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We present a multisite formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with intercluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multisite formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott-insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose-glass-to-superfluid transition, one an approximation based on the behavior of the condensate fraction, and one that relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non-self-averaging is discussed.

This paper presents the first plasmid DNA irradiations carried out with Very High Energy Electrons (VHEE) over 100–200 MeV at the CLEAR user facility at CERN to determine the Relative Biological Effectiveness (RBE) of VHEE. DNA damage yields were measured in dry and aqueous environments to determine that ~ 99% of total DNA breaks were caused by indirect effects, consistent with other published measurements for protons and photons. Double-Strand Break (DSB) yield was used as the biological endpoint for RBE calculation, with values found to be consistent with established radiotherapy modalities. Similarities in physical damage between VHEE and conventional modalities gives confidence that biological effects of VHEE will also be similar—key for clinical implementation. Damage yields were used as a baseline for track structure simulations of VHEE plasmid irradiation using GEANT4-DNA. Current models for DSB yield have shown reasonable agreement with experimental values. The growing interest in FLASH radiotherapy motivated a study into DSB yield variation with dose rate following VHEE irradiation. No significant variations were observed between conventional and FLASH dose rate irradiations, indicating that no FLASH effect is seen under these conditions.