The effect of non-Markovian terms on the Landau equation

1980 ◽  
Vol 371 (1746) ◽  
pp. 381-392 ◽  
Keyword(s):  
Time Series ◽  
Lower Bound ◽  
Landau Equation ◽  
Plasma Potential ◽  
Time Span ◽  
Time Interval ◽  
Number Density ◽  
Time Effects ◽  
Homogeneous Plasma ◽  
Short Time

The Landau equation can be derived as the sum of an expansion series in time provided certain non-Markovian short-time terms are neglected. The time series could be very useful for the solution of a variety of problems. It is necessary to estimate the time span over which the neglected term s are significant. The non-Markovian terms for the case of a homogeneous plasma are evaluated using a technique developed by Prigogine and Balescu. For typical values of plasma potential cut-offs the conditions under which the short-time terms may be ignored are estimated. It is found that for electrons of number density less than 1010 and protons of number density less than 1014 it may be possible to ignore the short-time effects. It is conjectured that for many situations the non-Markovian effects will be important for a time interval which has a lower bound t 0 and an upper bound several orders of magnitude greater than t .

scholarly journals Estimating the Concentration of Students from Time Series Images

10.29007/gl3b ◽  
2020 ◽  
Author(s):  
Hoang Son Nguyen ◽  
Yu Takahata ◽  
Masaaki Goto ◽  
Tetsuo Tanaka ◽  
Akihiko Ohsuga ◽  
...  
Keyword(s):  
Time Series ◽  
Learning Algorithm ◽  
Point Of View ◽  
Time Interval ◽  
Short Time Interval ◽  
Deep Learning Algorithm ◽  
Concentration Degree ◽  
Discrete Values ◽  
Short Time ◽  
Facial Images

In this study, we build a system that is able to estimate the concentration degree of students while they are working with computers. The purpose of learning is to gain knowledge of a subject and to reach sufficient performance level about the subject. Concentration is the key in the successful learning process. But the concept of concentration includes some ambiguity and lacks the clear definition form an engineering point of view, and it is difficult to measure its degree by observation from outside. We in this paper begins with a discussion of the concept of concentration, and then a discussion of how to measure it by using standard devices and sensors. The proposed system investigates the facial images of students recorded by the PC webcams attached to the computers to infer their concentration degree. In this study, we define the concentration degree over a short time interval. The value takes continues value from 0 to 1, and is determined based on the efficiency of simple work performed over the interval. We convert the continuous values into three discrete values: low, middle and high. In the first approach in this study, we apply deep learning algorithm with only the facial images. In the next, we obtain the data of face moves as a set of time series, and run the learning algorithm using both of the data. We explain an outline of the methods and the system with several experimental results.

scholarly journals Could Ramadan catalyze SARS-CoV-2 spread? Preliminary results

2020 ◽  
Author(s):  
Andrzej Jarynowski ◽  
Daniel Płatek
Keyword(s):  
Time Series ◽  
Transmission Dynamics ◽  
Mitigation Measures ◽  
Time Effects ◽  
Preliminary Results ◽  
Extended Families ◽  
Contact Rates ◽  
Short Time

Around 1.8 billion Muslims worldwide celebrate in some extent the holy month of Ramadan during COVID-19 pandemic. Some increase their attendance worship sites and traditional dining in extended families, so infectious contact rates could increase. Moreover, fasting could increase the probability of acquiring SARS-CoV-2 infection. There are mitigation measures (e.g. Healthy Ramadan by WHO) applied to reduce the SARS-CoV-2 spread, however their real impact is still unknown. Multiple studies assessed observed effects of contact rates increase during holidays as Chinese New Year in January and Passover and Easter in April and their short-time effects on COVID-19 transmission dynamics. However, there are any quantitative attempts considering epidemiological consequences of the holy Ramadan (at least up to our knowledge and keywords search in various databases until the submission day). We analyze the fractions of Muslims and time series of COVID-19 daily incidence and cases numbers for 197 countries and territories. We found statistically significant positive link with proportion of Islam adherents with increase in normalized new cases of COVID-19 during 1-18 May 2020. Moreover, growth of incidences in May is statistically significantly greater than in a control (April).

