Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Increased pain intensity is associated with greater verbal communication difficulty and increased production of speech and co-speech gestures

Effective pain communication is essential if adequate treatment and support are to be provided. Pain communication is often multimodal, with sufferers utilising speech, nonverbal behaviours (such as facial expressions), and co-speech gestures (bodily movements, primarily of the hands and arms that accompany speech and can convey semantic information) to communicate their experience. Research suggests that the production of nonverbal pain behaviours is positively associated with pain intensity, but it is not known whether this is also the case for speech and co-speech gestures. The present study explored whether increased pain intensity is associated with greater speech and gesture production during face-to-face communication about acute, experimental pain. Participants (N = 26) were exposed to experimentally elicited pressure pain to the fingernail bed at high and low intensities and took part in video-recorded semi-structured interviews. Despite rating more intense pain as more difficult to communicate (t(25) = 2.21, p = .037), participants produced significantly longer verbal pain descriptions and more co-speech gestures in the high intensity pain condition (Words: t(25) = 3.57, p = .001; Gestures: t(25) = 3.66, p = .001). This suggests that spoken and gestural communication about pain is enhanced when pain is more intense. Thus, in addition to conveying detailed semantic information about pain, speech and co-speech gestures may provide a cue to pain intensity, with implications for the treatment and support received by pain sufferers. Future work should consider whether these findings are applicable within the context of clinical interactions about pain

Unprecedented within-species chromosome number cline in the Wood White butterfly Leptidea sinapis and its significance for karyotype evolution and speciation

Background: Species generally have a fixed number of chromosomes in the cell nuclei while between-species differences are common and often pronounced. These differences could have evolved through multiple speciation events, each involving the fixation of a single chromosomal rearrangement. Alternatively, marked changes in the karyotype may be the consequence of within-species accumulation of multiple chromosomal fissions/fusions, resulting in highly polymorphic systems with the subsequent extinction of intermediate karyomorphs. Although this mechanism of chromosome number evolution is possible in theory, it has not been well documented. Results: We present the discovery of exceptional intraspecific variability in the karyotype of the widespread Eurasian butterfly Leptidea sinapis. We show that within this species the diploid chromosome number gradually decreases from 2n = 106 in Spain to 2n = 56 in eastern Kazakhstan, resulting in a 6000 km-wide cline that originated recently (8,500 to 31,000 years ago). Remarkably, intrapopulational chromosome number polymorphism exists, the chromosome number range overlaps between some populations separated by hundreds of kilometers, and chromosomal heterozygotes are abundant. We demonstrate that this karyotypic variability is intraspecific because in L. sinapis a broad geographical distribution is coupled with a homogenous morphological and genetic structure. Conclusions: The discovered system represents the first clearly documented case of explosive chromosome number evolution through intraspecific and intrapopulation accumulation of multiple chromosomal changes. Leptidea sinapis may be used as a model system for studying speciation by means of chromosomally-based suppressed recombination mechanisms, as well as clinal speciation, a process that is theoretically possible but difficult to document. The discovered cline seems to represent a narrow time-window of the very first steps of species formation linked to multiple chromosomal changes that have occurred explosively. This case offers a rare opportunity to study this process before drift, dispersal, selection, extinction and speciation erase the traces of microevolutionary events and just leave the final picture of a pronounced interspecific chromosomal difference