The Method of Finding the Optimal Closed Path on Graph Gs

We consider a thought experiment, equivalent to the Sagnac effect, where a light signal performs a round trip over a closed path. If special relativity (SR) adopts Einstein synchronization, the result of the experiment shows that the local light speed cannot be c in every section of the closed path. No inconsistencies are found when adopting absolute synchronization. Since Einstein and absolute synchronizations can be discriminated, the conventionality of the one-way speed of light holds no longer. Thus, as sustained by specialists, it might be a viable formulation of SR that reinstates the conservation of simultaneity, even though it allows for relativistic effects, such as time dilation. Such an approach may lead to the discovery of new effects and a better understanding of relativistic theories.

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Topological Charge Detection Using Generalized Contour-Sum Method from Distorted Donut-Shaped Optical Vortex Beams: Experimental Comparison of Closed Path Determination Methods

Applied Sciences ◽

10.3390/app9193956 ◽

2019 ◽

Vol 9 (19) ◽

pp. 3956

Author(s):

Wang ◽

Huang ◽

Toyoda ◽

Liu

Keyword(s):

Topological Charge ◽

Circle Method ◽

Transformation Method ◽

Optical Vortex ◽

Experimental Comparison ◽

Average Intensity ◽

Closed Path ◽

Light Modulator ◽

Watershed Transformation ◽

Determination Methods

A generalized contour-sum method has been proposed to measure the topological charge (TC) of an optical vortex (OV) beam using a Shack–Hartmann wavefront sensor (SH-WFS). Moreover, a recent study extended it to be workable for measuring an aberrated OV beam. However, when the OV beam suffers from severe distortion, the closed path for circulation calculation becomes crucial. In this paper, we evaluate the performance of five closed path determination methods, including watershed transformation, maximum average-intensity circle extraction, a combination of watershed transformation and maximum average-intensity circle extraction, and perfectly round circles assignation. In the experiments, we used a phase-only spatial light modulator to generate OV beams and aberrations, while an SH-WFS was used to measure the intensity profile and phase slopes. The results show that when determining the TC values of distorted donut-shaped OV beams, the watershed-transformed maximum average-intensity circle method performed the best, and the maximum average-intensity circle method and the watershed transformation method came second and third, while the worst was the perfect circles assignation method. The discussions that explain our experimental results are also given.

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Comparison of Lyman-alpha and LI-COR infrared hygrometers for airborne measurement of turbulent fluctuations of water vapour

Atmospheric Measurement Techniques ◽

10.5194/amt-11-2523-2018 ◽

2018 ◽

Vol 11 (4) ◽

pp. 2523-2536 ◽

Cited By ~ 2

Author(s):

Astrid Lampert ◽

Jörg Hartmann ◽

Falk Pätzold ◽

Lennart Lobitz ◽

Peter Hecker ◽

...

Keyword(s):

Water Vapour ◽

Measurement Data ◽

Frequency Noise ◽

Closed Path ◽

Mixing Ratio ◽

Lyman Alpha ◽

Airborne Measurements ◽

Open Path ◽

Airborne Measurement ◽

Good Agreement

Abstract. To investigate if the LI-COR humidity sensor can be used as a replacement of the Lyman-alpha sensor for airborne applications, the measurement data of the Lyman-alpha and several LI-COR sensors are analysed in direct intercomparison flights on different airborne platforms. One vibration isolated closed-path and two non-isolated open-path LI-COR sensors were installed on a Dornier 128 twin engine turbo-prop aircraft. The closed-path sensor provided absolute values and fluctuations of the water vapour mixing ratio in good agreement with the Lyman-alpha. The signals of the two open-path sensors showed considerable high-frequency noise, and the absolute value of the mixing ratio was observed to drift with time in this vibrational environment. On the helicopter-towed sensor system Helipod, with very low vibration levels, the open-path LI-COR sensor agreed very well with the Lyman-alpha sensor over the entire frequency range up to 3 Hz. The results show that the LI-COR sensors are well suited for airborne measurements of humidity fluctuations, provided that a vibrationless environment is given, and this turns out to be more important than close sensor spacing.

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Eddy covariance methane measurements at a Ponderosa pine plantation in California

Atmospheric Chemistry and Physics ◽

10.5194/acp-9-8365-2009 ◽

2009 ◽

Vol 9 (21) ◽

pp. 8365-8375 ◽

Cited By ~ 50

Author(s):

C. J. P. P. Smeets ◽

R. Holzinger ◽

I. Vigano ◽

A. H. Goldstein ◽

T. Röckmann

Keyword(s):

Eddy Covariance ◽

Ponderosa Pine ◽

Power Spectra ◽

Methane Flux ◽

Forest Site ◽

Phase Lag ◽

Closed Path ◽

Pine Plantation ◽

Model Calculations ◽

Flux Measurements

Abstract. Long term methane flux measurements have been mostly performed with plant or soil enclosure techniques on specific components of an ecosystem. New fast response methane analyzers make it possible to use the eddy covariance (EC) technique instead. The EC technique is advantageous because it allows continuous flux measurements integrating over a larger and more representative area including the complete ecosystem, and allows fluxes to be observed as environmental conditions change naturally without disturbance. We deployed the closed-path Fast Methane analyzer (FMA) from Los Gatos Research Ltd and demonstrate its performance for EC measurements at a Ponderosa pine plantation at the Blodgett Forest site in central California. The fluctuations of the CH4 concentration measured at 10 Hz appear to be small and their standard deviation is comparable to the magnitude of the signal noise (±5 ppbv). Consequently, the power spectra typically have a white noise signature at the high frequency end (a slope of +1). Nevertheless, in the frequency range important for turbulent exchange, the cospectra of CH4 compare very well with all other scalar cospectra confirming the quality of the FMA measurements are good for the EC technique. We furthermore evaluate the complications of combined open and closed-path measurements when applying the Webb-Pearman-Leuning (WPL) corrections (Webb et al., 1980) and the consequences of a phase lag between the water vapor and methane signal inside the closed path system. The results of diurnal variations of CH4 concentrations and fluxes are summarized and compared to the monthly results of process-based model calculations.

