We consider a system of N particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the positive reals and 3) only the N right-most particles are retained, the others being removed from the system. This system has been introduced in the physics liter...

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83–125]. We revisit the Oster–Murray–Harris model and find that, due to the infinitesimal dis...

BACKGROUND Despite being an effective analgesic for children with fractures, some clinicians may avoid prescribing ibuprofen due to its potentially harmful effect on bone healing. OBJECTIVE To determine if exposure to ibuprofen is associated with an increased risk of bone healing complications in children with fractures. METHODS We performed a retrospective study of children aged 6 months t...

The aim of the present study was to estimate the wall effect of the self-made spherical graphite-walled cavity chamber with the Monte Carlo method for establishing the air-kerma primary standard of high-dose-rate (HDR) ¹⁹²Ir brachytherapy sources at the Institute of Nuclear Energy Research (INER, Taiwan). The Monte Carlo method established in this paper was also employed to respectively simulat...

ρ mass density in the present configuration ρ0 mass density in the reference configuration J determinant of the deformation gradient Fiα components of deformation gradient xi coordinates of a point in the present configuration Xα coordinates of a point in the reference configuration Tiα components of the first Piola Kirchhoff stress tensor vi components of velocity bi components of body force p...