Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Special feature
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- recent Special feature articles1471-2946Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[Uncertainty quantification and optimal decisions]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2200/20170115?rss=1
A mathematical model can be analysed to construct policies for action that are close to optimal for the model. If the model is accurate, such policies will be close to optimal when implemented in the real world. In this paper, the different aspects of an ideal workflow are reviewed: modelling, forecasting, evaluating forecasts, data assimilation and constructing control policies for decision-making. The example of the oil industry is used to motivate the discussion, and other examples, such as weather forecasting and precision agriculture, are used to argue that the same mathematical ideas apply in different contexts. Particular emphasis is placed on (i) uncertainty quantification in forecasting and (ii) how decisions are optimized and made robust to uncertainty in models and judgements. This necessitates full use of the relevant data and by balancing costs and benefits into the long term may suggest policies quite different from those relevant to the short term.
]]>2017-04-26T00:05:45-07:00info:doi/10.1098/rspa.2017.0115hwp:master-id:royprsa;rspa.2017.01152017-04-26Special feature47322002017011520170115<![CDATA[Multifunctional scanning ion conductance microscopy]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2200/20160889?rss=1
Scanning ion conductance microscopy (SICM) is a nanopipette-based technique that has traditionally been used to image topography or to deliver species to an interface, particularly in a biological setting. This article highlights the recent blossoming of SICM into a technique with a much greater diversity of applications and capability that can be used either standalone, with advanced control (potential–time) functions, or in tandem with other methods. SICM can be used to elucidate functional information about interfaces, such as surface charge density or electrochemical activity (ion fluxes). Using a multi-barrel probe format, SICM-related techniques can be employed to deposit nanoscale three-dimensional structures and further functionality is realized when SICM is combined with scanning electrochemical microscopy (SECM), with simultaneous measurements from a single probe opening up considerable prospects for multifunctional imaging. SICM studies are greatly enhanced by finite-element method modelling for quantitative treatment of issues such as resolution, surface charge and (tip) geometry effects. SICM is particularly applicable to the study of living systems, notably single cells, although applications extend to materials characterization and to new methods of printing and nanofabrication. A more thorough understanding of the electrochemical principles and properties of SICM provides a foundation for significant applications of SICM in electrochemistry and interfacial science.
]]>2017-04-12T01:01:34-07:00info:doi/10.1098/rspa.2016.0889hwp:master-id:royprsa;rspa.2016.08892017-04-12Special feature47322002016088920160889<![CDATA[The cross-over to magnetostrophic convection in planetary dynamo systems]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160731?rss=1
Global scale magnetostrophic balance, in which Lorentz and Coriolis forces comprise the leading-order force balance, has long been thought to describe the natural state of planetary dynamo systems. This argument arises from consideration of the linear theory of rotating magnetoconvection. Here we test this long-held tenet by directly comparing linear predictions against dynamo modelling results. This comparison shows that dynamo modelling results are not typically in the global magnetostrophic state predicted by linear theory. Then, in order to estimate at what scale (if any) magnetostrophic balance will arise in nonlinear dynamo systems, we carry out a simple scaling analysis of the Elsasser number , yielding an improved estimate of the ratio of Lorentz and Coriolis forces. From this, we deduce that there is a magnetostrophic cross-over length scale, LX(o2/Rmo)D, where _{o} is the linear (or traditional) Elsasser number, Rm_{o} is the system scale magnetic Reynolds number and D is the length scale of the system. On scales well above LX, magnetostrophic convection dynamics should not be possible. Only on scales smaller than LX should it be possible for the convective behaviours to follow the predictions for the magnetostrophic branch of convection. Because LX is significantly smaller than the system scale in most dynamo models, their large-scale flows should be quasi-geostrophic, as is confirmed in many dynamo simulations. Estimating _{o}~=1 and Rm_{o}~=10^{3} in Earth’s core, the cross-over scale is approximately 1/1000 that of the system scale, suggesting that magnetostrophic convection dynamics exists in the core only on small scales below those that can be characterized by geomagnetic observations.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0731hwp:master-id:royprsa;rspa.2016.07312017-03-15Special feature47321992016073120160731<![CDATA[Introduction for perspectives in geophysical and astrophysical fluids]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20170078?rss=1
2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2017.0078hwp:master-id:royprsa;rspa.2017.00782017-03-15Special feature47321992017007820170078<![CDATA[Resistive-pulse and rectification sensing with glass and carbon nanopipettes]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160931?rss=1
Along with more prevalent solid-state nanopores, glass or quartz nanopipettes have found applications in resistive-pulse and rectification sensing. Their advantages include the ease of fabrication, small physical size and needle-like geometry, rendering them useful for local measurements in small spaces and delivery of nanoparticles/biomolecules. Carbon nanopipettes fabricated by depositing a thin carbon layer on the inner wall of a quartz pipette provide additional means for detecting electroactive species and fine-tuning the current rectification properties. In this paper, we discuss the fundamentals of resistive-pulse sensing with nanopipettes and our recent studies of current rectification in carbon pipettes.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0931hwp:master-id:royprsa;rspa.2016.09312017-03-08Special feature47321992016093120160931<![CDATA['Full fusion is not ineluctable during vesicular exocytosis of neurotransmitters by endocrine cells]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160684?rss=1
Vesicular exocytosis is an essential and ubiquitous process in neurons and endocrine cells by which neurotransmitters are released in synaptic clefts or extracellular fluids. It involves the fusion of a vesicle loaded with chemical messengers with the cell membrane through a nanometric fusion pore. In endocrine cells, unless it closes after some flickering (‘Kiss-and-Run’ events), this initial pore is supposed to expand exponentially, leading to a full integration of the vesicle membrane into the cell membrane—a stage called ‘full fusion’. We report here a compact analytical formulation that allows precise measurements of the fusion pore expansion extent and rate to be extracted from individual amperometric spike time courses. These data definitively establish that, during release of catecholamines, fusion pores enlarge at most to approximately one-fifth of the radius of their parent vesicle, hence ruling out the ineluctability of ‘full fusion’.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0684hwp:master-id:royprsa;rspa.2016.06842017-01-11Special feature47321972016068420160684