静电场描绘实验的研讨

引言 静电场描绘是国内外高等院校普遍开设的物理实验.由于直接描绘静电场存在很大困难,而稳恒电流场在导体中的分布规律--电流与电势差的分布规律和静电场中场强与电位差的分布规律可以用相同的数学关系式表达,所以通常是用稳恒电流场来模拟静电场.     

逻辑函数的减-非和除-非展开式的最小化方法

讨论了布尔减和布尔除的定义以及逻辑函数在布尔减及非运算、布尔除及非运算完备集中的展开,给出了减-非和除-非逻辑函数的化简公式.在此基础上提出了减-非和除-非逻辑函数的代数化简法以及图形化简法,并给出了化简实例.实例验证了上述化简方法的有效性.     

The quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

Using a new tortoise coordinate transformation,we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time,and obtain the event horizon surface gravity and the Hawking temperature on that event horizon.The results show that there is a crossing of particle energy near the event horizon.We derive the maximum overlap of the positive and negative energy levels.It is also found that the Hawking temperature of a black hole depends not only on the time,but also on the angle.There is a problem of dimension in the usual tortoise coordinate,so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.     

新乌龟坐标变换下的动态Kinnersley黑洞的Hawking辐射

采用两种新的乌龟坐标变换,用改进的Damour-Ruffini方法研究了动态Kinnersley黑洞的Hawking辐射.在新乌龟坐标变换下,将Klein-Gordon方程在视界附近变换成平直时空的标准波动方程形式,得到了黑洞的表面引力及Hawking温度,该温度在黑洞表面不同点有不同的值.值得注意的是,旧的乌龟坐标变换存在量纲错误,新乌龟坐标变换没有量纲问题,选不同的旧乌龟坐标变换计算同一黑洞所得结果不同,但是采用不同的新乌龟坐标变换所得结果仍然不同. 关键词： 黑洞 乌龟坐标变换 Hawking辐射 Klein-Gorden方程     

Quantum nonthermal effect of the Vaidya-Bonner-de Sitter black hole

Using the Hamilton-Jacobi equation of a scalar particle in the curve space-time and a correct- dimension new tortoise coordinate transformation, the quantum nonthermal radiation of the Vaidya-Bonner-de Sitter black hole is investigated. The energy condition for the occurrence of the Starobinsky-Unruh process is obtained. The event horizon surface gravity and the Hawking temperature on the event horizon are also given.     

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.     

逻辑函数RM展开式和CRM展开式的转换

讨论了逻辑函数在与-异或和或-符合代数系统中的RM展开式和CRM展开式.根据异或和符合运算的性质详细讨论了逻辑函数bj系数和dj系数间的关系,并提出了两者的矩阵转换法,举例说明了转换过程.该方法揭示了bj系数和dj系数的内在联系,具有较好的实用性.     

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.     

Quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

With a new tortoise coordinate transformation, we discussed the quantum nonthermal radiation characteristics near the event horizon by studying the Hamilton-Jacobi equation of a scalar particle in the curve space-time, and obtained the event horizon surface gravity and the Hawking temperature on the event horizon. The results showed that there is a crossing of particle energy near the event horizon. We derived the maximum overlap of the positive and negative energy levels. It was also found that the Hawking temperature of a black hole depends on not only the time, but also the angle. There is a problem of dimension in the usual tortoise coordinate, so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.     

逻辑函数在布尔减-除-非代数系统中的标准展开式及其化简

布尔减、布尔除与非运算构成完备集．从与-或-非代数系统中的最小项、最大项展开式出发,推导了任意逻辑函数在减-除-非代数系统中的标准DOS（减之除）和标准SOD（除之减）展开式．在此基础上给出了DOS和SOD逻辑函数的代数化简法和图形化简法,给出的化简实例验证了上述化简方法的有效性．