Large Correlation Length Research Articles

A diffuse interface approach to injection-driven flow of different miscibility in heterogeneous porous media

Miscible and immiscible injection flows in heterogeneous porous media, for which the permeability is characterized by a log Gaussian distribution, are simulated by a robust diffuse-interface formulation. The robust numerical method enables direct qualitative and quantitative comparisons regarding pattern formations in various fluid miscibility conditions. For miscible injections, the typical size of fingering structures depends strongly on the correlation length and forms tapered fingers with sharper tips. On the other hand, the typical size of immiscible fingers is affected less significantly by the permeability heterogeneity, and wide spreading tips are retained in the fingering patterns. Prominence of fingering instability is quantitatively evaluated by the channeling width and the interfacial length. The channeling width shows strong and monotonic dependences on the heterogeneous variance. On the contrary, maximum channeling width occurs at intermediate correlation length due to local resonant effect between the faster penetrating fingers and permeability heterogeneity. On the other hand, effects of the correlation length and the permeability variance on the interfacial lengths are generally consistent. Longer interfacial length is perturbed by smaller correlation length or higher variance. Interesting invariant evolutions of interfacial lengths are revealed regardless of the permeability variance in sufficiently large correlation length under all miscibility conditions. In addition, the regime of slower growth of interfacial length at later times experimentally observed in homogeneous miscible injection is verified in heterogeneous porous media as well.

IDFT numerical simulation method for Gaussian rough surface with relatively large correlation length

A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir’s method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir’s method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.

Long-range correlations in glasses and glassy fluids

We argue that the existence of a non-decaying part of the self-intermediate scattering function implies a small wave-vector divergence of a four-point structure factor defined in terms of the microscopic self-intermediate scattering function. This divergence indicates long-range correlations of density fluctuations in direct space. We show that a signature of the divergence and the long-range correlations can be observed in computer simulations of glasses. Interestingly, remnants of this divergence can be easily observed in computer simulations of supercooled fluids. They manifest themselves as transient dynamic correlations with a very large correlation length; much larger than the correlation length characterizing the size of dynamic heterogeneities.

Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length $L$ compared with the acoustic wavelength, the specularity reduction is given by $4\eta^2k^2$, where $\eta$ is the RMS roughness and $k$ is the acoustic wavevector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to $\eta^2k^4L^2$, with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of $L$. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.

Discovery of an overdensity of Lyman alpha emitters around a z ∼ 4 QSO with the Large Binocular Telescope

Measurements of QSO clustering in the SDSS show that $\mathrm{z}>4$ QSOs are some of the most highly biased objects in the universe. Their large correlation lengths of $r_0 \sim 20h^{-1}$Mpc are comparable to the most massive clusters of galaxies in the universe today and suggest that these QSOs may mark the locations of massive cluster progenitors at high redshift. We report the discovery of an overdensity of LBGs around QSO SDSSJ114514.18+394715.9 as part of our survey to identify Lyman-Break galaxies (LBGs) around luminous $\mathrm{z}\sim4$ QSOs. In this field three of the eight LBGs with secure redshifts are consistent with the redshift of the QSO. We find that the likelihood that this is merely an apparent overdensity due to the chance selection of field galaxies is only 0.02%, based on comparisons to simulations and our modeled selection efficiency. Overall, our survey finds four of the 15 LBGs with secure redshifts are consistent with the redshifts of their respective QSOs, which is consistent with luminous QSOs residing in larger haloes.

Critical behavior in spherical and hyperbolic spaces

We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: d-dimensional spheres and hyperboloids. In the first part of the paper, by applying the Ginzburg criterion, we find that for a large correlation length the Gaussian approximation is valid on the hyperboloid for any dimension d ⩾ 2, while it is not trustable on the sphere for any dimension. This is understood in terms of various notions of the effective dimension, such as the spectral and Hausdorff dimension. In the second part of the paper, we apply functional renormalization group methods to develop a different perspective on such phenomena and to deduce them from a renormalization group analysis. By making use of the local potential approximation, we discuss the consequences of having a fixed scale in the renormalization group equations. In particular, we show that in the case of spheres there is no true phase transition, as symmetry restoration always occurs at large scales. In the case of hyperboloids, the phase transition is still present, but as the only true fixed point is the Gaussian one, mean field exponents are valid also in dimensions lower than four.

