Download 沙粒振动的仓室效应

沙粒振动的仓室效应
张逊 07300190041
1 Maxwell’s 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
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“temperature”
high
low
(2) Simulation
Sand as Maxwell’s
Demon
A = 0.3 cm,
• f = 50 Hz
20 cm
On one side initially
 equally to both sides
r=1mm
• f < 30 Hz
symmetry is spontaneously
broken
h
12 cm2
 on one side
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).
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Flux Function
(Eggers)
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)
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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
4 gh
2 2 r N 2
B
(1  e ) (
)
2
 (af )

2
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)
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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)
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实验仪器
实验结果
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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
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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。
• N左=0，N右=80，a=3.0mm，f=33.3Hz，
B=0.215，经过10秒后达到平衡态。
• N左=88，N右=112，a=3.0mm，f=20.0Hz，
B=3.72，经过55秒后达到平衡态。
• N左=100, N右=100，a=3.0mm，f=20.0Hz，
B=3.72，经过50秒后达到平衡态。
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