A calibration cover for multi-spectral space instruments

One-pot hydrothermal preparation of Ca3Cr2Si3O12 uvarovite nanoparticles under alkaline conditions was investigated for the first time. The experimental parameters selected for the study considered the concentration of the KOH solvent solution (0.01 to 5.0 M), the agitation of the autoclave (50 rpm), and the nominal content of Si4+ (2.2–3.0 mole). Fine uvarovite particles were synthesised at 200 °C after a 3 h interval in a highly concentrated 5.0 M KOH solution. The crystallisation of single-phase Ca3Cr2Si3O12 particles proceeded free of by-products via a one-pot process involving a single-step reaction. KOH solutions below 2.5 M and water hindered the crystallisation of the Ca3Cr2Si3O12 particles. The hydrothermal treatments carried out with stirring (50 rpm) and non-stirring triggered the crystallisation of irregular anhedral particles with average sizes of 8.05 and 12.25 nm, respectively. These particles spontaneously assembled into popcorn-shaped agglomerates with sizes varying from 66 to 156 nm. All the powders prepared by the present method exhibited CIE-L*a*b* values that correspond to the Victoria green colour spectral space and have a high near infrared reflectance property. The particle size and structural crystallinity are factors affecting the Victoria pigment optical properties, such as CIE-L*a*b* values, green tonality, and near-infrared reflectance.

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CHOICE-FREE STONE DUALITY

Journal of Symbolic Logic ◽

10.1017/jsl.2019.11 ◽

2019 ◽

Vol 85 (1) ◽

pp. 109-148

Author(s):

NICK BEZHANISHVILI ◽

WESLEY H. HOLLIDAY

Keyword(s):

Boolean Algebra ◽

Boolean Algebras ◽

Stone Space ◽

Spectral Space ◽

Topological Representation ◽

Stone Duality ◽

Closed Sets ◽

Spectral Spaces ◽

Basic Facts ◽

Regular Open

AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras.

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Large-scale vortices in rapidly rotating Rayleigh–Bénard convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.542 ◽

2014 ◽

Vol 758 ◽

pp. 407-435 ◽

Cited By ~ 55

Author(s):

Céline Guervilly ◽

David W. Hughes ◽

Chris A. Jones

Keyword(s):

Large Scale ◽

Reynolds Numbers ◽

Spectral Space ◽

Small Scale ◽

Convective Velocity ◽

Onset Of Convection ◽

Convective Structures ◽

Convective Scale ◽

Domain Of Existence ◽

Convective Motions

AbstractUsing numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal scale of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a measure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\gtrsim }100$. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, ${\lesssim }0.15$. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

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Pseudo-spectral space-time calculations of incompressible viscous flows

10.2514/6.1981-1 ◽

1981 ◽

Cited By ~ 4

Author(s):

Y. MORCHOISNE

Keyword(s):

Viscous Flows ◽

Space Time ◽

Spectral Space ◽

Incompressible Viscous Flows ◽

Pseudo Spectral

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Resource-efficient dynamic partial reconfiguration on FPGAs for space instruments

2017 NASA/ESA Conference on Adaptive Hardware and Systems (AHS) ◽

10.1109/ahs.2017.8046355 ◽

2017 ◽

Cited By ~ 2

Author(s):

Alexander Dorflinger ◽

Bjorn Fiethe ◽

Harald Michalik ◽

Sandor P. Fekete ◽

Phillip Keldenich ◽

...

Keyword(s):

Partial Reconfiguration ◽

Dynamic Partial Reconfiguration ◽

Space Instruments

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Scale-Selective Precision for Weather and Climate Forecasting

Monthly Weather Review ◽

10.1175/mwr-d-18-0308.1 ◽

2019 ◽

Vol 147 (2) ◽

pp. 645-655 ◽

Cited By ~ 11

Author(s):

Matthew Chantry ◽

Tobias Thornes ◽

Tim Palmer ◽

Peter Düben

Keyword(s):

Time Scales ◽

Weather Forecasting ◽

Forecast Accuracy ◽

Spectral Space ◽

Dynamical Equations ◽

Length Scales ◽

Climate Forecasting ◽

Spectral Models ◽

Weather And Climate ◽

Numerical Precision

Abstract Attempts to include the vast range of length scales and physical processes at play in Earth’s atmosphere push weather and climate forecasters to build and more efficiently utilize some of the most powerful computers in the world. One possible avenue for increased efficiency is in using less precise numerical representations of numbers. If computing resources saved can be reinvested in other ways (e.g., increased resolution or ensemble size) a reduction in precision can lead to an increase in forecast accuracy. Here we examine reduced numerical precision in the context of ECMWF’s Open Integrated Forecast System (OpenIFS) model. We posit that less numerical precision is required when solving the dynamical equations for shorter length scales while retaining accuracy of the simulation. Transformations into spectral space, as found in spectral models such as OpenIFS, enact a length scale decomposition of the prognostic fields. Utilizing this, we introduce a reduced-precision emulator into the spectral space calculations and optimize the precision necessary to achieve forecasts comparable with double and single precision. On weather forecasting time scales, larger length scales require higher numerical precision than smaller length scales. On decadal time scales, half precision is still sufficient precision for everything except the global mean quantities.

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