repetitive note on the pedals. the hammer and the vibration of the str

It sounds to me from your first sample, that on the real piano it's due to the hammer hitting an already vibrating string (as you've also noted). It can happen to hit it in phase with the oscillation of the string at the strike point (hammer and string both moving in the same direction), or out of phase (the two moving in opposite directions). And of course there is a continuous range from perfectly in-phase to perfectly out-of-phase. In the former case the hammer adds more energy to the string, in the latter less, or it can even dampen the oscillation (think of pushing a child on a swing the "wrong" way). Also there is the matter of harmonics, so different sets of harmonics get enhanced and suppressed each time. This is I think what makes the sound "sparkle" as you put it.

From your second sample, it seems that this aspect of the dynamics is not included in Pianoteq's model, which seems to react as if each time the hammer struck a new string that is at rest (i.e., set of strings that make up the note). This new sound sound is then combined with the residual sounds of what preceded it. The fact that the new strike of the hammer is treated as a new note can be seen by how the polyphony use goes up with repeated notes (under Options -> Perf).

You can explore this effect, and easily push even a fast modern PC to CPU overload, using the Mallet bounce settings: Set the delay to something short, and losses to low or zero (or simply, turn the effect on and pull all the sliders except maybe Humanization to the left and leave "Initial delay" sync off).

Your third sample with hammer position "Humanization" is a kind of a workaround, but as you've noted it does not correctly model what is really going on in a piano.

PS. sympathetic resonance and sustain pedal are secondary. You can try the same thing on a real grand piano with just the Sostenuto pedal and you'll get a similar effect. (Sure, all dampers off will enhance it, but it's not responsible for the main effect.) If you could play superhumanly fast (like pianoteq's mallet bounce can at up to 100 times a second when the CPU can keep up) then you'd also get the effect without engaging any pedals.

That's very interesting and impressive that it's already implemented. Is there a way to increase the effect so it sounds more like scherbakov.al's first example?

Actually with a bit of experimentation using the mallet bounce (all sliders to extreme left, except "Initial delay"), the repetition delay can be tuned to be in or out-of sync with the oscillation of certain strings to emphasise the effect.

@scherbakov.al You should try this. Set the Mallet Bounce Initial delay somewhere between 100 and 200 ms and then try it with different notes. On some notes the effect you demonstrate on the Bechstein will be quite pronounced, on some others, more suppressed (as one would expect depending on the relationship between repetition frequency and the note's fundamental frequency). You'll get an even stronger effect (more "colour" or "sparkle") and less dependence on which note you're on if you reduce the string length. That's because the overtones will be have more anharmonicity and their phase cancellations/reinforcements with each strike of the hammer will be more chaotic. What size is the Bechstein you used for your first recording?

The only thing I find puzzling is why polyphony goes out of control with fast lossless Mallet bounce (even without any pedal or sympathetic resonance). It's a bit of a shame because some cool effects can be achieved.

Try reducing the string length. Also experiment with the unison width and randomising the tuning a bit (e.g. using the condition slider). There are probably other things you can do but string length will likely be the most important factor. (Btw, I don't see this quality of the piano sound as a means of expression, since it's beyond the player's ability to control.)

scherbakov.al, FYI: I tried listening for this on our 6ft Kawai grand (which is a well maintained, regularly serviced instrument) and the effect is very comparable to what Pianoteq produces for a similar size instrument. So I think they've got it pretty much right. (My apologies to Philippe and the rest of the team for assuming otherwise.)

There are some internal parameters to control this, but they are not available in the UI. We always tried to keep the UI reasonably simple and comprehensible, without overhelming the user with too many parameters.

To create the examples I corrected parameter string length. To disharmony was similar .

Any chance some cluttered unreasonably full list of possible settings available in some future versions? Not that I that much insist I'll use them but anyway it's cool to have as much as possible available for control just in case.

There are associated with the following observation of sensations. When played a few chords on the open pedal, all sounds and strings resonate, adding bass requires a little less force pushing for what he showed and sounded. Perhaps this psycho-physiological deception? Or is indeed present in the piano? Based on the experiences in Pianoteq bass should really play, while the piano can touch softer ..
https://soundcloud.com/bgwoxxxjmwom/bass

Or game of repetitive chords crescendo pedal ..in Pianoteq need to "put pressure" and in paino think it took a little less effort for rocking sound ..
https://soundcloud.com/bgwoxxxjmwom/pedal-1
It may be the case in the speed of the curve?
This is a very minor differences, maybe I invented it, I do not know ..

Yep.