Determination Of Correlation Functions Research Articles

A computational modeling approach based on random fields for short fiber-reinforced composites with experimental verification by nanoindentation and tensile tests

In this study a modeling approach for short fiber-reinforced composites is presented which allows one to consider information from the microstructure of the compound while modeling on the component level. The proposed technique is based on the determination of correlation functions by the moving window method. Using these correlation functions random fields are generated by the Karhunen–Loève expansion. Linear elastic numerical simulations are conducted on the mesoscale and component level based on the probabilistic characteristics of the microstructure derived from a two-dimensional micrograph. The experimental validation by nanoindentation on the mesoscale shows good conformity with the numerical simulations. For the numerical modeling on the component level the comparison of experimentally obtained Young’s modulus by tensile tests with numerical simulations indicate that the presented approach requires three-dimensional information of the probabilistic characteristics of the microstructure. Using this information not only the overall material properties are approximated sufficiently, but also the local distribution of the material properties shows the same trend as the results of conducted tensile tests.

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

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 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.

An overview of recent developments in the interpretation and prediction of fast internal protein dynamics

During the past decades, NMR spectroscopy has emerged as a unique tool for the study of protein dynamics. Indeed, relaxation studies on isotopically labeled proteins can provide information on the overall motions as well as the internal fast, sub-nanosecond, dynamics. Therefore, the interpretation and the prediction of spin relaxation rates in proteins are important issues that have motivated numerous theoretical and methodological developments, including the description of overall dynamics and its possible coupling to internal mobility, the introduction of models of internal dynamics, the determination of correlation functions from experimental data, and the relationship between relaxation and thermodynamical quantities. A brief account of recent developments that have proven useful in this domain are presented.

Determination of site-occupancy pair correlation functions of CO adsorbed on Pt(111) adapted for DLEED intensity calculations

The aim of this paper is to determine the site-occupancy pair correlation functions of a partially ordered layer of CO adsorbed on Pt(111). These functions are needed to calculate the structure factor appearing in the diffuse LEED intensity expression. CO molecules can be adsorbed at on-top sites and at three kinds of bridge sites obtained from each other by rotation of 120°. Pair correlation functions Γ ij ( p, p′) = 〈 n i ( p) n j ( p′)〉 − 〈 n i ( p)〉〈 n j ( p′)〉 are obtained by a Monte Carlo simulation at constant coverage ϑ m and temperature T. The model involves adsorption energy and repulsive pair interaction potentials up to third neighbours, depending only on the distance. We deal with a N × N fcc (111) 2D lattice with periodic boundary conditions. We study the dependence of correlation functions on pair interaction potentials and coverage ϑ m. The determination of correlation functions is based on the experimental observations coming from the HREELS, IRAS and LEED techniques. In accordance with experiment, a diffuse (√3 × √3)R30° superstructure, involving only on-top sites, appears at low coverage. On increasing the coverage, more and more bridge sites are occupied and a c(4 × 2) superstructure grows progressively.

Determination of correlation function for aged metallic glass by SAXS

Heating metallic glass up to a certain temperature and holding it for some time at that temperature, causes crystallization. There is a density difference between the crystalline phase and the amorphous phase. For aged metallic glass, the small-angle X-ray scattering (SAXS) owes its origin to this density difference. Therefore, the SAXS technique is a useful method to study the structure of metallic glass. SAXS is not equally sensitive to all metallic glasses. A correlation function of two-phase systems can be determined by SAXS with some important parameters, such as inner specific surface, coherence length, etc. In this work, a correlation function for the two-phase system in aged Cu[sub 73]Sn[sub 6]Ni[sub 6]P[sub 15] metallic glass was determined by SAXS. The specific inner surface and coherence length for the two-phase system was determined by using the obtained correlation function.

Determination of correlation functions of composite materials with the stochastic structure by acoustic methods

Determination of correlation functions of composite materials with the stochastic structure by acoustic methods

Errata: A problem in the determination of correlation functions

Errata: A problem in the determination of correlation functions

A general theory of amplitude quantization with applications to correlation determination

A general theory of amplitude quantization is presented and is used to investigate the effects of signal quantization on the determination of correlation functions. Theoretical expressions are obtained for the cross-correlation between signals and quantization noises and for the cross-correlation between quantization noises.From considerations of the theory of amplitude quantization, a general form for multiplier correlators is determined. The perfect analogue correlator, the digital computer applied to correlation determination, the relay correlator and the polarity-coincidence correlator are all shown to be special cases of this general form. In addition, a new correlation method termed Stieltjes correlation is deduced. This method, in which one of the inputs is coarsely quantized and the other is not, is described in detail and is shown to possess many advantages over the correlators mentioned above.

Určení korelačních funkcí na výstupu generátoru spojitých náhodných procesů

Určení korelačních funkcí na výstupu generátoru spojitých náhodných procesů