Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes.

International audienceThis paper deals with the development and the analysis of asymptotic stable and consistent schemes in the joint quasi-neutral and fluid limits of the collisional Vlasov Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments

The Theory of Natural Resource Scarcity Indicators: Towards a Synthesis

I review the literature on natural resource scarcity indicators further developing my previous work on this issue (Cleveland and Stern, 1993). Scarcity indicators can be classified by what is being measured eg. in situ value, commodity value etc. and by the mode of valuation considered: exchange value and use value. Prices and rents are common measures of exchange value or indicators of "exchange scarcity" and unit costs can be seen as use value indicators or indicators of "use scarcity". "Use scarcity" supersedes the term "productive scarcity" used in our previous paper. One of the major aims of this paper is to demonstrate the links between productivity indicators like unit costs and the classical concept of use value. The two classes of indicator relate to the Hotelling or Ricardian scarcity models, Commons' discussions of scarcity and efficiency, and a non-marginal vs. a marginal approach to value and scarcity. Inverse MFP is a generalized version of unit cost which can be decomposed into the basic determinants of use scarcity. I review the critiques from Norgaard, Darwin, and Farzin which argue that none of these indicators captures all the dimensions of social scarcity. I continue to show that unit cost or inverse MFP is a more general use scarcity indicator than indicators derived using energy analysis. However, energy analysis has a role in examining limits to technical change in mitigating resource scarcity. Finally I suggest that the way forward will be in the empirical study of models of resource supply and demand and the building of scenarios regarding possible future trends in resource scarcity rather than in a search for a perfect indicator

A systematic review of the role of bisphosphonates in metastatic disease

Objectives: To identify evidence for the role of bisphosphonates in malignancy for the treatment of hypercalcaemia, prevention of skeletal morbidity and use in the adjuvant setting. To perform an economic review of current literature and model the cost effectiveness of bisphosphonates in the treatment of hypercalcaemia and prevention of skeletal morbidity Data sources: Electronic databases (1966-June 2001). Cochrane register. Pharmaceutical companies. Experts in the field. Handsearching of abstracts and leading oncology journals (1999-2001). Review methods: Two independent reviewers assessed studies for inclusion, according to predetermined criteria, and extracted relevant data. Overall event rates were pooled in a meta-analysis, odds ratios ( OR) were given with 95% confidence intervals (CI). Where data could not be combined, studies were reported individually and proportions compared using chi- squared analysis. Cost and cost-effectiveness were assessed by a decision analytic model comparing different bisphosphonate regimens for the treatment of hypercalcaemia; Markov models were employed to evaluate the use of bisphosphonates to prevent skeletal-related events (SRE) in patients with breast cancer and multiple myeloma. Results: For acute hypercalcaemia of malignancy, bisphosphonates normalised serum calcium in >70% of patients within 2-6 days. Pamidronate was more effective than control, etidronate, mithramycin and low-dose clodronate, but equal to high dose clodronate, in achieving normocalcaemia. Pamidronate prolongs ( doubles) the median time to relapse compared with clodronate or etidronate. For prevention of skeletal morbidity, bisphosphonates compared with placebo, significantly reduced the OR for fractures (OR [95% CI], vertebral, 0.69 [0.57-0.84], non-vertebral, 0.65 [0.54-0.79], combined, 0.65 [0.55-0.78]) radiotherapy 0.67 [0.57-0.79] and hypercalcaemia 0.54 [0.36-0.81] but not orthopaedic surgery 0.70 [0.46-1.05] or spinal cord compression 0.71 [0.47-1.08]. However, reduction in orthopaedic surgery was significant in studies that lasted over a year 0.59 [0.39-0.88]. Bisphosphonates significantly increased the time to first SRE but did not affect survival. Subanalyses were performed for disease groups, drugs and route of administration. Most evidence supports the use of intravenous aminobisphosphonates. For adjuvant use of bisphosphonates, Clodronate, given to patients with primary operable breast cancer and no metastatic disease, significantly reduced the number of patients developing bone metastases. This benefit was not maintained once regular administration had been discontinued. Two trials reported significant survival advantages in the treated groups. Bisphosphonates reduce the number of bone metastases in patients with both early and advanced breast cancer. Bisphosphonates are well tolerated with a low incidence of side-effects. Economic modelling showed that for acute hypercalcaemia, drugs with the longest cumulative duration of normocalcaemia were most cost-effective. Zoledronate 4 mg was the most costly, but most cost-effective treatment. For skeletal morbidity, Markov models estimated that the overall cost of bisphosphonate therapy to prevent an SRE was pound250 and pound1500 per event for patients with breast cancer and multiple myeloma, respectively. Bisphosphonate treatment is sometimes cost-saving in breast cancer patients where fractures are prevented. Conclusions: High dose aminobisphosphonates are most effective for the treatment of acute hypercalcaemia and delay time to relapse. Bisphosphonates significantly reduce SREs and delay the time to first SRE in patients with bony metastatic disease but do not affect survival. Benefit is demonstrated after administration for at least 6-12 months. The greatest body of evidence supports the use of intravenous aminobisphosphonates. Further evidence is required to support use in the adjuvant setting

Robust quantum parameter estimation: coherent magnetometry with feedback

We describe the formalism for optimally estimating and controlling both the state of a spin ensemble and a scalar magnetic field with information obtained from a continuous quantum limited measurement of the spin precession due to the field. The full quantum parameter estimation model is reduced to a simplified equivalent representation to which classical estimation and control theory is applied. We consider both the tracking of static and fluctuating fields in the transient and steady state regimes. By using feedback control, the field estimation can be made robust to uncertainty about the total spin number