Brownian Motion of Radioactive Particles: Derivation and Monte Carlo Test of Spatial and Temporal Distributions

Stochastic processes such as diffusion can be analyzed by means of a partial differential equation of the Fokker-Planck type (FPE), which yields a transition probability density, or by a stochastic differential equation of the Langevin type (LE), which yields the time evolution of a statistical process variable. Provided the stochastic process is continuous and certain boundary conditions are met, the two approaches yield equivalent information. However, Brownian motion of radioactively decaying particles is not a continuous process because the Brownian trajectories abruptly terminate when the particle decays. Recent analysis of the Brownian motion of decaying particles by both approaches has led to different mean-square displacements. In this paper, we demonstrate the complete equivalence of the two approaches by 1) showing quantitatively and operationally how the probability densities and statistical moments predicted by the FPE and LE relate to one another, 2) verifying that both approaches lead to identical statistical moments at all orders, and 3) confirming that the analytical solution to the FPE accurately describes the Brownian trajectories obtained by Monte Carlo simulations based on the LE. The analysis in this paper addresses both the spatial distribution of the particles (i.e. the question of displacement as a function of diffusion time) and the temporal distribution (i.e. the question of first-passage time to fixed absorbing boundaries)

High drug resistance among Gram-negative bacteria in sputum samples from an intensive care unit in Nepal

SETTING: Tribhuvan University Teaching Hospital, Kathmandu, Nepal.OBJECTIVES: 1) To report the number and proportion of Pseudomonas, Acinetobacter, Burkholderia, Stenotrophomonas (PABS) species among intensive care unit (ICU) patients with sputum culture; and 2) to assess antimicrobial resistance patterns, demographic and clinical characteristics associated with resistance to at least one antibiotic and ICU discharge outcomes among those patients with PABS species admitted to hospital between 14 April 2018 and 13 April 2019.DESIGN: This was a hospital-based, cross-sectional study using secondary data.RESULTS: Of 166 who underwent sputum culture, 104 (63%) had bacterial growth, of which, 67 (64%) showed PABS species. Of the positive cultures, Pseudomonas, Acinetobacter, Burkholderia and Stenotrophomonas were present in respectively 32 (30.7%), 31 (29.8%), 1 (1%) and 3 (2.8%). Pseudomonas showed a high level of resistance to levofloxacin (61%), cefepime (50%) and amikacin (50%). Acinetobacter was largely resistant to cefepime (95%), imipenem (92%) and levofloxacin (86%). Of the 67 with PABS infection, 32 (48%) died.CONCLUSION: The study showed a high prevalence of Pseudomonas and Acinetobacter and the emergence of Stenotrophomonas in sputum culture samples of ICU patients. This highlights the need for monitoring PABS and associated resistance patterns to reduce mortality in ICU patients.</jats:p