沙粒振动的仓室效应 张逊 07300190041

1 Maxwell’s Demon Demon (1) Phenomena The Second Law of Thermodynamics forbids (through statistical improbability) that two bodies of equal temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a stable state in which one of the two has a significantly higher temperature than the other. The second law -- in an isolated system, entropy never decreases. Demon

(2) Simulation Sand as Maxwell’s Demon “temperature” (2) Simulation Sand as Maxwell’s Demon high low A = 0.3 cm, f = 50 Hz 20 cm On one side initially  equally to both sides f < 30 Hz r=1mm symmetry is spontaneously broken h  on one side 12 cm2 A drawing of the experimental setup. The two sides of the box are connected by a hole at height h= 2.3 cm. The picture is taken below the bifurcation, so most particles have settled on the right hand side. As a result, the gas sinks to the bottom, reducing the flux. Jens Eggers, Sand as Maxwell’s Demon, PRL83, 5322 (1999).

(Eggers) Flux Function Flux nk = fraction of particles in k-th box N = number of compartments A  absolute flux rate (t) Maximum at nk = 1/(N√B). Normalized to nk = 1. The factors A and B depend -- on the particle properties (such as their radius r, and the restitution coefficient e of the interparticle collisions) and -- on experimental parameters (such as the height h of the wall and the frequency f and amplitude a of the driving). Jens Eggers, Sand as Maxwell’s Demon, PRL83, 5322 (1999). Europhys. Lett., 53 (3), pp. 328–334 (2001)

The phase transition towards the clustering state is only determined by the factor B, which for a 2D gas of spherical disks takes the form restitution coefficient P = total number of particles, l = width of each box. N = number of compartments. For a given granular material (r and e fixed), B ↑ either h ↑ or af ↓ (reducing the driving). Jens Eggers, Sand as Maxwell’s Demon, PRL83, 5322 (1999). Europhys. Lett., 53 (3), pp. 328–334 (2001)

nk B Compared theory and experiment for 2-box system: Theory -- dynamics  balance equation nk - 600 glass beads (r = 1.25 mm, e = 0.97) in a cylindrical perspex tube of inner radius 27.5 mm, - two equal compartments -- wall height h = 23.0 mm. - B varied: for a 3D gas, B ∝ 1/f2 still holding varying f, at a fixed a = 6.5 mm. B Bifurcation diagram for the 2-box system (k = 1, 2). Solid line - stable; Dashed line - unstable equilibria of the flux model. Dots: experiments. Transition to clustering state  via a pitchfork bifurcation. Europhys. Lett., 53 (3), pp. 328–334 (2001)

实验仪器

实验结果 仪器固有参数: h=30mm r=1mm Ω=(7.5x76x2)mm² e钢珠=0.56 于是B=1.34(N平均/af)² [a的单位是mm,f是Hz] 振幅不好测,暂时取a=3mm; 然后再取N总=104, f=20Hz时,B就差不多在1左右了

影响实验结果的外部因素 仪器的水平程度 仪器的使用方法问题 调节频率的同时会影响振幅 振幅不稳问题

播放视频时间 我的4组数据 N左=80，N右=0，a=3.0mm，f=33.3Hz，B=0.215，经过10秒后达到平衡态。

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