Darboux dressing and undressing for the ultradiscrete KdV equation

We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show how to reconstruct the potential in the scattering problem at any time, using an ultradiscrete analogue of a Darboux transformation. This is achieved by obtaining data uniquely characterising the soliton content and the `background' from the initial potential by Darboux transformation.Comment: 41 pages, 5 figures // Full, unabridged version, including two appendice

Multi-modal information processing for visual workload relief

The simultaneous performance of two single-dimensional compensatory tracking tasks, one with the left hand and one with the right hand, is discussed. The tracking performed with the left hand was considered the primary task and was performed with a visual display or a quickened kinesthetic-tactual (KT) display. The right-handed tracking was considered the secondary task and was carried out only with a visual display. Although the two primary task displays had afforded equivalent performance in a critical tracking task performed alone, in the dual-task situation the quickened KT primary display resulted in superior secondary visual task performance. Comparisons of various combinations of primary and secondary visual displays in integrated or separated formats indicate that the superiority of the quickened KT display is not simply due to the elimination of visual scanning. Additional testing indicated that quickening per se also is not the immediate cause of the observed KT superiority

Performance evaluation of a kinesthetic-tactual display

Simulator studies demonstrated the feasibility of using kinesthetic-tactual (KT) displays for providing collective and cyclic command information, and suggested that KT displays may increase pilot workload capability. A dual-axis laboratory tracking task suggested that beyond reduction in visual scanning, there may be additional sensory or cognitive benefits to the use of multiple sensory modalities. Single-axis laboratory tracking tasks revealed performance with a quickened KT display to be equivalent to performance with a quickened visual display for a low frequency sum-of-sinewaves input. In contrast, an unquickened KT display was inferior to an unquickened visual display. Full scale simulator studies and/or inflight testing are recommended to determine the generality of these results

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard

Evaluation of kinesthetic-tactual displays using a critical tracking task

The study sought to investigate the feasibility of applying the critical tracking task paradigm to the evaluation of kinesthetic-tactual displays. Four subjects attempted to control a first-order unstable system with a continuously decreasing time constant by using either visual or tactual unidimensional displays. Display aiding was introduced in both modalities in the form of velocity quickening. Visual tracking performance was better than tactual tracking, and velocity aiding improved the critical tracking scores for visual and tactual tracking about equally. The results suggest that the critical task methodology holds considerable promise for evaluating kinesthetic-tactual displays

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Logarithmic behavior of degradation dynamics in metal--oxide semiconductor devices

In this paper the authors describe a theoretical simple statistical modelling of relaxation process in metal-oxide semiconductor devices that governs its degradation. Basically, starting from an initial state where a given number of traps are occupied, the dynamics of the relaxation process is measured calculating the density of occupied traps and its fluctuations (second moment) as function of time. Our theoretical results show a universal logarithmic law for the density of occupied traps $\bar{} \sim \phi (T,E_{F}) (A+B \ln t)$, i.e., the degradation is logarithmic and its amplitude depends on the temperature and Fermi Level of device. Our approach reduces the work to the averages determined by simple binomial sums that are corroborated by our Monte Carlo simulations and by experimental results from literature, which bear in mind enlightening elucidations about the physics of degradation of semiconductor devices of our modern life