Transverse Correlation Function Research Articles

Adopting molecular tagging velocimetry for high-resolution measurements of oscillating grid turbulence

AbstractSingle-component molecular tagging velocimetry (1c-MTV) experiments are conducted in an oscillating grid turbulence facility to systematically clarify the trade-offs between maximizing measurement dynamic range and minimizing measurement uncertainty. The primary aim is to obtain reliable turbulence data with the maximum possible vector resolution ($$\varDelta {x}_{1}$$ Δ x 1 ). Four optical magnifications ($$M{_{0}}$$ M 0 =0.11, 0.22, 0.45, 1.11) with four interframe time delay ($$\varDelta {t}$$ Δ t ) values, for each optical magnification case, ranging from 3 to 10 ms, are investigated. The grid oscillates with a frequency (f) of 3.2 and 4.1 Hz, and a single fixed stroke length (S) of 55 mm. The measurement quality is quantified using three important turbulence descriptors — the second-order transverse velocity correlation function $$(\langle {g(r)}\rangle )$$ ( ⟨ g ( r ) ⟩ ) , the second-order transverse velocity structure function $$([\Delta {_{g}u}]^2)$$ ( [ Δ g u ] 2 ) , and the turbulence energy dissipation rate ($$\langle \epsilon \rangle$$ ⟨ ϵ ⟩ ). Other descriptors such as the longitudinal integral length scale (l) and the longitudinal Taylor microscale ($${\lambda }$$ λ ) are also used to compare with reference values reported in literature. The degree of agreement with the reference values from literature, and insensitivity of the descriptor estimates to different MTV design parameters are used to determine the most robust means of obtaining high-resolution turbulence data from 1c-MTV. The experimental design parameters are contextualized using the Kolmogorov length ($${\eta }$$ η ), time ($${\tau _{\eta }}$$ τ η ), and velocity ($${u_{\eta }}$$ u η ) scales that are based on the most reliable $$\langle {\epsilon }\rangle$$ ⟨ ϵ ⟩ estimates from the current experiments. The pixel-displacement corresponding to $${u_{\eta }}$$ u η $$({\varDelta {x}{_{2}}{_{\eta }}})$$ ( Δ x 2 η ) describes the interdependencies between $${M_{0}}$$ M 0 and $$\varDelta {t}$$ Δ t . The data set with $${M_{0}}=0.45$$ M 0 = 0.45 ($${\eta =}18{\varDelta {x}_{1}}$$ η = 18 Δ x 1 for f=3.2 Hz, and $${\eta =}13{\varDelta {x}_{1}}$$ η = 13 Δ x 1 for f=4.1 Hz) represents the most reliable and the highest resolution case. This conclusion was deduced by taking the performance of all the turbulence descriptors into account. As far as the interframe time delay is concerned, $$\varDelta {t} \ge$$ Δ t ≥ 4 ms ($${\varDelta {x}{_{2}}{_{\eta }}}\ge 0.5 \text {pixels}$$ Δ x 2 η ≥ 0.5 pixels ) works well for all $${{M}_{0}}$$ M 0 . To the authors’ knowledge, the present study documents the first instance of a series of 1c-MTV experiments conducted for a systematic clarification of the nature of balancing the available dynamic range and the measurement uncertainty. Additionally, since the study involves turbulent flow with negligible mean-flow, it serves as an adequate representation of 1c-MTV performance in a three-dimensional flow.

Ab initio study of longitudinal and transverse dynamics, including fast sound, in molten UO2 and liquid Li–Pb alloys

The disparity between the masses of the two components in a binary liquid system can lead to the appearance of a peculiar phenomenon named “fast sound,” which was identified for the first time in Li4Pb several decades ago and later observed in other Li based alloys. However, the exact characteristics and nature of this phenomenon and the reasons behind its appearance have not totally been identified yet. In this work, we analyze the longitudinal and transverse current correlation functions of UO2, Li4Pb, and Li0.17Pb0.83, as obtained from ab initio molecular dynamics simulations. We find that fast sound appears to occur in the two former systems but not in the latter. Additionally, we discuss some of the properties of the liquid mixtures that may be related to the appearance (or absence) of the phenomenon, such as the composition, the polyhedral structure of the melt, and the type of bonding in the system.

