Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Pharmacological enhancement of naltrexone treatment for opioid dependence: a review.

PURPOSE: Opioid dependence (OD) is a serious and growing clinical condition with increasing social costs that requires expanding treatment beyond opioid agonist substitution. The opioid antagonist naltrexone has displayed a remarkable association of theoretical effectiveness and poor clinical utility in treating OD due to noncompliant behavior and low acceptability among patients, only partly modified by psychosocial interventions. We reviewed pharmacological studies, including naltrexone depot formulations and combination treatments. METHOD: We searched PubMed for clinical studies on the use of naltrexone implants and slow-release injections in OD, and investigations using adjunct medications to improve naltrexone maintenance therapy of OD. We discussed the results in view of their application to the clinical practice. RESULTS: Significant reduction in opioid use and improved retention in treatment have been found in several studies using depot naltrexone formulations, some of which are controlled clinical trials. Pilot investigations have gathered initial positive results on the use of naltrexone in combination with serotonin reuptake inhibitors, α-2 adrenergic, opioid, and γ-aminobutyric acid agonist medications. CONCLUSION: Current evidence suggests that more research on effectiveness and safety is needed in support of depot naltrexone treatment for OD. Further research comparing slow-release with oral naltrexone and opioid agonist medications will help characterize the role of opioid antagonist-mediated treatment of OD. Preliminary investigations on naltrexone combination treatments suggest the opportunity to continue study of new mixed receptor activities for the treatment of OD and other drug addictions.

Dimensional dependence of the Stokes-Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension du = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.