The formula derived by Nobuyasu Sato (1980 J. Phys. D: Appl. Phys. 13 L3-L6), for the current flowing in an external circuit due to the motion of charged particles in a gap is extended to include a time-dependent applied voltage. The effects of negative ions, and electron, positive ion and negative ion diffusion are also included. It is found that Sato's original equation still describes the contribution of charged particle motion to the external circuit current. The total circuit current is determined by adding the displacement current that effectively flows across the gap to the current determined by Sato's equation. Some comments are also made about the interpretation of Sato's equation in three dimensions.

A formula for discharge current flowing in a space charge filled gap is derived for a general geometry of electrodes from the energy balance equation in which the displacement current caused by the motion of the charged particles in the gap is taken into account. It is found that in the formula obtained the influence of the field component produced by the space charge does not appear explicitly and the formula is compatible with the principle of superposition.

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In polyandrous mating systems, sperm competition and cryptic female choice (CFC) are well recognized as postcopulatory evolutionary forces. However, it remains challenging to separate CFC from sperm competition and to estimate how much CFC influences insemination success because those processes usually occur inside the female's body. The Japanese pygmy squid, Idiosepius paradoxus, is an ideal species in which to separate CFC from sperm competition because sperm transfer by the male and sperm displacement by the female can be observed directly at an external location on the female's body. Here, we counted the number of spermatangia transferred to, removed from, and remaining on the female body during single copulation episodes. We measured behavioral and morphological characteristics of the male, such as duration of copulation and body size. Although males with larger body size and longer copulation time were capable of transferring larger amounts of sperm, females preferentially eliminated sperm from males with larger body size and shorter copulation time by spermatangia removal; thus, CFC could attenuate sperm precedence by larger males, whereas it reinforces sperm precedence by males with longer copulation time. Genetic paternity analysis revealed that fertilisation success for each male was correlated with remaining sperm volume that is adjusted by females after copulation.