Correlation functions for confined wormlike chains

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance.

Modulation instability of incoherent beams revisited.

We examine the spatial modulation instability (MI) of a partially incoherent laser beam. We show that the P < (a/rc)2P0 criterion of beam stability, with a laser peak power P, beam radius a, correlation radius rc, and critical power of self-focusing P0, is applicable only to a limited class of MIs, viz., MIs that can be described as instabilities of a pertinent transverse correlation function found as a solution to the evolution equation, where the expectation of the four-field-product nonlinear source term is factorized as a product of the field intensity and a two-point transverse correlation function. When extended to a more general class of MIs, field evolution analysis of partially coherent beams suggests that MIs can be attenuated, but never completely suppressed. We show that spatial incoherence can lower the MI-buildup rate, thus helping avoid MI-induced beam breakup in physical settings where the MI-buildup length lMI can be kept longer than the length of the nonlinear medium L. Because the lMI > L condition sets a limitation on the field intensity rather than the laser peak power, MI-induced beam breakup can be avoided, even at laser peak powers well above the critical power of self-focusing P0.

Disentanglement of hard and soft QCD processes using two-particle correlation functions

Transverse spherocity (S 0) has evolved as a powerful method to distinguish between soft and hard contributions in an event in small collision systems. We used the two-particle differential-number correlation functions (R 2) and transverse momentum correlation functions (P 2) of charged particles produced in pp collisions at TeV with the PYTHIA8 model to explore this phenomena. The Δφ projections of these correlation functions in different multiplicity and S 0 classes are discussed. We find that these correlation functions show different shapes and sizes in both near- and away-side with multiplicity and S 0 classes. We observe a strong correlation in the near- and away-side of these correlation functions for jetty-like (hard QCD processes), which become weaker for isotropic (soft QCD processes) in spherocity classes as compared to multiplicity classes. Finally, it is observed that S 0 should be a good observable as compared to multiplicity to disentangle hard and soft QCD processes in a small collision system.

Inertial dynamics and equilibrium correlation functions of magnetization at short times

The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series expansion of the correlation functions and the estimation of the expansion coefficients. This method significantly reduces the complexity of analysis of equilibrium correlation functions. Analytical expressions are derived for the first three coefficients for the longitudinal and transverse correlation functions for the uniaxial magnetocrystalline anisotropy of ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting cases of very strong and negligibly weak external longitudinal fields are considered. The Gordon sum rule for inertial magnetization dynamics is discussed. In addition, we show that finite analytic series can be used as a simple and satisfactory approximation for the numerical calculation of correlation functions at short times.

An Orbital Free Ab-initio Molecular Dynamics Study of Liquid Pt for Static and Dynamic Properties

Using the orbital free ab-initio molecular dynamics (OF-AIMD) simulation scheme we have examined the static and dynamic properties of liquid Pt at the thermodynamic state near to its melting point. In this simulation scheme, the Hohenberg and Kohn orbital free density functional theory (OF-DFT) has been employed. In OF-DFT, we have estimated the electron-ion interaction by a local pseudopotential and also controlled the exchange-correlation energy functional by using the local density approximation (LDA). The static properties, for instance, static structure factor, S(q), pair correlation function, g(r), coordination number, Nc, and isothermal compressibility, κT, are examined. Using the familiar single-particle dynamics, the self-diffusion coefficient and self-intermediate scattering function are studied. It is found that the self-intermediate scattering function is controlled by the selfdiffusion coefficient. While for studying the collective dynamics of the system, we have calculated velocity of sound from the longitudinal dispersion relation and shear viscosity from the transverse current correlation function, JT(q, t). The OF-AIMD results are nicely fit with the theoretical and experimental results accessible to us for comparison. Dhaka Univ. J. Sci. 69(3): 179-185, 2022 (June)

