scholarly journals Entropy Multiparticle Correlation Expansion for a Crystal

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1024
Author(s):  
Santi Prestipino ◽  
Paolo V. Giaquinta
Keyword(s):  
Spatial Distribution ◽  
Numerical Data ◽  
Distribution Functions ◽  
Identical Particles ◽  
Classical Fluid ◽  
Entropy Formula ◽  
Similar Correlation ◽  
Combinatorial Derivation ◽  
Crystalline System

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

Comparison of gridded temperature dataset of IMD and Sheffield over India

2021 ◽  
pp. 285-293
Author(s):  
Anurag Sharma ◽  
Deepak Swami ◽  
Nitin Joshi
Keyword(s):  
Spatial Distribution ◽  
Probability Distribution ◽  
Minimum Temperature ◽  
Climate Extremes ◽  
Western Himalaya ◽  
Distribution Functions ◽  
Climate Modelling ◽  
Reanalysis Dataset ◽  
Box Plots ◽  
Modelling Studies

Climate modelling and prediction studies play crucial role in identifying suitable mitigation techniques to minimize or avoid adverse consequences of climate extremes. The accurate spatially and temporally distributed temperature and rainfall dataset are key components in climate prediction studies. Reanalysis datasets provide better spatial and temporal coverage than observational datasets; therefore, reanalysis datasets are widely used for global and regional studies. However, before using the reanalysis dataset in climate modelling studies, it is crucial to compare the robustness and accuracy of the reanalysis dataset with the observational dataset. In this study, daily gridded maximum and minimum temperature datasets of Indian Meteorological Department (IMD) (1°?×?1°) and Sheffield (0.25°×0.25°) are compared using 62-years data i.e 1951-2012. The comparison is based on differences in spatial distribution pattern, probability distribution functions plots and box-plots of the respective gridded dataset. The spatial distribution of grid-wise averaged maximum and minimum temperature dataset generally compare well across pan India in both IMD and Sheffield; however, the significant differences are observed over western Himalaya (WH) and northeast (NE) region. The probability distribution of the pooled mean minimum temperature dataset of IMD is found significantly different from Sheffield using the two-sample Kolmogorov-Smirnov (KS) test. This study will be helpful for researchers who are planning to use Sheffield gridded temperature dataset for climate modelling studies.

Spatial distribution functions: liquid CH3CN and CO2

1996 ◽  
Vol 251 (3-4) ◽  
pp. 157-163 ◽  
Author(s):  
A.F. Terzis ◽  
E.T. Samulski
Keyword(s):  
Spatial Distribution ◽  
Distribution Functions

Spatial Distribution Maps for Atom Probe Tomography

2007 ◽  
Vol 13 (6) ◽  
pp. 437-447 ◽  
Author(s):  
Brian P. Geiser ◽  
Thomas F. Kelly ◽  
David J. Larson ◽  
Jason Schneir ◽  
Jay P. Roberts
Keyword(s):  
Spatial Distribution ◽  
Atom Probe Tomography ◽  
Detection Efficiency ◽  
Structural Information ◽  
Atom Probe ◽  
Dark Field ◽  
Distribution Functions ◽  
Orientation Relationships ◽  
Distribution Maps ◽  
Space Technique

A real-space technique for finding structural information in atom probe tomographs, spatial distribution maps (SDM), is described. The mechanics of the technique are explained, and it is then applied to some test cases. Many applications of SDM in atom probe tomography are illustrated with examples including finding crystal lattices, correcting lattice strains in reconstructed images, quantifying trajectory aberrations, quantifying spatial resolution, quantifying chemical ordering, dark-field imaging, determining orientation relationships, extracting radial distribution functions, and measuring ion detection efficiency.

scholarly journals Cartographic form of comparison of demographic indicators in Vojvodina

2006 ◽  
pp. 111-118
Author(s):  
Dragica Zivkovic ◽  
Marina Janic-Siridzanski ◽  
Jasminka Jovanovic
Keyword(s):  
Spatial Distribution ◽  
Population Density ◽  
Structural Changes ◽  
Numerical Data ◽  
Demographic Characteristics ◽  
Thematic Content ◽  
Quantitative Parameters ◽  
Demographic Indicators ◽  
Temporal System ◽  
Comparative Aspect

Demographic characteristics of a specific geospace represent its most dynamic part and one of the basic goals of the research in the geographic science. The cartographic method, as a part of the system of methods in the geographic science, is very important in the research concerning quantitative parameters of the population (the number of inhabitants, population density), the structure (contingents), dynamics (structural changes), natural trends and migrations. The complexity of the application of the cartographic method could be exemplified in the following phases: 1. Spatial distribution of the population in the specific spatial units, 2. Temporal changeability of the cartographic facts (fixing the temporal determination, change of demographic indicators in a specific temporal system) The development of science and informatics led to the application of metricity in the process of cartography and interpretation of the thematic content of a chart. Demographic indicators are presented as numeric series, which graphically could be represented in the three aspects of semio-proportional cartography: the differentiated, the comparative and the unified one. These three aspects would be applied for the numerical data of demographic indicators of the population of Vojvodina (according to different census years and counties). The differentiated aspect of semio-proportions would show the changes in the number of inhabitants according to the census years in relation to the year 1953, the comparative aspect would compare the number of inhabitants, areas and population density in 1981 and 2002, and the unified aspect would show the number of the employed in different branches of business in 1991 and 2002. Presentation of numerical data as graphic indicators enables a faster and easier observation of changes in the demographic indicators in Vojvodina, as well as perception of regularities in further trends.

Sign in / Sign up

Export Citation Format

Share Document