Entanglement entropy of non-unitary conformal field theory

Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as , where is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ( with N nilpotent), then there is an additional term proportional to . These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

X-ray study of femtosecond structural dynamics in the 2D charge density wave compound 1T-TaS2

1T-TaS2 is a 2D metallic compound which undergoes a series of electronically driven phase transitions toward charge density wave and Mott phases. Its intricate electron–phonon interactions and electron–electron correlations have been promising peculiar out-of-equilibrium dynamics. In this paper, we provide the first direct information on the atomic structure response to an ultra-fast infrared laser pulse in the commensurate phase of 1T-TaS2, by using femtosecond time-resolved X-ray diffraction. We show that ultra-fast excitation with near-infrared photons drives a displacive excitation of the amplitude mode of the commensurate charge density wave. About 3ps after laser excitation, the system reaches a new, photo-induced state that is maintained for at least 10ps. We give evidence that this long-lived state exhibits the same structural modulation as in the thermodynamically stable commensurate phase, with a large correlation length. Only the average amplitude of the modulation is found to decrease. We propose that the long-lived state is formed from the commensurate phase by reducing the modulation amplitude on few superlattice nodes. The underlying mechanism proposed is the annihilation of self-trapped polarons.

Ambient magnetic field amplification in shock fronts of relativistic jets: an application to GRB afterglows

Strong downstream magnetic fields of order of $\sim 1$G, with large correlation lengths, are believed to cause the large synchrotron emission at the afterglow phase of gamma ray bursts (GRBs). Despite of the recent theoretical efforts, models have failed to fully explain the amplification of the magnetic field, particularly in a matter dominated scenario. We revisit the problem by considering the synchrotron emission to occur at the expanding shock front of a weakly magnetized relativistic jet over a magnetized surrounding medium. Analytical estimates and a number of high resolution 2D relativistic magneto-hydrodynamical (RMHD) simulations are provided. Jet opening angles of $\theta = 0^{\circ} - 20^{\circ}$, and ambient to jet density ratios of $10^{-4} - 10^2$ were considered. We found that most of the amplification is due to compression of the ambient magnetic field at the contact discontinuity between the reverse and forward shocks at the jet head, with substantial pile-up of the magnetic field lines as the jet propagates sweeping the ambient field lines. The pile-up is maximum for $\theta \rightarrow 0$, decreasing with $\theta$, but larger than in the spherical blast problem. Values obtained for certain models are able to explain the observed intensities. The maximum correlation lengths found for such strong fields is of $l_{\rm corr} \leq 10^{14}$ cm, $2 - 6$ orders of magnitude larger than the found in previous works.

Finite-size scaling analysis of pseudocritical region in two-dimensional continuous-spin systems.

At low temperatures, the two-dimensional continuous-spin systems exhibit large correlation lengths. Some of them show the Berezinskii-Kosterlitz-Thouless-like transitions, and some others show pseudocritical behaviors for which correlation lengths are extremely large but finite. To distinguish pseudo and genuine critical behaviors, it is important to understand the nature of spin-spin correlations and topological defects at low temperatures in continuous-spin systems. In this paper, I develop a finite-size scaling analysis which is suitable for distinguishing the critical behavior and its applications to the two-dimensional XY, Heisenberg, and RP(2) models.

