yade-dev team mailing list archive

["Sergei D." <sj2001@xxxxxxxxx>]

>> we have tc and en:
>>
>> (*) tc = pi 2 m_eff / sqrt( 4 kn m_eff - cn^2 )   (note your delta in
>> brackets)
>> en = exp( -cn tc / 2 / meff )
>>
>> where we have kn and cn:
>>
>> kn = m_eff / tc^2 * ( pi^2 + ln^2(en) )
>> cn = -2 * m_eff / tc * ln(en)
>>
>> Then, for pair spheres with mass m1 we have
>> m1_eff = m1/2, en1, tc1 => kn1 and cn1.
>>
>> For pair spheres with mass m2 we have
>> m2_eff = m2/2, en2, tc2 => kn2 and cn2.
>>
>> For pair spheres with mass m1 and m2 we have
>> 1) 1/m12_eff = 1/m1+1/m2, en12, tc12 => kn12, cn12,
>> OR we have
>> 2) 1/kn12 = 1/kn1 + 1/kn2 and 1/cn12 = 1/cn1 + 1/cn2.
>>
>>> From (*) cn^2 can't be more  than cn_crit^2 = (4 kn m_eff)...
>
> OK, now I believe that I understand.
>
> Does _OR_ means that 1) is equivalent to 2)?
> Can you tell me more about the time step and the physical meaning of tc?
>
tc is the collision time.

I'm don't dare to prove equivalence strictly...
But in (1) we have the parameters {en12, tc12} for the pair spheres of
specie 1 and 2.
>From them we have derived kn12 and cn12 using linear spring model .

In (2) we have the parameters {en11, tc11} and {en22, tc22} for the pair
spheres of specie 1 and for pair spheres of specie 2.
Then, from them we have derived kn12 and cn12 using linear spring model.

Thus, in the linear model framework, these two approaches seem to be
equivalent...