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

Context Differences Reveal Insulator and Activator Functions of a Su(Hw) Binding Region

Insulators are DNA elements that divide chromosomes into independent transcriptional domains. The Drosophila genome contains hundreds of binding sites for the Suppressor of Hairy-wing [Su(Hw)] insulator protein, corresponding to locations of the retroviral gypsy insulator and non-gypsy binding regions (BRs). The first non-gypsy BR identified, 1A-2, resides in cytological region 1A. Using a quantitative transgene system, we show that 1A-2 is a composite insulator containing enhancer blocking and facilitator elements. We discovered that 1A-2 separates the yellow (y) gene from a previously unannotated, non-coding RNA gene, named yar for y-achaete (ac) intergenic RNA. The role of 1A-2 was elucidated using homologous recombination to excise these sequences from the natural location, representing the first deletion of any Su(Hw) BR in the genome. Loss of 1A-2 reduced yar RNA accumulation, without affecting mRNA levels from the neighboring y and ac genes. These data indicate that within the 1A region, 1A-2 acts an activator of yar transcription. Taken together, these studies reveal that the properties of 1A-2 are context-dependent, as this element has both insulator and enhancer activities. These findings imply that the function of non-gypsy Su(Hw) BRs depends on the genomic environment, predicting that Su(Hw) BRs represent a diverse collection of genomic regulatory elements

Evaluation of Site Amplification for the Seismic Protection of a Strategic District in Naples

Since the 1980s, a Business District is located in the eastern area of Naples. The first pioneer studies carried out in this area showed that a significant variability of site amplification can be predicted due to the morphology of seismic bedrock and to the presence of vanishing lenses of peat. More recently, the seismic vulnerability of the New Law Court was assessed adopting the hypothesis of 1D conditions for the seismic response analysis. This paper aims at verifying the reliability of this assumption, evaluating the 2D seismic site response of a representative geological section. Geotechnical characterization of the soil deposits has been carried out by integrating the available experimental data with literature data. Two suites of accelerograms have been considered as input motions, representative of ‘near field’ and ‘far field’ seismic events. Equivalent linear and non-linear 2D analyses have been carried out through a finite element and a finite difference code, respectively. Results provide insights on the non-linear soil behaviour of peat and allow for recognizing the limits and advantages of both adopted approaches. Finally, the comparison between the results of 2D and 1D analyses allows for highlighting the effects of focalization of seismic waves on the amplification of the ground motion at the surface