scholarly journals Ex Machina Determination of Structural Correlation Functions

2020 ◽  
Vol 11 (11) ◽  
pp. 4372-4378
Author(s):  
Galen T. Craven ◽  
Nicholas Lubbers ◽  
Kipton Barros ◽  
Sergei Tretiak
Keyword(s):  
Correlation Functions ◽  
Structural Correlation

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

scholarly journals The correlation functions of the regular tetrahedron and octahedron

2014 ◽  
Vol 47 (4) ◽  
pp. 1445-1448 ◽  
Author(s):  
Salvino Ciccariello
Keyword(s):  
Correlation Functions ◽  
Rational Functions ◽  
Regular Tetrahedron ◽  
Numerical Determination ◽  
Algebraic Form ◽  
Autocorrelation Functions ◽  
Regular Octahedron ◽  
Size Dispersion ◽  
Arctangent Function

The expressions of the autocorrelation functions (CFs) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and (a + br 2)1/2, a and b being appropriate integers and r a distance. The CF expressions make the numerical determination of the corresponding scattering intensities fast and accurate even in the presence of a size dispersion.

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