentation results on a physical basis. However, we open a simple way to obtain absolute values (though still on the blackbox instrument’s unsuitable force calibration). We do not iterate but calculate algebraically on the basis of the correct, physically deduced exponent of the loading force parabolas with h3/2 instead of false “h2” (for the spherical indentation, there is a calotte-radius over depth correction), and we reveal the physical errors taken up in the official worldwide “14577-Standard”. Importantly, we reveal the hitherto fully overlooked phase transitions under load that are not detectable with the false exponent. Phase-transition twinning is even present and falsifies the iteration standards. Instead of elasticity theory, we use the well-defined geometry of these indentations. By doing so, we reach simple algebraically calculable formulas and find the physical indentation hardness of materials with their onset depth, onset force and energy, as well as their phase-transition energy (temperature dependent also its activation energy). The most important phase transitions are our absolute algebraically calculated results. The now most easily obtained phase transitions under load are very dangerous because they produce polymorph interfaces between the changed and the unchanged material. It was found and published by high-enlargement microscopy (5000-fold) that these trouble spots are the sites for the development of stable, 1 to 2 µm long, micro-cracks (stable for months). If however, a force higher than the one of their formation occurs to them, these grow to catastrophic crash. That works equally with turbulences at the pickle fork of airliners. After the publication of these facts and after three fatal crashing had occurred in a short sequence, FAA (Federal Aviation Agency) reacted by rechecking all airplanes for such micro cracks. These were now found in a new fleet of airliners from where the three crashed ones came. These were previously overlooked. FAA became aware of that risk and grounded 290 (certainly all) of them, because the material of these did not have higher phase-transition onset and energy than other airplanes with better material. They did so despite the 14577-Standard that does not find (and thus formally forbids) phase transitions under indenter load with the false exponent on the indentation parabola. However, this “Standard” will, despite the present author’s well-founded petition, not be corrected for the next 5 years.展开更多
Inverse bremsstrahlung absorption in laser-heated plasmas is studied using the Fokker–Planck equation in the low-field limit.Compared with the commonly used fitting formulas of Langdon and Matte et al.,our work emplo...Inverse bremsstrahlung absorption in laser-heated plasmas is studied using the Fokker–Planck equation in the low-field limit.Compared with the commonly used fitting formulas of Langdon and Matte et al.,our work employs fewer approximations and provides more accurate predictions for the super-Gaussian orderβand the heating rate.Simulation results show that the super-Gaussian order is generally lower than the fitting results of Matte et al.,which leads to an increase in absorption.However,we find two other factors that reduce absorption:the high-order term of the collision frequency and the effects caused by high laser intensity.Therefore,the final simulated absorption can either be higher or lower,depending on the conditions.These phenomena are theoretically analyzed using the Fokker–Planck equation.Fitting formulas are proposed for the super-Gaussian order and the heating rate,showing a discrepancy within∼10%of the simulation results.We also compare the simulation results with the experimental results from several recent papers.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 50572089)the Basic Research Foundation of Northwestern Polytechnical University (Grant No. JC201269)
文摘Armchair （n, n） single walled boron nitride nanotubes with n = 2-17 are studied by the density functional theory at the B3LYP/3-21G（d） level combined with the periodic boundary conditions for simulating the ultra long model. The results show that the structure parameters and the formation energies bear a strong relationship to n. The fitted analytical equations are developed with correlation coefficients larger than 0.999. The energy gaps of （2, 2） and （3, 3） tubes are indirect gaps, and the larger tubes （n = 4-17） have direct energy gaps. Results show that the armchair boron nitride nanotubes （n = 2-17） are insulators with wide energy gaps of between 5.93 eV and 6.23 eV.
基金financially supported by Mid-Career Researcher Program NRF(Grant No.NRF-2013R1A2A2A01017021)funded by the Ministry of ScienceICT and Future Planning of Korea,and HIT Discipline Guide Fund(Grant No.WH20140102)
文摘The main objective of this study is to numerically investigate the characteristics of ultimate compressive strength of stiffened panels with opening and also to fit the design-oriented formulae. For this purpose, three series of well executed experimental data on longitudinally stiffened steel plates with and without opening subjected to the uniform axial in-pane load which is carried out to study the buckling and post-buckling up to the final failure are chosen. Also, a nonlinear finite element method capable of efficiently analyzing the large elasto-plastic deflection behavior of stiffened panels is developed and used for simulation. The feasibility of the present simulation process is confirmed by a good agreement with the experimental results. More case studies are developed employing the simulation process to analyze the influence of various design variables on the reduction rate of ultimate strength of stiffened panel induced by opening. Based on the computed results, two design formulae are fitted and the accuracy of design formulae is studied. Furthermore, the viability of the design formulae for practical engineering is proved.
文摘Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.
基金Supported by Meteorological Scientific Research Plan Project of Guangxi Meteorological Bureau(2019M16)Independent Scientific Research Project of Guilin Meteorological Bureau(201904)。
文摘A total of 58 years self-recording rainfall records at Guilin National Weather Station from January 1957 to December 1957 were used. Using the annual maximum sampling method,11 short-duration maximum rainfall records in every year were selected,and statistical samples of rainstorm intensity formula were obtained. Fitting of statistical samples was conducted by using three kinds of frequency distribution curves: Pearson-Ⅲdistribution,Gumbel distribution and exponential distribution. The formula of rainstorm intensity was derived by the least square method and Gauss Newton method,and then the accuracy of results was inspected. The results showed that the fitting effect based on the Pearson-Ⅲdistribution and Gumbel distribution was better than that of the exponential distribution;the accuracy of rainstorm intensity formula based on Pearson-Ⅲdistribution was better than that of Gumbel distribution and exponential distribution;the accuracy of rainstorm intensity formula derived by the least square method was better than that of Gauss Newton method;the accuracy of interval parameter formula of rainstorm intensity was better than that of rainstorm intensity formula.