Differential two-particle number and momentum correlations with the AMPT, UrQMD, and EPOS models in Pb-Pb collisions at sNN=2.76 TeV

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential number correlation functions, $R_{2} \left( \Delta \eta, \Delta \varphi \right)$, and transverse momentum correlation functions, $P_2 \left( \Delta \eta, \Delta \varphi \right)$ of charged particles produced in \PbPb\ collisions at the LHC centre-of-mass energy $\sqrt{s_{\rm NN}} =$ 2.76 TeV with the UrQMD, AMPT and EPOS models. Model predictions for $R_2$ and $P_2$ correlation functions are presented for inclusive charged hadrons ($h^\pm$) in selected transverse momentum ranges and with full azimuthal coverage in the pseudorapidity range $|\eta|< 1.0$. We compare these predictions for the strength, shape, and particularly the width of the correlation functions with recent measurements of these observables by the ALICE collaboration. Our analysis indicate that comparative studies of $R_2$ and $P_2$ correlation functions provide valuable insight towards the understanding of particle production in Pb--Pb collisions. We find, in particular, that these models have quantitatively different predictions for these three observables but none reproduce the measured correlation functions reported by the ALICE collaboration. Accounting for quantum number conservation in models, particularly charge conservation, is mandatory to reproduce the detailed measurements of number and transverse momentum correlation functions.

Transverse Viscous Transport in Classical Solid States.

The transverse velocity time correlation function C[over ˜]_{T}(k,ω) with k and ω being the wave number and the frequency, respectively, is a fundamental quantity in determining the transverse mechanical and transport properties of materials. In ordinary liquids, a nonzero value of C[over ˜]_{T}(k,0) is inevitably linked to viscous material flows. Even in solids where significant material flows are precluded due to almost frozen positional degrees of freedom, our molecular dynamics simulations reveal that C[over ˜]_{T}(k,0) takes a nonzero value, whereby the time integration of the velocity field shows definite diffusive behavior with diffusivity C[over ˜]_{T}(k,0)/3. This behavior is attributed to viscous transport accompanying a small random convection of the velocity field (the inertia effect), and the resultant viscosity is measurable in the Eulerian description: the constituent particles that substantially carry momenta fluctuate slightly around their reference positions. In the Eulerian description, the velocity field is explicitly associated with such fluctuating instantaneous particle positions, whereas in the Lagrangian description, this is not the case. The present study poses a fundamental problem for continuum mechanics: reconciling liquid and solid descriptions in the limit of the infinite structural relaxation time.

Azimuthal dependence of two-particle transverse momentum current correlations

Two-particle transverse momentum correlation functions are a powerful technique for understanding the dynamics of relativistic heavy-ion collisions. Among these, the transverse momentum correlator G_{2}left( varDelta eta ,varDelta varphi right) is of particular interest for its potential sensitivity to the shear viscosity per unit of entropy density eta /s of the quark-gluon plasma formed in heavy-ion collisions. We use the UrQMD, AMPT, and EPOS models for Au–Au at sqrt{s_mathrm{NN}} = 200 GeV and Pb–Pb at sqrt{s_mathrm{NN}} = 2760 GeV to investigate the long range azimuthal dependence of G_{2}left( varDelta eta ,varDelta varphi right) , and explore its utility to constrain eta /s based on charged particle correlations. We find that the three models yield quantitatively distinct transverse momentum Fourier harmonics coefficients a^{p_mathrm{T}}_{n}. We also observe these coefficients exhibit a significant dependence on eta /s in the context of the AMPT model. These observations suggest that exhaustive measurements of the dependence of G_{2}left( varDelta varphi right) with collision energy, system size, collision centrality, in particular, offer the potential to distinguish between different theoretical models and their underlying assumptions. Exhaustive analyses of G_{2}left( varDelta varphi right) obtained in large and small systems should also be instrumental in establishing new constraints for precise extraction of eta /s.