Transition between two Kosterlitz-Thouless phases in Sc-doped TiOCl

The compound TiOCl is a quasi-1-dimensional (1D) quantum magnet (Seidel et al., 2003). Upon cooling, TiOCl undergoes a phase transition at Tc2 = 90 K towards a state with incommensurate magnetic order, followed by a second phase transition at Tc1 = 67 K towards a spin-Peierls state (Seidel et al., 2003; Shaz et al., 2005; van Smaalen et al., 2005). Both low-temperature phases involve structural distortions that have been characterized by x-ray diffraction. The absence of any phase transitions has been reported for scandium-doped TiOCl with doping levels 0.01 < x < 0.1 for ScxTi1-xOCl (Glancy et al., 2008, 2010; Zhang et al., 2010; Aczel et al., 2011). We have synthesized ScxTi1-xOCl for x = 0.005. Based on temperature-dependent x-ray diffraction experiments and specific-hear measurements, we have found that the x = 0.005 compound transforms into incommensurate and spin-Peierls-like phases on cooling. Despite apparent large correlation lengths, these phases lack long-range order. A sluggish transformation is thus found between states of ScxTi1-xOCl that support different kinds of fluctuations.

Neutron diffuse scattering of (1 − x)(Na0.5Bi0.5)TiO3–xBaTiO3 relaxor ferroelectric single crystals

Peculiar L-shaped diffuse streaks along pc were observed in (Na 0.5 Bi 0.5 )TiO 3 (NBT) below the Burns temperature, revealing the existence of polar nanoregions (PNRs). The displacement of Bi 3+ cations is ∼0.26 A along pc in the PNRs, with a size of ∼13 A in NBT. The BaTiO 3 doping drives the diffuse scattering patterns to evolve from the L-shape into an ellipsoidal along pc in (Na 0.5 Bi 0.5 )TiO 3 –x BaTiO 3 . An abnormally large correlation length was observed in the morphotropic phase boundary composition with x = 0.05.

Obtaining topological degenerate ground states by the density matrix renormalization group

We develop the density matrix renormalization group approach to systematically identify the topological order of the quantum spin liquid (QSL) through adiabatically obtaining different topological sectors of the QSL on an infinite cylinder. As an application, we study the anisotropic kagome Heisenberg model known for hosting a Z$_2$ QSL, however no numerical simulations have been able to access all four sectors before. We obtain the complete set of four topological degenerate ground states distinguished by the presence or absence of the spinon and vison quasiparticle line, which fully characterizes the topological nature of the quantum phase. We have also studied the kagome Heisenberg model, which has attracted a lot of recent attention. We find two topological sectors accurately and also estimate various properties of the other topological sectors, where the larger correlation length is found indicating the possible proximity to another phase.

A reduced-order model for Monte Carlo simulations of stochastic groundwater flow

We explore the ability of the greedy algorithm to serve as an effective tool for the construction of reduced-order models for the solution of fully saturated groundwater flow in the presence of randomly distributed transmissivities. The use of a reduced model is particularly appealing in the context of numerical Monte Carlo (MC) simulations that are typically performed, e.g., within environmental risk assessment protocols. In this context, model order reduction techniques enable one to construct a surrogate model to reduce the computational burden associated with the solution of the partial differential equation governing the evolution of the system. These techniques approximate the model solution with a linear combination of spatially distributed basis functions calculated from a small set of full model simulations. The number and the spatial behavior of these basis functions determine the computational efficiency of the reduced model and the accuracy of the approximated solution. The greedy algorithm provides a deterministic procedure to select the basis functions and build the reduced-order model. Starting from a single basis function, the algorithm enriches the set of basis functions until the largest error between the full and the reduced model solutions is lower than a predefined tolerance. The comparison between the standard MC and the reduced-order approach is performed through a two-dimensional steady-state groundwater flow scenario in the presence of a uniform (in the mean) hydraulic head gradient. The natural logarithm of the aquifer transmissivity is modeled as a second-order stationary Gaussian random field. The accuracy of the reduced basis model is assessed as a function of the correlation scale and variance of the log-transmissivity. We explore the performance of the reduced model in terms of the number of iterations of the greedy algorithm and selected metrics quantifying the discrepancy between the sample distributions of hydraulic heads computed with the full and the reduced model. Our results show that the reduced model is accurate and is highly efficient in the presence of a small variance and/or a large correlation length of the log-transmissivity field. The flow scenarios associated with large variances and small correlation lengths require an increased number of basis functions to accurately describe the collection of the MC solutions, thus reducing significantly the computational advantages associated with the reduced model.

