9,544 research outputs found
Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
We show how to obtain a fast component-by-component construction algorithm
for higher order polynomial lattice rules. Such rules are useful for
multivariate quadrature of high-dimensional smooth functions over the unit cube
as they achieve the near optimal order of convergence. The main problem
addressed in this paper is to find an efficient way of computing the worst-case
error. A general algorithm is presented and explicit expressions for base~2 are
given. To obtain an efficient component-by-component construction algorithm we
exploit the structure of the underlying cyclic group.
We compare our new higher order multivariate quadrature rules to existing
quadrature rules based on higher order digital nets by computing their
worst-case error. These numerical results show that the higher order polynomial
lattice rules improve upon the known constructions of quasi-Monte Carlo rules
based on higher order digital nets
Landscape influence on small-scale water temperature variations in a moorland catchment
Acknowledgements Iain Malcolm and staff at Marine Scotland (Pitlochry) are thanked for the provision of data from the AWS. Finally, the two anonymous reviewers are greatly acknowledged for their constructive comments.Peer reviewedPostprin
Modelling landscape controls on dissolved organic carbon sources and fluxes to streams
Acknowledgments We thank the Natural Environment Research Council NERC (project NE/K000268/1) for funding. Iain Malcolm and staff at Marine Scotland (Pitlochry) are also thanked for the provision of data from the AWS as are the Scottish Environmental Protection Agency and British Atmospheric Data Centre for the provision of meteorological data.Peer reviewedPublisher PD
New ion trap for atomic frequency standard applications
A novel linear ion trap that permits storage of a large number of ions with reduced susceptibility to the second-order Doppler effect caused by the radio frequency (RF) confining fields has been designed and built. This new trap should store about 20 times the number of ions a conventional RF trap stores with no corresponding increase in second-order Doppler shift from the confining field. In addition, the sensitivity of this shift to trapping parameters, i.e., RF voltage, RF frequency, and trap size, is greatly reduced
Atomic frequency standards for ultra-high-frequency stability
The general features of the Hg-199(+) trapped-ion frequency standard are outlined and compared to other atomic frequency standards, especially the hydrogen maser. The points discussed are those which make the trapped Hg-199(+) standard attractive: high line Q, reduced sensitivity to external magnetic fields, and simplicity of state selection, among others
The JPL trapped mercury ion frequency standard
In order to provide frequency standards for the Deep Space Network (DSN) which are more stable than present-day hydrogen masers, a research task was established under the Advanced Systems Program of the TDA to develop a Hg-199(+) trapped ion frequency standard. The first closed-loop operation of this kind is described. Mercury-199 ions are confined in an RF trap and are state-selected through the use of optical pumping with 194 nm UV light from a Hg-202 discharge lamp. Absorption of microwave radiation at the hyperfine frequency (40.5 GHz) is signaled by atomic fluorescence of the UV light. The frequency of a 40.5 GHz oscillator is locked to a 1.6 Hz wide atomic absorption line of the trapped ions. The measured Allan variance of this locked oscillator is currently gamma sub y (pi) = 4.4 x 10 to the minus 12th/square root of pi for 20 is less than pi is less than 320 seconds, which is better stability than the best commercial cesium standards by almost a factor of 2. This initial result was achieved without magnetic shielding and without regulation of ion number
Stream water age distributions controlled by storage dynamics and nonlinear hydrologic connectivity : Modeling with high-resolution isotope data
Peer reviewedPublisher PD
Operational parameters for the superconducting cavity maser
Tests of the superconducting cavity maser (SCM) ultra-stable frequency source have been made for the first time using a hydrogen maser for a frequency reference. In addition to characterizing the frequency stability, the sensitivity of the output frequency to several crucial parameters was determined for various operating conditions. Based on this determination, the refrigeration and thermal control systems of the SCM were modified. Subsequent tests showed substantially improved performance, especially at the longest averaging times
Successive Coordinate Search and Component-by-Component Construction of Rank-1 Lattice Rules
The (fast) component-by-component (CBC) algorithm is an efficient tool for
the construction of generating vectors for quasi-Monte Carlo rank-1 lattice
rules in weighted reproducing kernel Hilbert spaces. We consider product
weights, which assigns a weight to each dimension. These weights encode the
effect a certain variable (or a group of variables by the product of the
individual weights) has. Smaller weights indicate less importance. Kuo (2003)
proved that the CBC algorithm achieves the optimal rate of convergence in the
respective function spaces, but this does not imply the algorithm will find the
generating vector with the smallest worst-case error. In fact it does not. We
investigate a generalization of the component-by-component construction that
allows for a general successive coordinate search (SCS), based on an initial
generating vector, and with the aim of getting closer to the smallest
worst-case error. The proposed method admits the same type of worst-case error
bounds as the CBC algorithm, independent of the choice of the initial vector.
Under the same summability conditions on the weights as in [Kuo,2003] the error
bound of the algorithm can be made independent of the dimension and we
achieve the same optimal order of convergence for the function spaces from
[Kuo,2003]. Moreover, a fast version of our method, based on the fast CBC
algorithm by Nuyens and Cools, is available, reducing the computational cost of
the algorithm to operations, where denotes the number
of function evaluations. Numerical experiments seeded by a Korobov-type
generating vector show that the new SCS algorithm will find better choices than
the CBC algorithm and the effect is better when the weights decay slower.Comment: 13 pages, 1 figure, MCQMC2016 conference (Stanford
Using geophysical surveys to test tracer-based storage estimates in headwater catchments
Acknowledgements The authors are grateful to Stian Bradford, Chris Gabrielli, and Julie Timms for practical and logistical assistance. The provision of transport by Iain Malcolm and Ross Glover of Marine Scotland Science was greatly appreciated. We also thank the European Research Council ERC (project GA 335910 VEWA) for funding through the VeWa project and the Leverhulme Trust for funding through PLATO (RPG-2014-016).Peer reviewedPostprin
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