Space Correlation Function Research Articles

Comparison between velocity- and vorticity-based POD methods in a turbulent wake

In this paper, the velocity-based POD and the vorticity-based POD have been systematically compared in three characteristic regions of the flow downstream of a two-dimensional circular cylinder, namely the near, intermediate and far wakes. The two-point space correlation function is used to determine which of the two methods is better suited for extracting the large-scale flow structures based on the repartition of energy among the different POD modes. It is found that the POD, based on the lateral velocity fluctuation v, leads to the most optimum extraction in all three flow regions, while the vorticity-based POD is only effective in the near and intermediate wakes. Based on two-point space correlation functions, a scenario is proposed for the application of POD to the present two-dimensional wake .

Aging at the spin-glass/ferromagnet transition: Monte Carlo simulations using graphics processing units

We study the the non-equilibrium ageing behaviour of the +/-J Edwards-Anderson model in three dimensions for samples of size up to N=128^3 and for up to 10^8 Monte Carlo sweeps. In particular we are interested in the change of the ageing when crossing from the spin-glass phase to the ferromagnetic phase. The necessary long simulation times are reached by employing a CUDA-based GPU implementation, which allows for single-spin flip times as small as 8ps. We measure typical spin glass correlation functions in space and time to determine the growing length scale and extract the constituting exponents. We observe a clear signature of the disorder-driven equilibrium transition in the non-equilibrium behavior.

Space-time coherence of low-frequency acoustic waves in a shallow-water area with fluctuating parameters

The space-time correlations of narrowband acoustic signals propagating in shallow water are theoretically investigated. It is assumed that acoustic field fluctuations are caused by the combined effect of wind waves and random internal waves. The acoustic field is represented as a superposition of two components: one of them is characterized by relatively small space-time scales and is formed by wind waves, whereas the other is characterized by large scales and is caused by both random internal waves and wind waves. A numerical simulation is performed for space and time correlation functions of tone signals under typical conditions of the Barents Sea. It is demonstrated that the results of numerical calculations are in good agreement with experimental data.

Nonequilibrium spatiotemporal formation of the Kondo screening cloud on a lattice

We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high precision density matrix renormalization group results for the interacting single impurity Anderson model we discuss the real time evolution after a quantum quench in the impurity-reservoir hybridization using time evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of non-local correlation functions in the spin- and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length-scales show good agreement with existing results, as do local time dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a "light cone" moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power law decays of the correlation functions in space, with time and interaction strength independent exponents.

The IR-resummed Effective Field Theory of Large Scale Structures

We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in ΛCDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to k∼ 0.6 h Mpc−1 to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.

Theoretical Study of the Protein Folding Dynamics from a Time Correlation Function Approach

With the development of experimental approaches such as single molecule experiments and the advances in computer simulation techniques (including the emerge of the specialized hardware Anton), the knowledge of protein folding mechanism, especially in the microsecond regime, has greatly deepened over the last few decades. While the sub-millisecond to millisecond long simulations at atomic detail can be extremely insightful, extracting the events mined in the high dimensional trajectory and understanding the dynamics in detail is still a challenging issue; especially how to interpret such high dimensional, long time-series data is not well established.We propose a protocol to extract the “slow” modes directly from the trajectory with the use of the time correlation functions in the high dimensional space. We apply the current approach to a previously reported 100 μs trajectory of the FiP35 WW domain (Science 330 (2010), 341-346). We show that the slowest mode extracted successfully describes the folding/unfolding event with the time scale of ∼8 μs, consistent with previous studies. In addition, we find that the formation of only the longer β-sheet seems to be the dominant intermediate state along the folding pathway, and furthermore identify a misfolded state which lasts up to a few μs. The time scale of the latter two events are found to be a few hundred ns, respectively. These results show that by using the time-series information, the dynamics of protein folding can be understood in greater detail.

The hydrate shell of a Cl− Ion in a planar nanopore, structure

The formation of nanoelectrolyte is simulated by the Monte-Carlo method in the stage of penetration of solvent molecules into a nanopore that contains one ion. The detailed model of many-body intermolecular interactions including covalent interactions and the effects of bond saturation and excessive charge transfer is used. The molecular structure of the chloride-anion hydrate shell growing from water vapors at 298 K inside planar model pores with smooth walls and the width of 0.5 and 0.7 nm is analyzed. The maxima of the space correlation function ion-molecule are not shifted in the pore. The pore induces changes mainly in the orientational molecular order of the system. The effect of molecules that “creep” over the pore surface in the ion field is revealed. The earlier observed effect of ion displacement from its hydrate shell to the periphery of the molecular cluster is reproduced stably.

