The roles of interaural time difference (ITD) and interaural level difference (ILD) were studied in free-field source localization experiments for sine tones of low frequency (250-750 Hz). Experiments combined real-source trials with virtual trials created through transaural synthesis based on real-time ear canal measurements. Experiments showed the following: (1) The naturally occurring ILD is physically large enough to exert an influence on sound localization well below 1000 Hz. (2) An ILD having the same sign as the ITD modestly enhances the perceived azimuth of tones for all values of the ITD, and it eliminates left-right confusions that otherwise occur when the interaural phase difference (IPD) passes 180°. (3) Increasing the ILD to large, implausible values can decrease the perceived laterality while also increasing front-back confusions. (4) Tone localization is more directly related to the ITD than to the IPD. (5) An ILD having a sign opposite to the ITD promotes a slipped-cycle ITD, sometimes with dramatic effects on localization. Because the role of the ITD itself is altered by the ILD, the duplex processing of ITD and ILD reflects more than mere trading; the effect of the ITD can be reversed in sign.

Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long-standing problem until recently. It was shown that if consistent spatial basis functions are used, one can indeed create a methodology that was charge conserving, albeit using a leapfrog time stepping method. While this is a significant advance, leapfrog schemes are only conditionally stable and time step sizes are closely tied to the underlying mesh. Ideally, to take full advantage of advances in finite element methods (FEMs), one needs a charge conserving PIC methodology that is agnostic to the time stepping method. This is the principal contribution of this paper. In what follows, we shall develop this methodology, prove that both charge and Gauss' laws are discretely satisfied at every time step, provide the necessary details to implement this methodology for both the wave equation FEM and Maxwell solver FEM, and finally demonstrate its efficacy on a suite of test problems. The method will be demonstrated by single particle evolution, non-neutral beams with space-charge, and adiabatic expansion of a neutral plasma, where the Debye length has been resolved, and real mass ratios are used.

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