The quantum mechanical Landau equation

1983 ◽  
Vol 388 (1795) ◽  
pp. 393-400 ◽  
Keyword(s):  
Landau Equation ◽  
Time Development ◽  
Feynman Diagrams ◽  
Quantum Mechanical ◽  
Number Density ◽  
Short Discussion ◽  
Mechanical Effects ◽  
Quantum Mechanical Effects ◽  
Apparent Similarity ◽  
Short Time

The significance of quantum mechanical effects on the short time development of the Landau equation is examined. The analysis is undertaken using the density diagram technique of Prigogine and Balescu. Owing to the apparent similarity that exists between the density diagrams and the more familiar Feynman diagrams derived from generalized Green functions a short discussion of both techniques is presented. The solution is undertaken for small h/m and does not necessarily apply to electrons. It is found that quantum mechanical effects may become significant at a number density around 10 14 , which is the lower bound in density that an earlier analysis suggested. Non-Markovian effects may be significant.

An inhomogeneous Landau-like equation

1981 ◽  
Vol 378 (1774) ◽  
pp. 385-400 ◽  
Keyword(s):  
Power Series ◽  
Statistical Mechanics ◽  
Weak Coupling ◽  
Landau Equation ◽  
Time Development ◽  
Sample Problem ◽  
Homogeneous Plasma ◽  
Vector Generation ◽  
Short Time ◽  
Infinite Temperature

The problem of the mixing of two plasmas is very difficult to solve if the methods of statistical mechanics are used. When both plasmas are homogeneous in space, and the limit of weak coupling is appropriate, the Landau equation describes the motion. An equation, similar to the Landau equation, is developed for the case when one of the plasmas is initially inhomogeneous in space. The equation is a power series in time and involves wave vectors in space. The short-time-after-mixing limit is considered, which restricts the number of wave vectors. A sample problem is presented of the short time development of an infinite-temperature spike interacting with a homogeneous plasma. The spike is found to move very rapidly from the origin owing to the long range of the forces. Extension of the time development past the initial short time requires consideration of destructive wave vectors in addition to the wave vector generation considered here.

scholarly journals Sensitivity Analysis of Sentinel-1 Backscatter to Oil Palm Plantations at Pluriannual Scale: A Case Study in Gabon, Africa

2021 ◽  
Vol 13 (11) ◽  
pp. 2075
Author(s):  
J. David Ballester-Berman ◽  
Maria Rastoll-Gimenez
Keyword(s):  
Time Series ◽  
Sensitivity Analysis ◽  
Oil Palm ◽  
Time Interval ◽  
Potential Candidate ◽  
Initial Growth ◽  
Natural Forests ◽  
Wet Season ◽  
Radar Signatures ◽  
The Times

The present paper focuses on a sensitivity analysis of Sentinel-1 backscattering signatures from oil palm canopies cultivated in Gabon, Africa. We employed one Sentinel-1 image per year during the 2015–2021 period creating two separated time series for both the wet and dry seasons. The first images were almost simultaneously acquired to the initial growth stage of oil palm plants. The VH and VV backscattering signatures were analysed in terms of their corresponding statistics for each date and compared to the ones corresponding to tropical forests. The times series for the wet season showed that, in a time interval of 2–3 years after oil palm plantation, the VV/VH ratio in oil palm parcels increases above the one for forests. Backscattering and VV/VH ratio time series for the dry season exhibit similar patterns as for the wet season but with a more stable behaviour. The separability of oil palm and forest classes was also quantitatively addressed by means of the Jeffries–Matusita distance, which seems to point to the C-band VV/VH ratio as a potential candidate for discrimination between oil palms and natural forests, although further analysis must still be carried out. In addition, issues related to the effect of the number of samples in this particular scenario were also analysed. Overall, the outcomes presented here can contribute to the understanding of the radar signatures from this scenario and to potentially improve the accuracy of mapping techniques for this type of ecosystems by using remote sensing. Nevertheless, further research is still to be done as no classification method was performed due to the lack of the required geocoded reference map. In particular, a statistical assessment of the radar signatures should be carried out to statistically characterise the observed trends.

