Furthermore, the ideal cycle efficiency is 1-T_low/T_high, where T_low would be the exhaust temperature and T_high the combustion temperature for this engine, in deg K.

T_high is limited by chemistry and materials to abt 1400 K, T_low depends on a whole pile of stuff, but in practice cannot be lower than 700 K or so for a simple (as opposed to compound) cycle that this engine uses. So the absolute maximum theoretical efficiency, using perfect insulators, frictionless bearings and ideal gases is about 50%.

Modern car turbo-diesel engines get abt 40% efficiency, stationary diesels reach 50% efficiency. Note these are compound cycles.

tldr: 3.5x efficiency improvement claim is bullshit.

The inefficiency is reduced, and making it 'twice as efficient' would be .7*.7=.49 inefficiency. 3.5 would be about .29, or a 71% efficiency. Though it's cute that you tried to make it come out to more than 100%.

the article claims standard car engine efficiency is 0.15, so 3.5*0.15 = 0.45

They really cheat with that number. They are using engine-to-wheels efficiency, but then talk about the wave-disk in a hybrid presumably with no drive-train losses. A gasoline engine running over a much smaller RPM range will run much more efficient than 15%.

An efficient car may run at about 18% on average (hence the 15% after external losses), but quite possibly have a peak efficiency of 30%

Also, they compare to a gasoline Otto cycle engine. The diesel cycle is more efficient than the Otto cycle. A cars turbocharged diesel may run nearly 30% average efficiency, and peak efficiency in the 40s. (The ratio of peak/average eefficiency in diesel engines tends to be closer to unity than in gasoline engines).

There are actual operating now diesel engines operating at over 50% efficiency, but they are not the sort of thing you would put in your car (more the sort of thing where your car would fit inside the engine).

[edit]I wanted to find info on the prius before posting this, but was unable to. I finally did, and the complexity of the drivetrain is to (among other things) maximize the amount of the time that the engine is in it's peak efficiency area of 230g/kWh which is roughly an efficiency of 33%. Since the article specifically talks about running the engine in a hybrid comparison, this is apples-to-apples, and it is less than a 2x improvement, not 3.5x

[edit2]The Prius is not a vanilla Otto cycle, but it's pretty close. I really think of it as more of a Miller cycle than an Atkinson, but in any event it's a 4-stroke spark-ignited reciprocating piston engine.

Note also that the Prius engine employs the Atkinson cycle rather than the Otto.