Belousov–Zhabotinsky reaction
An example of spatiotemporal patterns
Theory Seminar, 11:00am., FRIB 1200 lab, Gregory Potel, University of Seville, Spain, Some recent trends in nuclear reaction theory for basic science and applications
High Energy Physics Seminar, 1:00 pm, 1400 BPS, Elena Pinetti, Flatiron Institute at the Simons Foundation in NYC, Hunting axions with the James Webb Space Telescope
My 14 year old asked me to ask you this question.
Just a vibe check. How are the vibes after spring break?
We were solving nonlinear first order differential equations of the homogenous type
where is a nonlinear function of . We found critical points where .
We demonstrated the utility of phase diagrams to visualize the behavior of solutions to nonlinear differential equations.
We showed that we can learn something about systems we know little about at first using this approach (i.e., Firefly synchronization).
Synchronization always (no phase difference)
Entrainment is possible (constant phase difference)
No entrainment (). Stimulus is too fast.
We then moved on to 2D phase spaces, where we had a system of two first order equations:
We focused on the simple harmonic oscillator as an example.
And we graphed it's phase space diagram.
Phase space diagram for a simple harmonic oscillator. The ellipses are curves of constant energy, .
In the case of a large angle pendulum, we have a nonlinear differential equation:
Here, we can write this as a system of two first order equations:
We can then plot the phase space diagram for this system.
Consider the phase diagram for a large angle pendulum. What do the upper and lower flows represent?
Click when you and your table are done.
Consider the following notation:
Is this an idea you've seen before? How do you feel about it?
There is no option for not learning, sorry.
We constructed a solution of the form:
We can plot it in the complex plane and see the real and imaginary parts, and how they change in time.
We can plot the solution on the complex plane. For this, , and the amplitude is .
The solution rotates counterclockwise in the complex plane, following the rainbow from violet to red.
The real part is just the projection of the complex solution onto the real axis. Just how far along the real axis is the solution at any given time.
That looks like a time trace, but not quite, it's the real projection. The colors scheme is the same as before.
We just flip the axes to produce the time trace that you are used to seeing. The color scheme is the same as before.