Influence Of Spatial Correlations Research Articles

Fatigue reliability assessment of steel bridges considering spatial correlation in system evaluation

Fatigue is among the most critical forms of deterioration damage that occurs to steel bridges. The performance of steel bridges, which may be seriously affected due to fatigue, should be assessed and predicted. However, the code-based reliability assessment only provides a clear criterion for single details. The whole bridge or a splitting system from the bridge may contain many details which brings system impact on the fatigue assessment. In this paper the system reliability of steel bridges is addressed with focus on the influence of spatial correlations between similar fatigue sensitive details. The study is conducted on a typical riveted railway bridge, from which a subsystem is selected and modelled as a weakest link system. It is assumed that all details in the system are equicorrelated. An efficient modeling approach has been developed to quantify the correlation and help estimate the system reliability analytically. A parametric study was performed to determine the system effects on the fatigue reliability assessment and identify the decisive variables.

Correlated gluonic hot spots meet symmetric cumulants data at LHC energies

We present a systematic study on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, their size and their number on the symmetric cumulant SC(2,3), at the eccentricity level, within a Monte Carlo Glauber framework [J.L. Albacete, H. Petersen, A. Soto-Ontoso, Symmetric cumulants as a probe of the proton substructure at LHC energies, Phys. Lett. B778 (2018) 128–136. arXiv:1707.05592, doi:10.1016/j.physletb.2018.01.011]. When modeling the proton as composed by 3 gluonic hot spots, the most common assumption in the literature, we find that the inclusion of spatial correlations is indispensable to reproduce the negative sign of SC(2,3) in the highest centrality bins as dictated by data. Further, the subtle interplay between the different scales of the problem is discussed. To conclude, the possibility of feeding a 2+1D viscous hydrodynamic simulation with our entropy profiles is exposed.

Symmetric cumulants as a probe of the proton substructure at LHC energies

We present a systematic study of the normalized symmetric cumulants, NSC(n,m), at the eccentricity level in proton-proton interactions at s=13TeV within a wounded hot spot approach. We focus our attention on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, on this observable. We notice that the presence of short-range repulsive correlations between the hot spots systematically decreases the values of NSC(2,3) and NSC(2,4) in mid- to ultra-central collisions while increases them in peripheral interactions. In the case of NSC(2,3) we find that, as suggested by data, an anti-correlation of ε2 and ε3 in ultra-central collisions, i.e. NSC(2,3)<0, is possible within the correlated scenario while it never occurs without correlations when the number of gluonic hot spots is set to three. We attribute this fact to the decisive role of correlations on enlarging the probability of interaction topologies that reduce the value of NSC(2,3) and, eventually, make it negative. Further, we explore the dependence of our conclusions on the number of hot spots, the values of the hot spot radius and the repulsive core distance. Our results add evidence to the idea that considering spatial correlations between the subnucleonic degrees of freedom of the proton may have a strong impact on the initial state properties of proton-proton interactions [1].

Correlation effects in multiple small-angle neutron scattering at the surface layers of inhomogeneities

The influence of spatial correlations on the angular distribution of multiple small-angle neutron scattering (MSANS) at the surface layers of inhomogeneities is studied. Calculations are carried out by taking instrumental distortions into account when observing multiple small-angle neutron scattering by means of methods of a double-crystal diffractometer and a small-angle diffractometer with a position-sensitive detector. Within the framework of the eikonal approximation, the MSANS line is calculated, and the influence of the surface-layer thickness and the inhomogeneity concentration on its width is studied.

On the influence of spatial correlations on sound propagation in concentrated solutions of rigid particles

In a previous paper [J. Acoust. Soc. Am. 121, 3386-3387 (2007)], a self-consistent effective medium theory has been used to account for hydrodynamic interactions between neighboring rigid particles, which considerably affect the sound propagation in concentrated solutions. However, spatial correlations were completely left out in this model. They correspond to the fact that the presence of one particle at a given position locally affects the location of the other ones. In the present work, the importance of such correlations is demonstrated within a certain frequency range and particle concentration. For that purpose, spatial correlations are integrated in our two-phase formulation by using a closure scheme similar to the one introduced by Spelt et al. [''Attenuation of sound in concentrated suspensions theory and experiments," J. Fluid Mech. 430, 51-86 (2001)]. Then, the effect is shown through a careful comparison of the results obtained with this model, the ones obtained with different self-consistent approximations and the experiments performed by Hipp et al. ["Acoustical characterization of concentrated suspensions and emulsions. 2. Experimental validation," Langmuir, 18, 391-404 (2002)]. With the present formulation, an excellent agreement is reached for all frequencies (within the limit of the long wavelength regime) and for concentrations up to 30% without any adjustable parameter.

Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation

We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.

Influence of spatial correlations on the lasing threshold of random lasers

The lasing threshold of a random laser is computed numerically from a generic model. It is shown that spatial correlations of the disorder in the medium (i.e., dielectric constant) lead to an increase of the decay rates of the eigenmodes and of the lasing threshold. This is in conflict with predictions that such correlations should lower the threshold. While all results are derived for photonic systems, the computed decay rate distributions also apply to electronic systems.

Island-Size Distributions for Submonolayer Epitaxy: Rate Equations and Beyond

AbstractThe scanning tunnelling microscope has revolutionized the quantitative analysis of epitaxial phenomena. This, in turn, has spawned a huge theoretical effort aimed at analyzing various aspects of the morphology of growing surfaces. One of the most important general approaches to have emerged from this effort is based on the application of scaling concepts to epitaxial island-size distributions in the regime of submonolayer coverage prior to coalescence. We first discuss the analytical basis for scaling solutions to rate equations. In the limit of irreversible aggregation, a solution is obtained in terms of the capture numbers which agrees with previous work. For reversible aggregation, we identify a new quantity that may be regarded as a continuous analogue of a critical island size. We then examine the influence of spatial correlations by introducing a method for modeling epitaxial phenomena in terms of the motion of island boundaries, which is implemented numerically using the level set method. This island dynamics model is continuous in the lateral directions, but retains atomic scale discreteness in the growth direction. Several choices for the island boundary velocity are discussed and computations of the island dynamics model using the level set method are presented.

Influence of spatial correlations on crack bridging by frictional fibres

The effect of fibre interaction on matrix cracking in a unidirectional fibre-reinforced composite is analyzed. It is assumed that the matrix material contains a crack in a plane perpendicular to the fibres. Fibres, remaining intact, debond from the matrix and then act as bridging ligaments in the crack wake. The debonding process is accompanied by frictional sliding governed by a Coulomb friction law. Fibres are considered to be randomly located in the transverse plane. The fibre axial stress and longitudinal displacement are expressed in terms of the solution to a model problem for a single fibre in an ambient stress field due to all other fibres and applied load. The stress field produced by the other fibres is described using an ensemble averaging procedure. The radial distribution function g( r) that provides a quantitative measure of the correlations between the positions of different fibres is evaluated numerically from the Percus-Yevick equation for hard disks. The dependence of the fibre axial stress on the relative fibre-matrix displacement is examined for different values of the volume fraction of fibres. The resulting stress-displacement law is compared with results for other choices of the function g( r) and with a law given by a concentric cylinder model.

Influence of Spatial Correlations on Permeability and Connectivity of Sandstone

ABSTRACTSedimentary rocks have complicated permeability patterns arising from the geological processes that formed them. Here we address the longstanding question of how such patterns are generated. We also analize data on two sandstone samples from different geological environments, and find that the permeability fluctuations display long-range power-law correlations characterized by an exponent H. For both samples, we find H ≈ 0.82 – 0.90. These permeability fluctuations significantly affect the flow of fluids through the rocks.

On the influence of spatial correlations on the rate of chemical reactions in dense systems. II. Numerical results

The explicit expressions for the rate constant kf and kb of a dense system obtained in the preceding paper are investigated numerically. The pair correlation functions representing the spatial correlations are calculated from an associate nonreactive hard sphere system by means of the multicomponent Percus—Yevick equation. The rate constants are found to differ in their dependence on density and time up to an order of magnitude from the corresponding dilute gas value. The time behaviour of kf and kb was found to depend sensitively on a relation between the total volumes of the reactant and product molecules.

On the influence of spatial correlations on the rate of chemical reactions in dense gases. I. Quantum statistical theory

An approximate rate equation for a dense-gas chemical reaction of the type A + B ⇌ C + D is derived from first; principles starting from a hamiltonian formulated in terms of the field operators of the species. The rate equation considers the reactive binary collisions together with the spatial correlations between the molecules of the reactive pair the correlations being produced by the collisions of the surrounding molecules with the molecules of this pair. Simplifying the reaction mechanism the rate constants are written as a product of the dilute-gas rate constants times the pair distribution function which accounts for the spatial correlation.