两条道路

lakobe · 发表于 2006-6-13 19:35:08

话说有两条道路,R1 和R2, 上面都有两种车, A型和B型. 总车流量,R1和R2相等. R1 上开着

5% A型车, R2上开着25% A型车. 若A型车的排放量是B型车的2倍. 请问站在R1,R2路边,

受到污染的比例与在R1,R2上开车所受到污染的比例是否相同? 假设其他条件相同.

ob · 发表于 2006-6-13 21:29:15

Welcome

Have not seen you long time

lakobe · 发表于 2006-6-13 21:34:24

其实我经常潜水. 这不,工作中遇到点问题,到这来求援了.

ob · 发表于 2006-6-14 19:37:18

you come here more often.

ob · 发表于 2006-6-14 19:51:20

Based on the condition given in this topic, on R1 and R2, the contamination ratio is 21/25. The contamination is diffused to the side of R1 and R2, the concentration of the contamination is not as high as that on the roads. There is a contamination concentration distribution. I think the contamination ratio on the side of the roads is smaller. Think an extreme case, a place somewhere between R1 and R2, the contamination ratio is 1. Then move the place to R1 and R2, the ratio increases gradually when the place is getting closer to R1 and R2.

husonghu · 发表于 2006-6-14 19:53:30

欢迎真正的老前辈lakobe

lakobe · 发表于 2006-6-14 20:14:32

没想到还有这么多人记的我的ID.

lakobe · 发表于 2006-6-14 20:34:11

这是我实际研究中遇到的问题.我们观测的结果是,路边相差不大(~21/25),

但是路上则相差很大,几乎有2-3倍 (or 30-50%). 我想可能是由于:在路边两种车的影响

average out,即每一辆车都对观测点有同样的影响,所以是21/25. ob兄提到

dispersion,我们假设dispersion的程度相当. 但是在路上,testing vehicle is

more likely to follow vehicle type A on R2. 即每一辆车对观测车有不同的影响.

在R2上,观测车更容易受到 TYPE A vehicle 的影响. 这里大概有个probability的问题,

我还没有想明白. 所以上来请教.

husonghu · 发表于 2006-6-14 20:37:13

WXC脑坛之初的元老之一嘛，哪能不记得呢(我是后来者了)。望您多亮相，助本坛一把

ob · 发表于 2006-6-15 09:28:25

Dispersion is a more suitable word than diffusion. Since the air of road is disturbed frequently by moving car, the contamination concentration at the side of the road is kind of uniform comparing with the concentration at the center of the road. Consider a case similar to this: put several bottles of ink in a big water tank, than move the ink bottles and watch the color distribution, you can see the color near the bottles is much thinker than the water color at a place far from the bottle. Actually, the water color at rmote area is more uniform. And the color of remote area is directly related to the number of bottles in the tank. Hope this can have some help to you.

lakobe · 发表于 2006-6-15 21:52:45

I believe you are right. This is also what I thought. But your ink bottle example is more vivid

and easy to understand. Do you think we can build up some math models to estimate the ratio of darkness of a random placed spot in two large water tanks, say one has 5 ink bottle, one has 10 ink bottle? Assume all bottles are evenly distributed and other factors are the same.

ob · 发表于 2006-6-16 08:58:46

The mathematical model for this can be a general mass transfer equation. A simiplified equation (2-D) is:

Ux dc/dx=Dy d2C/dy2

Here d stand for partial differential

Ux is horizontal moving rate and Dy is the transverse diffusion coefficient or dispersion coefficient.

d2C/dy2 is the secondary partial differential of C at y direction. C is the concentration.

Now you can set the boundary condition as C(x,y)=Cs at x,y=0.

I used to be able to solve this kind of equations. Now I am too lazy to even think about this

.

You can find the solution for this kind of equations by searching mass transfer text book.

LOTUSEATER · 发表于 2006-6-16 17:29:19

原来有前辈来指教，

这厢有礼了

lakobe · 发表于 2006-6-16 18:57:59

本想偷点懒,用probability简单的处理一下.看来还是得认真对待.还好,我还记得如何解

PDE. 多谢!

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两条道路

Welcome[>:D<] Have not seen you long time[:-M]

ob兄请了

lakobe, really happy to see you[>:D<][:-M] Hope

回复：两条道路

欢迎真正的老前辈lakobe[@};-][@};-][@};-][@};-]

受宠若惊

讨论讨论

WXC脑坛之初的元老之一嘛，哪能不记得呢(我是后来者了)。望您多亮相，助本坛一把[:P][:P]

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原来有前辈来指教，[:P]这厢有礼了[@};-]

多谢ob兄