文摘In this work, new cross section formulae for (n, p) and (n, d) reactions of He-3 have been investigated as a function of incident neutron energy. The new Empirical formulae were produced by using the least squares method to the experimental cross sections data, which were taken from Experimental Nuclear Reaction Data EXFOR Database Version of 2021. Several functions were examined to choose the best one that fits the data. Statistical hypothesis testing was used to insure how well the suggested equations fit the set of data. Two statistical indicators were used for each case for goodness-of-fit. Very high compatibility was found between the empirical values and the experimental data for both reactions.
文摘The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved to be very complicated, and various trials were published between the 1900s and 2000s. The development of indentation instruments and the wish to make the application in numerous steps easier, led in 1992 to trials with iterations by using relative values instead of absolute ones. Excessive iterations of computers with 3 + 8 free parameters of the loading and unloading curves became possible and were implemented into the instruments and worldwide standards. The physical formula for hardness was defined as force over area. For the conical, pyramidal, and spherical indenters, one simply took the projected area for the calculation of the indentation depth from the projected area, adjusted it later by the iterations with respect to fused quartz or aluminium as standard materials, and called it “contact height”. Continuously measured indentation loading curves were formulated as loading force over depth square. The unloading curves after release of the indenter used the initial steepness of the pressure relief for the calculation of what was (and is) incorrectly called “Young’s modulus”. But it is not unidirectional. And for the spherical indentations’ loading curve, they defined the indentation force over depth raised to 3/2 (but without R/h correction). They till now (2025) violate the energy law, because they use all applied force for the indenter depth and ignore the obvious sidewise force upon indentation (cf. e.g. the wood cleaving). The various refinements led to more and more complicated formulas that could not be reasonably calculated with them. One decided to use 3 + 8 free-parameter iterations for fitting to the (poor) standards of fused quartz or aluminium. The mechanical values of these were considered to be “true”. This is till now the worldwide standard of DIN-ISO-ASTM-14577, avoiding overcomplicated formulas with their complexity. Some of these are shown in the Introduction Section. By doing so, one avoided the understanding of indentation results on a physical basis. However, we open a simple way to obtain absolute values (though still on the blackbox instrument’s unsuitable force calibration). We do not iterate but calculate algebraically on the basis of the correct, physically deduced exponent of the loading force parabolas with h3/2 instead of false “h2” (for the spherical indentation, there is a calotte-radius over depth correction), and we reveal the physical errors taken up in the official worldwide “14577-Standard”. Importantly, we reveal the hitherto fully overlooked phase transitions under load that are not detectable with the false exponent. Phase-transition twinning is even present and falsifies the iteration standards. Instead of elasticity theory, we use the well-defined geometry of these indentations. By doing so, we reach simple algebraically calculable formulas and find the physical indentation hardness of materials with their onset depth, onset force and energy, as well as their phase-transition energy (temperature dependent also its activation energy). The most important phase transitions are our absolute algebraically calculated results. The now most easily obtained phase transitions under load are very dangerous because they produce polymorph interfaces between the changed and the unchanged material. It was found and published by high-enlargement microscopy (5000-fold) that these trouble spots are the sites for the development of stable, 1 to 2 µm long, micro-cracks (stable for months). If however, a force higher than the one of their formation occurs to them, these grow to catastrophic crash. That works equally with turbulences at the pickle fork of airliners. After the publication of these facts and after three fatal crashing had occurred in a short sequence, FAA (Federal Aviation Agency) reacted by rechecking all airplanes for such micro cracks. These were now found in a new fleet of airliners from where the three crashed ones came. These were previously overlooked. FAA became aware of that risk and grounded 290 (certainly all) of them, because the material of these did not have higher phase-transition onset and energy than other airplanes with better material. They did so despite the 14577-Standard that does not find (and thus formally forbids) phase transitions under indenter load with the false exponent on the indentation parabola. However, this “Standard” will, despite the present author’s well-founded petition, not be corrected for the next 5 years.
基金supported by the Natural Science Foundation of China(Grant Nos.12035002,12405235,and U2430207)the China Postdoctoral Science Foundation(Grant No.2023M740336)the CAEP foundation(Grant No.YZJJZQ2023020).
文摘Inverse bremsstrahlung absorption in laser-heated plasmas is studied using the Fokker–Planck equation in the low-field limit.Compared with the commonly used fitting formulas of Langdon and Matte et al.,our work employs fewer approximations and provides more accurate predictions for the super-Gaussian orderβand the heating rate.Simulation results show that the super-Gaussian order is generally lower than the fitting results of Matte et al.,which leads to an increase in absorption.However,we find two other factors that reduce absorption:the high-order term of the collision frequency and the effects caused by high laser intensity.Therefore,the final simulated absorption can either be higher or lower,depending on the conditions.These phenomena are theoretically analyzed using the Fokker–Planck equation.Fitting formulas are proposed for the super-Gaussian order and the heating rate,showing a discrepancy within∼10%of the simulation results.We also compare the simulation results with the experimental results from several recent papers.