Effect of the interaction of corrosion pits among multiple tensile rebars on the reliability of RC structures: Experimental and numerical investigation

The deterioration of reinforced concrete (RC) structures due to chloride-induced corrosion is not spatially uniform because of the spatial variability related to material properties and environmental stressors. This variation has a substantial effect on the reliability of RC structures. However, few experimental studies have focused on the effect of the interaction of corrosion pits among tensile rebars on the reliability of RC structures. Therefore, in this paper, an experimental procedure that incorporates X-ray and digital image processing techniques was conducted on RC slab specimens subjected to accelerated corrosion. Using the experimental results, the parameter of the transverse correlation function of steel weight loss distributions was estimated to investigate how the corrosion pits in corroded rebars are correlated. Based on the experimentally obtained model parameters, the spatial steel weight loss distributions were simulated by spectral representation method. A three-dimensional (3D) nonlinear finite element (FE) analysis of RC structures with simulated steel weight loss distributions was conducted to obtain the ultimate bending capacity of RC structures. In an illustrative example, the effect of the transverse correlation among steel weight loss distributions of multiple tensile rebars on the failure probability of RC girders was quantified.

Towards structural imaging using seismic ambient field correlation artefacts

SUMMARY Correlations of the ambient seismic field recorded by seismic stations carry information about the wave propagation between the stations. They also contain information about the ambient field—both the source of the ambient field, and sources of scattering that contribute to it. The waves that comprise the ambient field are subject to scattering due to the heterogeneous Earth, which can generate supplementary arrivals on the correlation functions. We use these effects to locate sources of signals linked to scattering. For this analysis, we use correlation functions computed from continuous signals recorded between 2013 and 2015 by a line of seismic stations in Central California. We identify spurious arrivals on the Vertical to Vertical and Transverse to Transverse correlation functions and use array analysis to map the source of scattering, which is linked to strong structural variations in the Coast ranges and at the border of the Great Valley.

Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime

We derive an explicit expression for the leading term in the long-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This expression is valid for all nonzero finite temperatures and for all magnetic fields below the saturation threshold. It is obtained here by means of a straightforward term-by-term analysis of a thermal form factor series, derived in previous work, and demonstrates the usefulness of the latter.

High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain

We analyze the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm determinant of an integrable integral operator. This connects it with a matrix Riemann-Hilbert problem. We express the correlation function in terms of the solution of the matrix Riemann-Hilbert problem. The matrix Riemann-Hilbert problem is then solved asymptotically in the high-temperature limit. This allows us to obtain the leading high-temperature contribution to the two-point correlation function at any fixed space-time separation.

Pressure evolution of transverse collective excitations in liquid Al along the melting line.

Evolution of structure and dynamics of liquid Al with pressure along the melting line up to 300 GPa has been studied by means of ab initio molecular dynamics simulations. An analysis of structural properties shows that liquid Al undergoes uniform compression with pressure associated with a competition of the existing icosahedral local order with bcc ordering above 200 GPa. Dispersion of collective excitations indicates the presence of two branches of transverse nonpropagative modes in the second pseudo-Brillouin zone. Under pressure, the second high-frequency branch manifests as the second peak position in transverse current correlation functions, while, for ambient pressure, it corresponds to a smeared-out high-frequency shoulder. We report a correspondence of the peak locations in vibrational density of states with these two transverse collective excitations as well as their linear evolution with density.

