As explained in a previous post, I thought I could use a MOSFET as alternative to the PUT originally used in experiment 11 of "Make electronics" from Charles Pratt.
See original circuit below: 
And my proposed alternative with MOSFET below: 
As you can see, the original circuit is a slow speed oscillator, making the LED flicker. For obscure reasons, my proposed alternative doesn't work. Any idea how to make it work?
Answer
It doesn't work because they are radically different components.
The PUT is a strange beast; it's like a hybrid between a bipolar junction transistor and an avalanche diode. It has non-linear behaviour: once the current flowing through it has gone above a certain value, its resistance collapses and it becomes "more on", until the current falls much futher than the trigger level.
This lets the oscillator work: it charges up the capacitor, until the trigger of the PUT is reached, at which point it discharges through the LED until the current falls below the turn-on point, and the PUT turns off again.
In some ways this is quite a lot like the 555: you could almost just substitute it with the "discharge" and "trigger" pins wired to the capacitor-resistor junction and the "threshold" pin wired to the 15k/27k voltage divider.
(For practical purposes the 555 obsoletes the PUT, which is why everyone is suprised to find the PUT in a book that's in print today)
In your circuit, the MOSFET will just adjust itself into its linear region such that the gate-source voltage is at the turnon point, and stay there. There's no nonlinearity to produce oscillation.
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