Depth charges

Depth charges

A defining moment in President Bill Clinton’s presidency came when he argued that his entanglement with an intern hinged on the definition of the word “is.” Likewise, President Barack Obama’s administration is now taking considerable heat for attempting to redefine the word “gone.” That’s the word that Obama aide (and former Clinton official) Carol Browner used when describing what has happened...

Counting charges

Voltage-gated ion channels of excitable tissue have evolved an exquisite sensitivity to membrane potential. The open probability of a typical potassium or sodium channel, for example, may be increased by two orders of magnitude in response to a depolarization of less than 10 mV (Zagotta et al., 1994; Hirschberg et al., 1995). As recognized by Hodgkin and Huxley (1952), this responsiveness to ch...

Mystery of Point Charges

We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in Rn. This question goes back to J. C. Maxwell and M. Morse. Using fewnomial theory we show that for a given number of charges there exists an upper bound independent of the dimension, and show it to be at most 12 for three charges. We conjecture an exact upper bo...

Bound charges and currents

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Two Dimensional Adsorbed Charges