so minimally that far... this was pretty good from wiki:

Shock waves form when the speed of a fluid changes by more than the speed of sound.[3] At the region where this occurs sound waves travelling against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region, and a high pressure shock wave rapidly forms.

Shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties on the order of a few mean free paths (roughly micrometers at atmospheric conditions) in thickness. Shock waves in air are heard as a loud "crack" or "snap" noise. Over longer distances a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom, commonly created by the supersonic flight of aircraft.

Old news. I invented this two years ago with some paper clips, a watch battery, lemon juice and four pointy cups from a water cooler. They'll soon discover the magnetic field "domes" fall prey to quantum nonlinear space-time diffeomorphisms that thwart all attempts at clear readouts of volume resolution.

(All right, I'm lying. I used two paper cups).

Memristors /memˈrɪstɚ/ ("memory resistors") are a class of passive two-terminal circuit elements that maintain a functional relationship between the time integrals of current and voltage. This results in resistance varying according to the device's memristance function. Specifically engineered memristors provide controllable resistance useful for switching current. The memristor is a special case in so-called "memristive systems", a class of mathematical models useful for certain empirically observed phenomena, such as the firing of neurons.[3] The definition of the memristor is based solely on fundamental circuit variables, similar to the resistor, capacitor, and inductor. Unlike those more familiar elements, the necessarily nonlinear memristors may be described by any of a variety of time-varying functions. As a result, memristors do not belong to linear time-invariant (LTI) circuit models. A linear time-invariant memristor is simply a conventional resistor.[4]

Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. This symmetry follows from the description of basic passive circuit elements as defined by a relation between two of the four fundamental circuit variables, namely voltage, current, charge and flux.[5] A device linking charge and flux (themselves defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. He did acknowledge that other scientists had already used fixed nonlinear flux-charge relationships.[6] However, it would not be until thirty-seven years later, on April 30, 2008, that a team at HP Labs led by the scientist R. Stanley Williams would announce the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device.[7][8][9] Being much simpler than currently popular MOSFET switches and also able to implement one bit of non-volatile memory in a single device, memristors integrated with transistors may enable nanoscale computer technology. Chua also speculates that they may be useful in the construction of artificial neural networks.[10]

I am need to look into this guy some more, but people like this often make linear assumptions about nonlinear systems.