Negative resistance
From Academic Kids

In electrical circuits, static resistance is the ratio of the voltage across a circuit element to the current through it. However, the ratio of the voltage to the current may vary with either voltage or current. The ratio of the change in voltage to the change in current is known as dynamic resistance.
Circuit elements composed of certain materials exhibit the property that, over certain voltage ranges, current is a decreasing function of the voltage. This range of voltages is known as a negative resistance region.
It may be more correct to say that a circuit element has a negative differential resistance region than to say that it exhibits negative resistance because even in this region the static resistance of the circuit element is positive, while it is more precisely the slope of the resistance curve which is negative.
An example of an electronic component exhibiting the negative differential resistance region is the tunnel diode. Such a device, when biased into its negative differential resistance region, will act as an amplifier.
In conformance with the known law of conservation of energy, a plot of the negative differential resistance region of a component cannot normally pass through the origin.
Some work by Professor Deborah Chung at the University of Buffalo has discovered a composite configuration of carbon nanotubes which appears to exhibit anomalous results which resemble a static negative resistor. However, the physical interpretation of this observation is still controversial.
Gabriel Kron, while a scientist for General Electric,[1] (http://www.quantumchemistryhistory.com/Kron_Dat/KronGabriel1.htm) is thought to have built a negative resistor for the US Navy's "Network Analyser" (probably an analogue computer) in the 1930s; but as it was a military project no details have ever come to the public.[2] (http://www.cheniere.org/misc/kron.htm) One of his papers does contain a blasé "Although negative resistances are available for use with a network analyzer..."[3] (http://www.quantumchemistryhistory.com/Kron_Dat/Kron1945/KronPR1945/KronPR1945.htm)
Another concept of negative resistance exists in the domain of radio frequency antenna design. This is also known as negative impedance. It is not uncommon for an antenna containing multiple driven elements to exhibit apparent negative impedance in one or more of the driven elements.
There are many mechanical systems that exhibit ranges of negative differential resistance. In fact, this is a common design element in systems that are designed to have "detents" or a "positive action" or a "click." A good example is an ordinary toggle switch (or a key on a computer keyboard), which, as the handle is moved from "off" to "on", initially presents a firm and increasing downward force. As the center point is passed, a zone is entered in which the downward force decreases, which feels like a "sudden" yielding. This is often referred to as a "collapse action" mechanism. A general characteristic of negative resistance systems it is possible to traverse the negative resistance region if driven "firmly," but act as bistable switching devices if driven "loosely." The turn signal lever in most cars acts this way, allowing one to signal a lane change and then release the lever.
Negative resistance circuits
Many circuit topologies are capable of producing negative resistance. The simplest case requires an amplifier with voltage gain greater than one. If a resistor R is connected from input to output, the input current, <math>i_i<math>, for a given input voltage <math>v_i<math> is:
<math>i_i = \frac{v_i  v_o}{R}<math>
Where <math>v_o<math> is the output voltage. This assumes an ideal amplifier with infinite input impedance and zero output impedance. If the voltage gain, <math>A_v<math>, of the amplifier is defined as:
<math>A_v = \frac{v_o}{v_i}<math>
The input resistance, <math>R_i<math> is:
<math>R_i = \frac{v_i}{i_i} = \frac{R}{1A_v}<math>
The input resistance is negative for values of <math>A_v > 1<math>.
In the case of a nonideal amplifier, negative resistance is still possible as long as the amplifier input impedance is sufficiently high. The net resistance is reduced to:
<math>R_i = \frac{1}{\frac{1}{Z_{i}} + \frac{1A_v}{R + Z_{o}}}<math>
Where <math>Z_i<math> is the amplifier input impedance and <math>Z_o<math> is the amplifier output impedance.
References
 Shoukai Wang and D.D.L. Chung, "Apparent negative electrical resistance in carbon fiber composites," Composites, Part B, Vol. 30, 1999, p. 579590.
 Peter D. Hooper, G. McHale, and M. I. Newton, "Negative differential resistance in MIM devices from vacuum to atmospheric pressure", Proc. SPIE Int. Soc. Opt. Eng., 2780, 38 (1996)da:Negativ differentiel modstand
de:Elektrischer_Widerstand#Negativer_differentieller_Widerstand nl:negatieve weerstand