Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Numerical study of a M-cycle cross-flow heat exchanger for indirect evaporative cooling

In this paper, numerical analyses of the thermal performance of an indirect evaporative air cooler incorporating a M-cycle cross-flow heat exchanger has been carried out. The numerical model was established from solving the coupled governing equations for heat and mass transfer between the product and working air, using the finite-element method. The model was developed using the EES (Engineering Equation Solver) environment and validated by published experimental data. Correlation between the cooling (wet-bulb) effectiveness, system COP and a number of air flow/exchanger parameters was developed. It is found that lower channel air velocity, lower inlet air relative humidity, and higher working-to-product air ratio yielded higher cooling effectiveness. The recommended average air velocities in dry and wet channels should not be greater than 1.77 m/s and 0.7 m/s, respectively. The optimum flow ratio of working-to-product air for this cooler is 50%. The channel geometric sizes, i.e. channel length and height, also impose significant impact to system performance. Longer channel length and smaller channel height contribute to increase of the system cooling effectiveness but lead to reduced system COP. The recommend channel height is 4 mm and the dimensionless channel length, i.e., ratio of the channel length to height, should be in the range 100 to 300. Numerical study results indicated that this new type of M-cycle heat and mass exchanger can achieve 16.7% higher cooling effectiveness compared with the conventional cross-flow heat and mass exchanger for the indirect evaporative cooler. The model of this kind is new and not yet reported in literatures. The results of the study help with design and performance analyses of such a new type of indirect evaporative air cooler, and in further, help increasing market rating of the technology within building air conditioning sector, which is currently dominated by the conventional compression refrigeration technology.

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Numerical simulation of the Filchner overflow

The plume of Ice Shelf Water (ISW) flowing into the Weddell Sea over the Filchner sill contributes to the formation of Antarctic Bottom Water. The Filchner overflow is simulated using a hydrostatic, primitive equation three-dimensional ocean model with a 0.5–2 Sv ISW influx above the Filchner sill. The best fit to mooring temperature observations is found with influxes of 0.5 and 1 Sv, below a previous estimate of 1.6 ± 0.5 Sv based on sparse mooring velocities. The plume first moves north over the continental shelf, and then turns west, along slope of the continental shelf break where it breaks up into subplumes and domes, some of which then move downslope. Other subplumes run into the eastern submarine ridge and propagate along the ridge downslope in a chaotic manner. The next, western ridge is crossed by the plume through several paths. Despite a number of discrepancies with observational data, the model reproduces many attributes of the flow. In particular, we argue that the temporal variability shown by the observations can largely be attributed to the unstable structure of the flow, where the temperature fluctuations are determined by the motion of the domes past the moorings. Our sensitivity studies show that while thermobaricity plays a role, its effect is small for the flows considered. Smoothing the ridges out demonstrate that their presence strongly affects the plume shape around the ridges. An increase in the bottom drag or viscosity leads to slowing down, and hence thickening and widening of the plume

Standardized test to evaluate numerical weather prediction algorithms

In order to assist in comparing the computational techniques used in different models, the authors propose a standardized set of one-dimensional numerical experiments that could be completed for each model. The results of these experiments, with a simplified form of the computational representation for advection, diffusion, pressure gradient term, Coriolis term, and filter used in the models, should be reported in the peer-reviewed literature. Specific recommendations are described in this paper.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Numerical prediction of atmospheric blocking-A case study

A series of numerical models have been used to investigate the predictability of atmospheric blocking for an episode selected from FGGE Special Observing Period I. Level II-b FGGE data have been used in the experiment. The blocking took place over the North Atlantic region and is a very characteristic example of high winter blocking. It is found that the very high resolution models developed at ECMWF, in a remarkable way manage to predict the blocking event in great detail, even beyond 1 week. Although models with much less resolution manage to predict the blocking phenomenon as such, the actual evolution differs very much from the observed and consequently the practical value is substantially reduced. Wind observations from the geostationary satellites are shown to have a substantial impact on the forecast beyond 5 days, as well as an extension of the integration domain to the whole globe. Quasi-geostrophic baroclinic models and, even more, barotropic models, are totally inadequate to predict blocking except in its initial phase. The prediction experiment illustrates clearly that efforts which have gone into the improvement of numerical prediction models in the last decades have been worth while.

Numerical modelling of the energy and water cycle of the Baltic Sea

This paper will introduce the Baltex research programme and summarize associated numerical modelling work which has been undertaken during the last five years. The research has broadly managed to clarify the main mechanisms determining the water and energy cycle in the Baltic region, such as the strong dependence upon the large scale atmospheric circulation. It has further been shown that the Baltic Sea has a positive water balance, albeit with large interannual variations. The focus on the modelling studies has been the use of limited area models at ultra-high resolution driven by boundary conditions from global models or from reanalysis data sets. The programme has further initiated a comprehensive integration of atmospheric, land surface and hydrological modelling incorporating snow, sea ice and special lake models. Other aspects of the programme include process studies such as the role of deep convection, air sea interaction and the handling of land surface moisture. Studies have also been undertaken to investigate synoptic and sub-synoptic events over the Baltic region, thus exploring the role of transient weather systems for the hydrological cycle. A special aspect has been the strong interests and commitments of the meteorological and hydrological services because of the potentially large societal interests of operational applications of the research. As a result of this interests special attention has been put on data-assimilation aspects and the use of new types of data such as SSM/I, GPS-measurements and digital radar. A series of high resolution data sets are being produced. One of those, a 1/6 degree daily precipitation climatology for the years 1996–1999, is such a unique contribution. The specific research achievements to be presented in this volume of Meteorology and Atmospheric Physics is the result of a cooperative venture between 11 European research groups supported under the EU-Framework programmes.

Numerical simulations of intense tropical storms

A high resolution general circulation model has been used to study intense tropical storms. A five-year-long global integration with a spatial resolution of 125 km has been analysed. The geographical and seasonal distribution of tropical storms agrees remarkably well with observations. The structure of individual storms also agrees with observations, but the storms are generally more extensive in coverage and less extreme than the observed ones. A few additional calculations have also been done by a very high resolution limited-area version of the same model, where the boundary conditions successively have been interpolated from the global model. These results are very realistic in many details of the structure of the storms including simulated rain-bands and an eye structure. The global model has also been used in another five-year integration to study the influence of greenhouse warming. The sea surface temperatures have been taken from a transient climate change experiment carried out with a low resolution coupled ocean-atmosphere model. The result is a significant reduction in the number of hurricanes, particularly in the Southern Hemisphere. Main reasons for this can be found in changes in the largescale circulation, i.e. a weakening of the Hadley circulation, and a more intense warming of the upper tropical troposphere. A similar effect can be seen during warm ENSO events, where fewer North Atlantic hurricanes have been reported.