Potential fluctuations in graphene due to correlated charged impurities in substrate

We evaluate the autocorrelation function of the electrostatic potential in doped graphene due to nearby charged impurities. The screening of those impurities is described by a combination of the polarization function for graphene in random phase approximation with the electrostatic Green's function of the surrounding dielectrics. Using the hard-disk model for a two-dimensional distribution of impurities, we show that large correlation lengths between impurities can give rise to anti-correlation in the electrostatic potential, in agreement with recent experiments.

Depth dependent structure and magnetic properties and their correlation with magnetotransport in Fe/Au multilayers

A detailed study on the role of interface structure and magnetism in magnetoresistance (MR) in Fe/Au multilayers has been carried out. Two series of multilayers were deposited on Si substrate by sputtering: one series with varying Fe layer thickness, tFe=30–100Å, and another series with varying Au layer thickness tAu=50–150Å. MR measurements were done using a 4-probe technique. The multilayer interface structure and magnetic properties were studied by specular X-ray reflectometry and polarized neutron reflectometry (PNR). Details of the interface fractal morphology were obtained from diffuse X-ray reflectivity (DXRR). Bulk magnetic measurements were carried out on a superconducting quantum interference device magnetometer. Change in MR can be associated with magnetic and morphological properties of Fe/Au and Au/Fe interfaces in Fe/Au multilayer samples as obtained by reflectometry. Large MR is also associated to interfaces with larger magnetization, large in-plane correlation length and higher Hurst parameter, obtained from PNR and DXRR.

QUASARS PROBING QUASARS. VI. EXCESS H I ABSORPTION WITHIN ONE PROPER Mpc OFz∼ 2 QUASARS

With close pairs of quasars at different redshifts, a background quasar sightline can be used to study a foreground quasar's environment in absorption. We use a sample of 650 projected quasar pairs to study the HI Lya absorption transverse to luminous, z~2 quasars at proper separations of 30kpc < R < 1Mpc. In contrast to measurements along the line-of-sight, regions transverse to quasars exhibit enhanced HI Lya absorption and a larger variance than the ambient intergalactic medium, with increasing absorption and variance toward smaller scales. Analysis of composite spectra reveals excess absorption characterized by a Lya equivalent width profile W = 2.3A (R/100kpc)^-0.46. We also observe a high (~60%) covering factor of strong, optically thick HI absorbers (HI column log NHI > 17.3) at separations R<200kpc, which decreases to ~20% at R~1Mpc, but still represents a significant excess over the cosmic average. This excess of optically thick absorption can be described by a quasar-absorber cross-correlation function xi_QA(r) = (r/r_0)^gamma with a large correlation length r_0 = 12.5+2.7-1.4 Mpc/h (comoving) and gamma = 1.68+0.14-0.30. The HI absorption measured around quasars exceeds that of any previously studied population, consistent with quasars being hosted by massive dark matter halos Mhalo~10^12.5 Msun at z~2.5. The environments of these massive halos are highly biased towards producing optically thick gas, and may even dominate the cosmic abundance of Lyman limit systems and hence the intergalactic opacity to ionizing photons at z~2.5. The anisotropic absorption around quasars implies the transverse direction is much less likely to be illuminated by ionizing radiation than the line-of-sight, which we interpret in terms of the same obscuration effects frequently invoked in unified models of active galactic nuclei.