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Corrigendum to “Relative humidity effects on water vapour fluxes measured with closed-path eddy-covariance systems with short sampling lines” [Agric. Forest Meteorol. 165 (2012) 53–63]

Agricultural and Forest Meteorology ◽

10.1016/j.agrformet.2012.10.013 ◽

2012 ◽

Vol 166-167 ◽

pp. 234

Author(s):

Gerardo Fratini ◽

Andreas Ibrom ◽

Nicola Arriga ◽

George Burba ◽

Dario Papale

Keyword(s):

Relative Humidity ◽

Water Vapour ◽

Eddy Covariance ◽

Closed Path ◽

Humidity Effects ◽

Water Vapour Fluxes

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Dried, closed-path eddy covariance method for measuring carbon dioxide flux over sea ice

Atmospheric Measurement Techniques ◽

10.5194/amt-11-6075-2018 ◽

2018 ◽

Vol 11 (11) ◽

pp. 6075-6090 ◽

Cited By ~ 4

Author(s):

Brian J. Butterworth ◽

Brent G. T. Else

Keyword(s):

Carbon Dioxide ◽

Sea Ice ◽

Eddy Covariance ◽

Co2 Flux ◽

Carbon Dioxide Flux ◽

The Arctic ◽

Closed Path ◽

Eddy Covariance Method ◽

Open Path ◽

Flux Measurements

Abstract. The Arctic marine environment plays an important role in the global carbon cycle. However, there remain large uncertainties in how sea ice affects air–sea fluxes of carbon dioxide (CO2), partially due to disagreement between the two main methods (enclosure and eddy covariance) for measuring CO2 flux (FCO2). The enclosure method has appeared to produce more credible FCO2 than eddy covariance (EC), but is not suited for collecting long-term, ecosystem-scale flux datasets in such remote regions. Here we describe the design and performance of an EC system to measure FCO2 over landfast sea ice that addresses the shortcomings of previous EC systems. The system was installed on a 10 m tower on Qikirtaarjuk Island – a small rock outcrop in Dease Strait located roughly 35 km west of Cambridge Bay, Nunavut, in the Canadian Arctic Archipelago. The system incorporates recent developments in the field of air–sea gas exchange by measuring atmospheric CO2 using a closed-path infrared gas analyzer (IRGA) with a dried sample airstream, thus avoiding the known water vapor issues associated with using open-path IRGAs in low-flux environments. A description of the methods and the results from 4 months of continuous flux measurements from May through August 2017 are presented, highlighting the winter to summer transition from ice cover to open water. We show that the dried, closed-path EC system greatly reduces the magnitude of measured FCO2 compared to simultaneous open-path EC measurements, and for the first time reconciles EC and enclosure flux measurements over sea ice. This novel EC installation is capable of operating year-round on solar and wind power, and therefore promises to deliver new insights into the magnitude of CO2 fluxes and their driving processes through the annual sea ice cycle.

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A Novel Cooperative Path Planning for Multi-robot Persistent Coverage with Obstacles and Coverage Period Constraints

Sensors ◽

10.3390/s19091994 ◽

2019 ◽

Vol 19 (9) ◽

pp. 1994 ◽

Cited By ~ 2

Author(s):

Guibin Sun ◽

Rui Zhou ◽

Bin Di ◽

Zhuoning Dong ◽

Yingxun Wang

Keyword(s):

Path Planning ◽

Numerical Simulations ◽

Obstacle Avoidance ◽

Travelling Salesman Problem ◽

Region Of Interest ◽

Minimum Cost ◽

Closed Path ◽

Combinatorial Approach ◽

Travelling Salesman ◽

Multi Robot

In this paper, a multi-robot persistent coverage of the region of interest is considered, where persistent coverage and cooperative coverage are addressed simultaneously. Previous works have mainly concentrated on the paths that allow for repeated coverage, but ignored the coverage period requirements of each sub-region. In contrast, this paper presents a combinatorial approach for path planning, which aims to cover mission domains with different task periods while guaranteeing both obstacle avoidance and minimizing the number of robots used. The algorithm first deploys the sensors in the region to satisfy coverage requirements with minimum cost. Then it solves the travelling salesman problem to obtain the frame of the closed path. Finally, the approach partitions the closed path into the fewest segments under the coverage period constraints, and it generates the closed route for each robot on the basis of portioned segments of the closed path. Therefore, each robot can circumnavigate one closed route to cover the different task areas completely and persistently. The numerical simulations show that the proposed approach is feasible to implement the cooperative coverage in consideration of obstacles and coverage period constraints, and the number of robots used is also minimized.

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Studies in multiplicative solutions to linear differential equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500018424 ◽

1987 ◽

Vol 106 (3-4) ◽

pp. 277-305 ◽

Cited By ~ 2

Author(s):

F. M. Arscott

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Linear Differential Equation ◽

Floquet Theory ◽

Special Functions ◽

Linear Differential Equations ◽

Ordinary Linear Differential Equation ◽

Closed Path ◽

Starting Point ◽

Linear Differential

SynopsisGiven an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.

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