氢原子径向幂坐标矩阵元的一般递推关系

导出了氢原子径向幂坐标矩阵元（ｎ’ｌ’│ｎｌ）的递推关系,从而把曾谨言所著《量子力学卷Ｉ》中关于矩阵元（ｎｌ│ｒ＾ｋ│ｎｌ）的递推关系以及笔者在《在学物理》１９９６年第４期“氢原子径向矩阵元及其递推关系”一文中关于矩阵元（ｎｌ’│ｒ＾ｋ│ｎｌ）的递推关系推广到更为一般的情形。     

关于氢原子径向矩阵元〈n,l│r│n,l—1〉的一个注记

经研究指出流行文献中关于氢原子径向矩阵元〈ｎ，ｌ│ｌ│ｎ，ｌ－１〉的结果的符号是错误的。     

m维氢原子径向矩阵元的通项计算公式

给出了n维氢原子的归一化径向波函数,推导出了n维氢原子的任意径向矩阵元〈NJ|rq|N′J′〉的通项计算公式。     

n维氢原子径向矩阵元的通项计算公式

给出了ｎ维氢原子的归一化径向波函数,推导出了ｎ维氢原子的任意径向矩阵元〈ＮＪ｜ｒ＾ｑ｜Ｎ′Ｊ′〉的通项计算公式。     

也谈径向矩阵元的递推关系

利用超位力定理及其推广形式给出了一维、二维和三维系统径向矩阵元递推关系的一般表示式,并具体求出了谐振子系统及非相对论氢原子系统中径向矩阵元的递推关系．     

n维氢原子径向矩阵元的递推关系

给出了n维氢原子径向幂次矩阵元的递推关系,通常的三维氢原子的有关结果作为特例包含在本文的一般结论之中。     

常用基底下径向矩阵元的递推关系

给出了线谐振子基、球谐振子基和氢原子基下径向矩阵元所满足的递推关系。     

相对论性无自旋氢原子的径向矩阵元的递推关系

导出相对论性无自旋氢原子的径向矩阵元〈nl|rp|n′l′〉的递推关系.     

氢原子基下径向矩阵元的递推关系

推导出氢原子基下径向矩阵元〈nl|rk|n′l′〉所满足的递推关系.     

二维氢原子四类升降算符的矩阵元

重新定义了二维氢原子的四类升降算符，计算了它们的矩阵元，以使所求得的径向函数是归一化的。     

Azimuthal distributions of radial momentum and velocity in relativistic heavy ion collisions

Azimuthal distributions of radial (transverse) momentum, mean radial momentum, and mean radial velocity of final-state particles are suggested for relativistic heavy ion collisions. Using the AMPT transport model with string melting, the distributions of Au+Au collisions at 200 GeV are presented and studied. It is demonstrated that the distribution of total radial momentum is more sensitive to the anisotropic expansion, as the anisotropies of final-state particles and their associated transverse momentums are both counted in the measurement. The mean radial velocity distribution is compared with the radial flow velocity. The thermal motion contributes an isotropic constant to the mean radial velocity.     

阶梯圆环压电超声换能器径向振动性能的理论研究*

提出了一种阶梯圆环径向振动压电超声换能器,根据力电类比原理建立了阶梯圆环及阶梯圆环换能器的径向振动等效电路,推导了阶梯圆环的径向共振频率方程和位移放大系数,在此基础上进一步推导了换能器的径向共振和反共振频率方程。通过理论推导和有限元仿真模拟分析了阶梯圆环压电超声换能器的径向振动性能。结果表明,增大阶梯圆环中内外环的径向厚度之比K1或减小轴向厚度之比K2,阶梯圆环的一阶径向共振频率减小,二阶径向共振频率增大;在二阶径向共振模式下,K1、K2值在一定范围内阶梯圆环可实现由内向外的径向位移振幅放大;随着压电陶瓷圆环的内半径增大,阶梯圆环压电超声换能器的一阶、二阶径向共振和反共振频率减小,二阶径向共振下的有效机电转换系数趋于零;增大阶梯圆环内环的外半径,换能器的一阶径向共振和反共振频率减小,二阶径向共振和反共振频率先增大后减小,理论推导与仿真模拟结果符合良好。本文研究结果为阶梯圆环压电超声换能器的工程应用提供理论参考。     

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.     

