Short answer: Yes, I'd buy the Berkeley group's work; their value of $\mu$ is the highest I've seen...
Long answer: Yes. The question arises because of widespread confusion between the terms "adhesion" and "friction".
Crudely, adhesion is a force that resists the separation of in-contact surfaces in the normal direction. Friction is a force that opposes relative tangential motion between two in-contact surfaces. One need not imply the other, their causative mechanisms are distinct and in fact most models exclusively address one or the other.
Adhesion is driven by Van der Waals kinda forces.
"Coulomb" friction (solid-solid) is caused by the presence of asperities (think small bumps or protrusions) on surfaces. Due to the presence of these asperities, the "real" area of contact between two surfaces is much smaller than the "apparent" area of contact.
The Coulomb model is a phenomenological fit to experiments that was shown to be deducible assuming this type of contact. In some sense this sets an upper bound on the resistance to the tangential relative motion between surfaces.
If you somehow ensure these areas are very nearly the same, would $\mu$ then increase?
There are, indeed, "intimate" contacts where the apparent and real areas of contact are very nearly the same and the resistance to sliding large. In such cases, the frictional behavior is intimately linked to the mechanisms of deformation at the small scale (e.g. plasticity in metals). However, even this is not enough to get the largest possible $\mu$.
For instance, the maximum shear stress resisting relative motion in metals is capped to a maximum value, beyond which it cannot increase.
(i.e.) Instead of
Shear stress = $\mu\times$ Normal stress ...(I)
You would've
Shear stress = min ($\tau_{max}$ , $\mu\times$ Normal stress) ...(Ia)
Equation (I) is simply Coulomb's law applied locally.
Q = $\mu N$ ...(II)
Now, if someone devised a contact / material system that produces very high $Q$ for a given $N$ in equation (II) in an experiment, they could claim that they had devised a material with high friction coefficient.
This is essentially what the Berkeley group seems to have done. As I said, this kind of thing is hard to do with metals - even if intimate contact is achieved (say, under a state of severe deformation), something like Eqn. (Ia) kicks in and prevents the shear resistance from rising further. Previously, therefore, people achieved high $\mu$ using compliant, soft materials, but these guys use a microfiber array to engineer a surface with high $\mu$.
Their main advances are
(1) High $\mu$ than reported in soft materials
(2) Allowing control of $\mu$ by controlling the fiber layout etc
(3) Achieving high $\mu$ in combination with low adhesion, which was not the case in softer materials. This is the kind of property combination you'd need for automobile tyre.
Coming to the Gecko paper, it has far more to do with adhesion that friction. The Gecko paper and the Berkeley friction paper have little to do with each other. Also, contrary to popular myth, the Gecko mechanism has nothing to do with "suction". See these papers in Nature - it is largely adhesion driven.
Adhesive force of a single gecko foot-hair
K Autumn, YA Liang, ST Hsieh, W Zesch, WP Chan… - Nature, 2000
Micro-fabricated adhesive mimicking gecko foot-hair
AK Geim, SV Dubonos, IV Grigorieva… - Nature materials, 2003
For physicists interested in these areas - I understand that tribology and solid mechanics are not taught in US physics departments - it might help to refer to standard texts on Tribology by Bowden and Tabor, Kendall, Israelachvili, Persson, Maugis etc.
Or better still, talk to your colleagues who work in tribology (they're usually to be found in mechanical engineering, materials science and chemistry). They will be eager and willing to help, if only for the opportunity to brag at faculty meetings that a physicist asked them for advice :-)
I've been doing experiments related to this back in 1994, so it's going to take a bit of recall.
The idea of a flute is that you create standing waves, which have a frequency that depends on the (variable) geometry. The reason they're standing waves is because you fix specific boundary conditions. In particular, p=0 at an open end.
Now, consider that you have a standing wave in a flute, with an wavelength that is a fraction of your flute length. That means that you have several nodes in the middle. If you would open a key at a node, there would be no effect. If you'd open one near a node, the pitch would change slightly.
Best Answer
Slip and stick
The friction between your shoes and the floor is quite non-linear. As you put your foot down, your shoe comes under elastic strain as your foot moves forward but friction holds the bottom in place. This is the stick phase. As your foot moves forward, the strain becomes too big, and the friction between floor and shoe can't overcome it anymore.
The bottom of the shoe starts to move. The dynamic friction now is lower than the static friction before, which means the acceleration is rather large. However, the strain also dissipates quickly as the shoe flexes back to its original form. This slip phase is therefore also time-limited.
So, when you hear a high-pitched squeak, you're hearing your shoe stick and slip several thousand times per second, moving micrometers at a time.
Water definitely affects the static and dynamic friction, so that explains why it can matter. But note that there's no simple rule about the exact change in friction, and therefore adding water may also prevent squeaky noises in other situations (when it acts as a lubricant)