We study the effect of algebraically localized impurities on striped phases in one spatial dimension. We therefore develop a functional-analytic framework that allows us to cast the perturbation problem as a regular Fredholm problem despite the presence of the essential spectrum, caused by the soft translational mode. Our results establish the selection of jumps in wavenumber and phase, depending on the location of the impurity and the average wavenumber in the system. We also show that, for select locations, the jump in the wavenumber vanishes.

We study how mucosal dose in the oral or nasal cavity depends on the irradiated small segmental photon fields varying with beam energy, beam angle and mucosa thickness. Dose ratio (mucosal dose with bone underneath to dose at the same point without bone) reflecting the dose enhancement due to the bone backscatter was determined by Monte Carlo simulation (EGSnrc-based code), validated by measurements. Phase space files based on the 6 and 18 MV photon beams with small field size of 1 × 1 cm2, produced by a Varian 21 EX linear accelerator, were generated using the BEAMnrc Monte Carlo code. Mucosa phantoms (mucosa thickness = 1, 2 and 3 mm) with and without a bone under the mucosa were irradiated by photon beams with gantry angles varying from 0 to 30°. Doses along the central beam axis in the mucosa and the dose ratio were calculated with different mucosa thicknesses. For the 6 MV photon beams, the dose at the mucosa-bone interface increased by 44.9–41.7%, when the mucosa thickness increased from 1 to 3 mm for the beam angle ranging from 0 to 30°. These values were lower than those (58.8–53.6%) for the 18 MV photon beams with the same beam angle range. For both the 6 and 18 MV photon beams, depth doses in the mucosa were found to increase with an increase of the beam angle. Moreover, the dose gradient in the mucosa was greater for the 18 MV photon beams compared to the 6 MV. For the dose ratio, it was found that the dose enhancement due to the bone backscatter increased with a decrease of mucosa thickness, and was more significant at both the air-mucosa and mucosa-bone interface. Mucosal dose with bone was investigated by Monte Carlo simulations with different experimental configurations, and was found vary with the beam energy, beam angle and mucosa thickness for a small segmental photon field. The dosimetric information in this study should be considered when searching for an optimized treatment strategy to minimize the mucosal complications in the head-and-neck intensity-modulated radiation therapy.