径向复合圆柱压电超声换能器

提出一种三元径向复合圆柱压电超声换能器,并对其径向振动特性进行了研究。基于弹性力学理论及机电类比原理,导出了柱坐标系中分割处理径向极化压电陶瓷管准厚度模振动及薄壁短圆管径向振动的机电等效电路;利用径向力和振速连续的边界条件,得出了径向复合圆柱压电换能器系统的径向振动机电等效电路及其共振频率方程。探讨了换能器径向共振频率及有效机电耦合系数随其几何尺寸的变化关系。研究表明,换能器的径向共振频率及有效机电耦合系数随其内芯半径和预应力管壁厚度增大而降低。研制了一些径向复合圆柱压电换能器,并对其径向共振频率进行了测试。结果表明,理论与实验结果基本一致。      

基于多普勒天气雷达数据的中层径向辐合自动识别及其与强对流天气的相关性研究

本文提出了一种从多普勒天气雷达单仰角径向速度图中的正-负速度区域对入手自动识别一类强对流天气的中层径向辐合的方法.首先,根据雷达探测机理,解释了由气流形成的辐合场一定会在径向速度图中形成局部最大正速度区域和局部最大负速度区域的特点,然后构建正-负速度区域对的识别算法,通过来自多个单仰角径向速度图的区域对配准和相关信息,判断雷达径向速度图中是否存在着中层径向辐合,推算辐合的强度、延伸厚度等重要参数,确定得到最优垂直剖面图的剖切方位.经对客观存在显著中层径向辐合的384例样本和不存在明显中层径向辐合的356例样本的测试,本文方法对显著中层径向辐合的识别率达到100%、误识率为0,与人工方法相比,本文方法把对中层径向辐合的识别时间从分钟级缩短到秒级,同时自动给出其强度、高度、厚度、位置等丰富的定量信息和恰当的可视化垂直剖面图.利用给出的参数信息进行了与强对流天气的相关性研究,验证了中层径向辐合与对流行地面大风的较强相关性,同时发现,最强中层径向辐合的高度对区分强冰雹与强降水、中层径向辐合的强度对估计冰雹尺寸具有良好的指示性.     

Investigation of irradiance efficiency for LED phototherapy with different arrays

Red and yellow light emitting diodes (LEDs) are currently utilized as lighting sources during LED phototherapy. These LEDs were arranged on a disk with an external diameter of 70 mm with different arrays — radial, rhombus, square radial, and square rhombus arrays. The radial and square radial arrays had better irradiance efficiency than rhombus and square rhombus arrays by optical simulation. Additionally, the radial array had 76 sets of LEDs, but the square radial array had 100 sets. Thus, a mockup sample of radial array phototherapy was constructed for performance tests. The mixture efficiency of the radial array was observed at distances of 1-100 mm and lighting was well mixed when distance exceeded 50 mm by optical simulation. Irradiance variation with angle was approximated by experiment and theory at a treatment distance of 50 mm and 100 mm using the phototherapy mockup. The radial array was one good choice for LED phototherapy.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

新型高功率径向强流速调管振荡器

 提出了一种新结构的高功率径向强流速调管振荡器,该器件利用折叠式同轴谐振腔的微波场与接近空间电荷限制电流的径向电子束强烈相互作用产生高功率微波。首先对这种器件的实现机理进行了初步的分析，提出了有间隙电压情况时的径向同轴间隙的空间电荷限制电流1维近似估计模型。分析表明：对于电子束直流接近但小于直流空间限制电流的径向速调管，当有调制间隙电压时，空间限制电流要小于无调制间隙电压情况下的直流空间限制电流，径向强流电子束电流接近和超过空间电荷限制电流时会出现强烈的调制。然后用PIC程序对其特性进行了粒子模拟，在二极管输入电压500 kV、电子束电流为30 kA条件下，最终得到了峰值功率6 GW、频率1.3 GHz的微波输出。     

Radial drift invariant in long-thin mirrors

In omnigenous systems, guiding centers are constrained to move on magnetic surfaces. Since a magnetic surface is determined by a constant radial Clebsch coordinate, omnigeneity implies that the guiding center radial coordinate (the Clebsch coordinate) is a constant of motion. Near omnigeneity is probably a requirement for high quality confinement and in such systems only small oscillatory radial banana guiding center excursions from the average drift surface occur. The guiding center radial coordinate is then the leading term for a more precise radial drift invariant I _r , corrected by oscillatory “banana ripple” terms. An analytical expression for the radial invariant is derived for long-thin quadrupolar mirror equilibria. The formula for the invariant is then used in a Vlasov distribution function. Comparisons are first made with Vlasov equilibria using the adiabatic parallel invariant. To model radial density profiles, it is necessary to use the radial invariant (the parallel invariant is insufficient for this). The results are also compared with a fluid approach. In several aspects, the fluid and Vlasov system with the radial invariant give analogous predictions. One difference is that the parallel current associated with finite banana widths could be derived from the radial invariant.     

Tidal Forces in Dyonic Reissner-Nrdstrom Black Hole

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordstr¨om black hole.We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles.We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole.The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole.The radial geodesic component starts decreasing in dyonic Reissner-Nordstr¨om black hole unlike Schwarzschild case.We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.