Separate conductors for separate frequency ranges in cables

Electrical current flows through your speaker wires.  More current flows thorough wires with less resistance (i.e., wires with larger cross-sectional area....or smaller gauge).  Therefore, the larger wires will carry a proportionally larger amount of current.  However, in the absence of a cross-over, and ignoring any hysteria about skin-effect, I cannot think of any reason why the different wires in the cable you describe would be carrying different frequencies if they are all connected at the same place at both ends.  The frequencies certainly would not be isolated to different wires as is somewhat implied by the marketing blurb.

As to your question about

"what PS Audio is trying to accomplish with this cable construction"

my thought would be that they decided to try something they could advertise as being somewhat revolutionary and cutting-edge in order to create interest and sell more cables.

Many (including AQ) claim that skin effect is audible in audio. Perhaps because of that they use hollow conductor for the tweeter, In my opinion it would be sufficient to use wire gauge 18 (100% skin depth at 20kHz in copper), but there might be something else (inductance of the wire?). Why they use square conductors for the midrange I have no idea. As for the separation of the cables - the main purpose in my opinion, is to lower interaction of back EMF produced by different speakers at different frequencies. With separate wires there would be divider consisting of the wire inductance and amplifier’s output impedance. Only portion of this back EMF will go back to the other speaker. There is, of course, Xover but it isn’t perfect. It was observed that some speakers sound better bi-wired while others don’t. It might be related to Xover design.

Getting back to skin effect - common way of eliminating it is to use multiple strands, but as long as they are in magnetic field of each other there will be skin effect. Wires placed on hollow tube or arranged as flat "tape" are mostly in magnetic field of neighboring strands.

I’m not sure what is audible and what is gimmick. In my opinion it would be sufficient to use gauge 20 for the tweeter and 16 for the rest. On the other hand I had cable like that (AQ Indigo) and when I switched to Acoustic Zen Satori Shotgun (insulated strands on large hollow tube) sound changed dramatically - imaging improved, highs became "silky" while lower midrange became more pronounced. Cello started sounding more resonant, male voices got "chestiness" etc. while the bass got even better control. Overall gauge of this cable is 6. I’m not sure why they need it. I can only suspect that they try to reduce inductance.
They also use zero crystal copper (cooled in hot forms to avoid crystal formation), but many people claim that plain oxygen free copper is OK (thousands of crystals).

Like you, I’m trying to understand, but am getting more and more convinced that there has to be an element of magic in the audio. How otherwise explain stronger lower midrange of the cable in terms of RLC?

Using different conductors in one jacket for speaker cable has been done for many years by numerous manufacturers, however the OP is talking about an ad for POWER CABLES, not speaker cables. I'm having a very difficult time understanding how different conductors in a POWER CABLE affect specific frequencies. The power cable feeds the power supply of a component, then the AC is converted to DC. I would love to hear a reasonable explanation of why a power cable needs different conductors.

I appreciate everyone's input. @tls49 yes, perhaps I should have emphasized the point that this PS Audio product description is for a power cable, which generates additional bewilderment. 

it is BS

people who claim that skin effect is audible in interconnect or speaker cables do not understand electronics; that confusion is worse for AC cables

but why go thru all those equations using actual numbers when you can do a double-blind listening test?