scholarly journals Neuro-Inspired Computing with Spin-VCSELs

2021 ◽  
Vol 11 (9) ◽  
pp. 4232
Author(s):  
Krishan Harkhoe ◽  
Guy Verschaffelt ◽  
Guy Van der Sande
Keyword(s):  
Processing Speed ◽  
Delay Time ◽  
High Speed ◽  
State Of The Art ◽  
Polarization Modulation ◽  
Time Interval ◽  
Computing Technique ◽  
High Modulation ◽  
Short Time ◽  
Modulation Speed

Delay-based reservoir computing (RC), a neuromorphic computing technique, has gathered lots of interest, as it promises compact and high-speed RC implementations. To further boost the computing speeds, we introduce and study an RC setup based on spin-VCSELs, thereby exploiting the high polarization modulation speed inherent to these lasers. Based on numerical simulations, we benchmarked this setup against state-of-the-art delay-based RC systems and its parameter space was analyzed for optimal performance. The high modulation speed enabled us to have more virtual nodes in a shorter time interval. However, we found that at these short time scales, the delay time and feedback rate heavily influence the nonlinear dynamics. Therefore, and contrary to other laser-based RC systems, the delay time has to be optimized in order to obtain good RC performances. We achieved state-of-the-art performances on a benchmark timeseries prediction task. This spin-VCSEL-based RC system shows a ten-fold improvement in processing speed, which can further be enhanced in a straightforward way by increasing the birefringence of the VCSEL chip.

scholarly journals Neural Network Approach for Global Solar Irradiance Prediction at Extremely Short-Time-Intervals Using Particle Swarm Optimization Algorithm

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1213
Author(s):  
Ahmed Aljanad ◽  
Nadia M. L. Tan ◽  
Vassilios G. Agelidis ◽  
Hussain Shareef
Keyword(s):  
Neural Networks ◽  
Particle Swarm Optimization ◽  
Solar Irradiance ◽  
Particle Swarm ◽  
Time Interval ◽  
Time Intervals ◽  
Swarm Optimization ◽  
Backpropagation Neural Networks ◽  
Proposed Model ◽  
Short Time

Hourly global solar irradiance (GSR) data are required for sizing, planning, and modeling of solar photovoltaic farms. However, operating and controlling such farms exposed to varying environmental conditions, such as fast passing clouds, necessitates GSR data to be available for very short time intervals. Classical backpropagation neural networks do not perform satisfactorily when predicting parameters within short intervals. This paper proposes a hybrid backpropagation neural networks based on particle swarm optimization. The particle swarm algorithm is used as an optimization algorithm within the backpropagation neural networks to optimize the number of hidden layers and neurons used and its learning rate. The proposed model can be used as a reliable model in predicting changes in the solar irradiance during short time interval in tropical regions such as Malaysia and other regions. Actual global solar irradiance data of 5-s and 1-min intervals, recorded by weather stations, are applied to train and test the proposed algorithm. Moreover, to ensure the adaptability and robustness of the proposed technique, two different cases are evaluated using 1-day and 3-days profiles, for two different time intervals of 1-min and 5-s each. A set of statistical error indices have been introduced to evaluate the performance of the proposed algorithm. From the results obtained, the 3-days profile’s performance evaluation of the BPNN-PSO are 1.7078 of RMSE, 0.7537 of MAE, 0.0292 of MSE, and 31.4348 of MAPE (%), at 5-s time interval, where the obtained results of 1-min interval are 0.6566 of RMSE, 0.2754 of MAE, 0.0043 of MSE, and 1.4732 of MAPE (%). The results revealed that proposed model outperformed the standalone backpropagation neural networks method in predicting global solar irradiance values for extremely short-time intervals. In addition to that, the proposed model exhibited high level of predictability compared to other existing models.

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