Recent content by anuttarasammyak

We are sharing the situation. I do not find any essential difference in the drawings.

With no regard what function form F has, we can write $$\frac{d}{dt}[P_1(V_{10}-A_1vt)]=-\epsilon F(P_1,P_2)$$ $$\frac{d}{dt}[P_2(V_{20}+A_2vt)]= \epsilon F(P_1,P_2)$$ We expect ##0<\epsilon <<1## because oriffith is small. If there is no oriffith, pressures are...

Thanks for your comment. Due to my PC operation trouble I deleted my previous post in fail. I am sorry about it. Let me continue. As equation of gas1 and gas2 mols, (13) is written as $$RT \frac{d}{dt}n_1=\frac{d}{dt}(P_1V_1)=-2c_0\sqrt{(P_1-P_2)P_2}$$ loss of gas1 equals gain of gas2 so...

What are predetermined values of f(0) and c’s ?

A Gaussian wave packet has the property that its width increases with time while its overall shape is preserved. This behavior is consistent with the idea of a wave packet that remains stable over time. However, since I am not aware of any other wave packets that exhibit similar stability, this...

By the equations of post #4 $$x(0)=1-\frac{h(0)}{f(0)}=0$$ so $$(c_3+c_5)f(0)=c_1c_2$$ Is that correct ? We do not have freedom of initial condition f(0) ? Are c's not constant but function of f(0)? Is there any more relation to satisfy for the c's ? All the constants are positive ? I would...

What is your choice of constant c’s that makes divergence at t=0?

I do not find divergence at t=0 for ##c_3, c_5 \neq 0##. Could you explain it in detail?

You may carry out Taylor expansion $$ f(t) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!} t^n = \sum_{n=0}^\infty \frac{g^{(n-1)}(0)}{n!} t^n $$ in the way of post #3, where $$ g(f,t)=\frac{c_4-2c_0\frac{\sqrt{(c_1c_2f^{-1}-c_3+c_4t)\{(c_5-c_1c_2 -c_6t)f^{-1}+c_3-c_4t \}\ }\ }{|\ c_5-c_6t\...

RHS of (1) would be g which is made of f and t.

The cat keeps Schroedinger hear her meow. Quantum Zeno effect saves her life.:wink:

I observe no divergences at t=0 in post #3. Denominator ##V_1=0## at ##t=c_3/c_4## would matter. Say ##f(0)## and function form ##g(f(t),t)## are given, we may think of t evolution by continuing iteration,i.e., $$f(\triangle t) \approx f(0)+g(f(0),0) \triangle t $$ $$f(2\triangle t) \approx...

$$ f''=\frac{\partial g}{\partial f} f'+ \frac{\partial g}{\partial t} =\frac{\partial g}{\partial f} g+ \frac{\partial g}{\partial t} $$ Thus $$ f''(0)=\frac{\partial g}{\partial f} |_{t=0}\ g(f(0),0)+ \frac{\partial g}{\partial t}|_{t=0} $$ If some term here diverges at t=0, why don't you...

What actually is ##g(f(t),t)## in your case ?

I got ##x_1=1.8317... \ x_2=3-\frac{x_1}{4}=2.5421...## The equation of ##x_1##: Other two casese : ##(x_1.x_2)=(-1.3444, 3.3660),(-0.48370, 3.1215)##