Understanding the atomic-level Green-Kubo stress correlation function for a liquid through phonons in a model crystal

In order to gain insight into the connection between the vibrational dynamics and the atomic-level Green-Kubo stress correlation function in liquids, we consider this connection in a model crystal instead. Of course, vibrational dynamics in liquids and crystals are quite different and it is not expected that the results obtained on a model crystal should be valid for liquids. However, these considerations provide a benchmark to which the results of the previous molecular dynamics simulations can be compared. Thus, assuming that vibrations are plane waves, we derive analytical expressions for the atomic-level stress correlation functions in the classical limit and analyze them. These results provide, in particular, a recipe for analysis of the atomic-level stress correlation functions in Fourier space and extraction of the wave-vector and frequency-dependent information. We also evaluate the energies of the atomic-level stresses. The energies obtained are significantly smaller than the energies previously determined in molecular dynamics simulations of several model liquids. This result suggests that the average energies of the atomic-level stresses in liquids and glasses are largely determined by the structural disorder. We discuss this result in the context of equipartition of the atomic-level stress energies. Analysis of the previously published data suggests that it is possible to speak about configurational and vibrational contributions to the average energies of the atomic-level stresses in a glass state. However, this separation in a liquid state is problematic. We also introduce and briefly consider the atomic-level transverse current correlation function. Finally, we address the broadening of the peaks in the pair distribution function with increase of distance. We find that the peaks' broadening (by $\ensuremath{\approx}40%$) occurs due to the transverse vibrational modes, while contribution from the longitudinal modes does not change with distance.

Isolating relativistic effects in large-scale structure

We present a fully relativistic calculation of the observed galaxy number counts in the linear regime. We show that besides the density fluctuations and redshift-space distortions, various relativistic effects contribute to observations at large scales. These effects all have the same physical origin: they result from the fact that our coordinate system, namely the galaxy redshift and the incoming photons’ direction, is distorted by inhomogeneities in our Universe. We then discuss the impact of the relativistic effects on the angular power spectrum and on the two-point correlation function in configuration space. We show that the latter is very well adapted to isolate the relativistic effects since it naturally makes use of the symmetries of the different contributions. In particular, we discuss how the Doppler effect and the gravitational redshift distortions can be isolated by looking for a dipole in the cross-correlation function between a bright and a faint population of galaxies.

Scattering Studies for Two-Dimensional Exponential Correlation Textured Rough Surfaces Using Small-Slope Approximation Method

Two-dimensional exponential correlation rough surfaces characterized by textures are combined with the small-slope approximation (SSA) method to comparatively study electromagnetic (EM) scattering features of textured surfaces. The normalized copolarized radar cross section from 2-D exponential correlation rough surfaces characterized by stripe texture and block texture, respectively, is analyzed. Several numerical results show the effects of incident angle, texture angle, correlation length, and root-mean-square height on the copolarimetric scattering from the textured rough surface. The validity of the SSA method is verified by comparisons of theoretical value and measured data. Moreover, normalized amplitude distributions of backscattering fields from cells in a scene are studied through its statistical distribution and space correlation function, which are particularly useful for analysis and simulation of remote sensing images. Finally, based on the statistical distribution and space correlation function, the zero memory nonlinear transformation method is utilized to simulate EM scattering from very large scenes. The simulated scene coincides with the original one quite well.

Inter-particle correlations in a hard-sphere colloidal suspension with polymer additives investigated by Spin Echo Small Angle Neutron Scattering (SESANS)

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages.

SEA QUARK TRANSVERSE MOMENTUM DISTRIBUTIONS AND DYNAMICAL CHIRAL SYMMETRY BREAKING

Recent theoretical studies have provided new insight into the intrinsic transverse momentum distributions of valence and sea quarks in the nucleon at a low scale. The valence quark transverse momentum distributions ([Formula: see text]) are governed by the nucleon's inverse hadronic size R-1 ~ 0.2 GeV and drop steeply at large pT. The sea quark distributions ([Formula: see text]) are in large part generated by non–perturbative chiral–symmetry breaking interactions and extend up to the scale ρ-1 ~ 0.6 GeV. These findings have many implications for modeling the initial conditions of perturbative QCD evolution of TMD distributions (starting scale, shape of pT distributions, coordinate–space correlation functions). The qualitative difference between valence and sea quark intrinsic pT distributions could be observed experimentally, by comparing the transverse momentum distributions of selected hadrons in semi–inclusive deep–inelastic scattering, or those of dileptons produced in pp and [Formula: see text] scattering.

Particle clustering in Monte Carlo criticality simulations

Strong space and cycle correlations affecting the neutron flux have been recently reported to occur in Monte Carlo criticality simulations of pressurized water reactors pin-cells with reflective boundary conditions: when the system size is large, neutrons are observed to gather together and form ‘clusters’ that wander around in space over many cycles. In most cases, the outcome of such clustering is that simulations display wild fluctuations, largely exceeding those expected around the equilibrium distribution. In this paper, we analyze the reasons behind the emergence of these phenomena: we show that the key mechanism is due to the asymmetry between neutron disappearance being uniformly distributed along the pin-cell, and neutron generation being localized at fission sites (i.e., only next to a parent particle). An explanation is provided by resorting to a simplified Brownian transport model coupled with a Galton–Watson birth and death process, which is sufficient to retain the essential features observed in realistic Monte Carlo simulations. An empirical space correlation function is proposed as a diagnostic tool for detecting clustering in criticality simulations.

Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model

We present a multireference configuration mixing scheme for describing ground and excited states, with well-defined spin and space-group symmetry quantum numbers, of the one-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each state is expanded in terms of nonorthogonal and variationally determined symmetry-projected configurations. The results for lattices up to 30 and 50 sites compare well with the exact Lieb-Wu solutions as well as with results from other state-of-the-art approximations. In addition to spin-spin correlation functions in real space and magnetic structure factors, we present results for spectral functions and density of states computed with an Ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the systems with ${N}_{e}$ and ${N}_{e}\ifmmode\pm\else\textpm\fi{}1$ electrons. The intrinsic symmetry-broken determinants resulting from the variational calculations have rich structures in terms of defects that can be regarded as basic units of quantum fluctuations. Given the quality of the results here reported, as well as the parallelization properties of the considered scheme, we believe that symmetry-projection techniques, which have found ample applications in nuclear structure physics, deserve further attention in the study of low-dimensional correlated many-electron systems.

Local electronic nematicity in the two-dimensional one-band Hubbard model

Nematicity is a well-known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen in many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high Tc superconductors have shown that even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional one-band Hubbard model provides strong support for the recent experimental results on local rotational C4 symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity.

Capillarylike fluctuations of a solid-liquid interface in a noncohesive granular system

One of the most noticeable collective motion of noncohesive granular matter is clustering under certain conditions. In particular, when a quasi-two-dimensional monolayer of monodispersed noncohesive particles is vertically vibrated, a solid-liquid-like transition occurs when the driving amplitude exceeds a critical value. Here the physical mechanism underlying particle clustering relies on the strong interactions mediated by grain collisions, rather than on grain-grain cohesive forces. In average, the solid cluster resembles a drop, with a striking circular shape. We experimentally investigate the coarse-grained solid-liquid interface fluctuations, which are characterized through the static and dynamic correlation functions in the Fourier space. These fluctuations turn out to be well described by the capillary wave theory, which allows us to measure the solid-liquid interface surface tension and mobility once the granular "thermal" kinetic energy is determined. Despite that the system is strongly out of equilibrium and that the granular temperature is not uniform, there is energy equipartition at the solid-liquid interface, for a relatively large range of angular wave numbers. Furthermore, both surface tension and mobility are consistent with a simple order of magnitude estimation considering the characteristic energy, length, and time scales, which is very similar to what can be done for atomic systems.

Fitting methods for baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9

We describe fitting methods developed to analyze fluctuations in the Lyman-α forest and measure the parameters of baryon acoustic oscillations (BAO). We apply our methods to BOSS Data Release 9. Our method is based on models of the three-dimensional correlation function in physical coordinate space, and includes the effects of redshift-space distortions, anisotropic non-linear broadening, and broadband distortions. We allow for independent scale factors along and perpendicular to the line of sight to minimize the dependence on our assumed fiducial cosmology and to obtain separate measurements of the BAO angular and relative velocity scales. Our fitting software and the input files needed to reproduce our main BOSS Data Release 9 results are publicly available.

Convolution Lagrangian perturbation theory for biased tracers

We present a new formulation of Lagrangian perturbation theory which allows accurate predictions of the real- and redshift-space correlation functions of the mass field and dark matter halos. Our formulation involves a non-perturbative resummation of Lagrangian perturbation theory and indeed can be viewed as a partial resummation of the formalism of Matsubara (2008a,b) in which we keep exponentiated all of the terms which tend to a constant at large separation. One of the key features of our method is that we naturally recover the Zel'dovich approximation as the lowest order of our expansion for the matter correlation function. We compare our results against a suite of N-body simulations and obtain good agreement for the correlation functions in real-space and for the monopole correlation function in redshift space. The agreement becomes worse for higher multipole moments of the redshift-space, halo correlation function. Our formalism naturally includes non-linear bias and explains the strong bias-dependence of the multipole moments of the redshift-space correlation function seen in N-body simulations.

Hydrodynamic correlations in multiparticle collision dynamics fluids

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales.

Phase-sensitive detection for unconventional Bose-Einstein condensation

We propose a phase-sensitive detection scheme to identify the unconventional ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ symmetry of the condensate wave functions of bosons, which have already been proposed and realized in high bands in optical lattices. Using the impulsive Raman operation combined with time-of-flight imaging, the off-diagonal correlation functions in momentum space give rise to the relative phase information between different components of condensate wave functions. This scheme is robust against the interaction and interband effects, and provides evidence of unconventional Bose-Einstein condensations with nontrivial condensation symmetries.