Surface Folding-Induced Attraction and Motion of Particles in a Soft Elastic Gel: Cooperative Effects of Surface Tension, Elasticity, and Gravity

We report some experimental observations regarding a new type of long-range interaction between rigid particles that prevails when they are suspended in an ultrasoft elastic gel. A denser particle submerges itself to a considerable depth inside the gel and becomes elasto-buoyant by balancing its weight against the elastic force exerted by the surrounding medium. By virtue of a large elasto-capillary length, the surface of the gel wraps around the particle and closes to create a line singularity connecting the particle to the free surface of the gel. A substantial amount of tensile strain is thus developed in the gel network parallel to the free surface that penetrates to a significant depth inside the gel. The field of this tensile strain is rather long-range because of a large gravito-elastic correlation length and sufficiently strong to pull two submerged particles into contact. The particles move toward each other with an effective force following an inverse linear distance law. When more monomers or dimers of the particles are released inside the gel, they orient rather freely inside the capsules where they are located and attract each other to form closely packed clusters. Eventually, these clusters themselves interact and coalesce. This is an emergent phenomenon in which gravity, capillarity, and elasticity work in tandem to create a long-range interaction. We also present the results of a related experiment, in which a particle suspended inside a thickness-graded gel moves accompanied by the continuous folding and the relaxation of the gel's surface.

Active temperature and velocity correlations produced by a swimmer suspension

The agitation produced in a fluid by a suspension of microswimmers in the low Reynolds number limit is studied. In this limit, swimmers are modeled as force dipoles all with equal strength. The agitation is characterized by the active temperature defined, as in kinetic theory, as the mean square velocity, and by the equal-time spatial correlations. Considering the phase in which the swimmers are homogeneously and isotropically distributed in the fluid, it is shown that the active temperature and velocity correlations depend on a single scalar correlation function of the dipole-dipole correlation function. By making a simple medium-range order model, in which the dipole-dipole correlation function is characterized by a single correlation length k(0)(-1) it is possible to make quantitative predictions. It is found that the active temperature depends on the system size, scaling as L(4-d) at large correlation lengths L<<k(0)(-1), while in the opposite limit it saturates in three dimensions and diverges logarithmically with the system size in two dimensions. In three dimensions the velocity correlations decay as 1/r for small correlation lengths, while at large correlation lengths the transverse correlation function becomes negative at maximum separation r~L/2, an effect that disappears as the system increases in size.

Mapping between finite temperature classical and zero temperature quantum systems: Quantum critical jamming and quantum dynamical heterogeneities

Many electronic systems (e.g., the cuprate superconductors and heavy fermions) exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are some empirical suggestions of particular increasing length scales that accompany such transitions in some cases, this identification is not universal and in numerous instances no large correlation length is evident. To better understand, as a matter of principle, such behavior in quantum systems, we extend a known mapping (earlier studied in stochastic or supersymmetric quantum mechanics) between finite temperature classical Fokker-Planck systems and related quantum systems at zero temperature to include general nonequilibrium dynamics. Unlike Feynman mappings or stochastic quantization methods in field theories (as well as more recent holographic type dualities), the classical systems that we consider and their quantum duals reside in the same number of space-time dimensions. The upshot of our very broad and rigorous result is that a Wick rotation exactly relates (i) the dynamics in general finite temperature classical dissipative systems to (ii) zero temperature dynamics in the corresponding dual many-body quantum systems. Using this correspondence, we illustrate that, even in the absence of imposed disorder, many continuum quantum fluid systems (and possible lattice counterparts) may exhibit a zero-point ``quantum dynamical heterogeneity'' wherein the dynamics, at a given instant, is spatially nonuniform. While the static length scales accompanying this phenomenon do not seem to exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We further study ``quantum jamming'' and illustrate how a hard-core bosonic system can undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent $z&gt;4$ that is consistent with length scales that increase far more slowly than the relaxation time as a putative critical transition is approached. Similar results may hold for spin-liquid-type as well as interacting electronic systems. We suggest ways to analyze experimental data in order to adduce such phenomena. Our approach may be used to analyze other quenched quantum systems.