Microdynamics of bow rosin and strings

Discussion in comments here questions whether the rosin on bow hairs changes physical characteristics in the course of stimulating vibration in a string.

Consensus seems to be that: the physical mechanism by which a rosined bow hair stimulates vibration in a tensioned string is that it grips the string and pulls it a laterally until the lateral tension overcomes the grip of the hair and the string slips back.

I assume that in order to create a loud tone the string must slip laterally past its stationary position – i.e., opposite the direction in which the bow is pulling it – before the bow is able to grip it again and repeat the cycle. (Presumably this cycle repeats with a frequency corresponding to the first harmonic of the note being played. E.g., 440Hz for A4.)

The first question is whether the above description is accurate?

The second question, raised in the aforementioned discussion, is: Does the rosin liquefy or otherwise change its physical characteristics during this process? Or are the static and dynamic friction coefficients of the string and rosined bow constant during a bowed note?

To get loud, the string does need to vibrate at a greater amplitude. There are two ways to get there (roughly speaking). You can use a lot of pressure to "snap-start" the string at high amplitude, or you can bow with slowly increasing pressure and/or speed to build up the resonance.
Next: the bow's required speed to maintain a given amplitude varies with the distance from the bridge. In simple math, you can see that the amplitude of the string is greatest at the half-way point of the string (fingered) length and is zero at the bridge.

Edit:

The following information is based partly on Scott Wallace's comments in this question

The bow hair, then, as you surmise, pulls the string in one direction until the string breaks free and rebounds in the far direction. When the string as reached the farthest point, its transverse velocity is zero, and the bow hair can most easily re-grab. The string then returns to the near point based both on its internal tension and the drag force from the bow. Since the bow is moving (you Hope!!! :-) ) at constant speed, the string follows along at constant transverse speed until it breaks loose again.

While the free "snap-back" is not strictly at constant speed, the overall waveform is very close to a sawtooth pattern -- which BTW is one reason bowed notes sound different from pizzicato; the latter producing more of a sine pattern than sawtooth.

Final comment: listen to someone playing sul ponte (very close to the bridge). Everything goes to hell, pun intended.

• Cool – yet more insight provided by this description: The reason bowing far from the bridge results in a quieter note is that the same bow "tug" provokes lower string amplitude. And bowing close to the bridge gets tricky because it's increasingly difficult to get a consistent tug when pulling from the anchor-point of the string. (It's like trying to move a lever arm right next to its pivot point instead of at a distance.) – feetwet Jan 30 '19 at 16:40