Effect of centrality bin width corrections on two-particle number and transverse momentum differential correlation functions

Two-particle number and transverse momentum differential correlation functions are powerful tools for unveiling the detailed dynamics and particle production mechanisms involved in relativistic heavy-ion collisions. Measurements of transverse momentum correlators $P_2$ and $G_2$, in particular, provide added information not readily accessible with better known number correlation functions $R_2$. However, it is found that the $R_2$ and $G_2$ correlators are somewhat sensitive to the details of the experimental procedure used to measure them. They exhibit, in particular, a dependence on the collision centrality bin width, which may have a rather detrimental impact on their physical interpretation. A technique to correct these correlators for collision centrality bin-width averaging is presented. The technique is based on the hypothesis that the shape of single- and pair- probability densities vary slower with collision centrality than the corresponding integrated yields. The technique is tested with Pb-Pb simulations based on the HIJING and ultrarelativistic quantum molecular dynamics models and shown to enable a precision better than 1% for particles in the kinematic range $0.2 \leq p_{\rm T} \leq 2.0$ GeV/$c$.

Time correlation functions of simple liquids: A new insight on the underlying dynamical processes.

Extensive molecular dynamics simulations of liquid sodium have been carried out to evaluate correlation functions of several dynamical quantities. We report the results of a novel analysis of the longitudinal and transverse correlation functions obtained by evaluating directly their self- and distinct contributions at different wavevectors k. It is easily recognized that the self-contribution remains close to its k → 0 limit, which turns out to be exactly the autocorrelation function of the single particle velocity. The wavevector dependence of the longitudinal and transverse spectra and their self- and distinct parts is also presented. By making use of the decomposition of the velocity autocorrelation spectrum in terms of longitudinal and transverse parts, our analysis is able to recognize the effect of different dynamical processes in different frequency ranges.

Fractional Time Fluctuations in Viscoelasticity: A Comparative Study of Correlations and Elastic Moduli.

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time derivatives and then introduce time fractional derivatives in their equations of motion and calculate the corresponding fractional correlation function. We find that the magnitude of the fractional correlation is always lower than the non-fractional one and decays more rapidly. The relationship between the fractional loss modulus and is also calculated analytically. The difference between the values of for two specific viscoelastic fluids is quantified. Our model calculation shows that the fractional effects on this measurable quantity may be three times as large as compared with its non-fractional value. The fact that the dynamic shear modulus is related to the light scattering spectrum suggests that the measurement of this property might be used as a suitable test to assess the effects of temporal fractional derivatives on a measurable property. Finally, we summarize the main results of our approach and emphasize that the eventual validity of our model calculations can only come from experimentation.

A note on hydrodynamics from dissipative particle dynamics

We calculate current correlation functions (CCFs) of dissipative particle dynamics (DPD) and compare them with results of molecular dynamics (MD) and solutions of linearized hydrodynamic equations. In particular, we consider three versions of DPD, the empirical/classical DPD, coarse-grained (CG) DPD with radial-direction interactions only and full (radial, transversal, and rotational) interactions between particles. To facilitate quantitative discussions, we consider specifically a star-polymer melt system at a moderate density. For bonded molecules, it is straightforward to define the CG variables and to further derive CG force fields for DPD within the framework of the Mori-Zwanzig formalism. For both transversal and longitudinal current correlation functions (TCCFs and LCCFs), we observe that results of MD, DPD, and hydrodynamic solutions agree with each other at the continuum limit. Below the continuum limit to certain length scales, results of MD deviate significantly from hydrodynamic solutions, whereas results of both empirical and CG DPD resemble those of MD. This indicates that the DPD method with Markovian force laws possibly has a larger applicability than the continuum description of a Newtonian fluid. This is worth being explored further to represent generalized hydrodynamics.

Rapidity dependence of proton cumulants and correlation functions

The dependence of multi-proton correlation functions and cumulants on the acceptance in rapidity and transverse momentum is studied. We find that the preliminary data of various cumulant ratios are consistent, within errors, with rapidity and transverse momentum independent correlation functions. However, rapidity correlations which moderately increase with rapidity separation between protons are slightly favored. We propose to further explore the rapidity dependence of multi-particle correlation functions by measuring the dependence of the integrated reduced correlation functions as a function of the size of the rapidity window.