Typical Correlation Length Research Articles

COSMOGLOBE: Towards end-to-end CMB cosmological parameter estimation without likelihood approximations

We implement support for a cosmological parameter estimation algorithm in Commander and quantify its computational efficiency and cost. For a semi-realistic simulation similar to Planck LFI 70 GHz, we find that the computational cost of producing one single sample is about 20 CPU-hours and that the typical Markov chain correlation length is ∼100 samples. The net effective cost per independent sample is ∼2000 CPU-hours, in comparison with all low-level processing costs of 812 CPU-hours for Planck LFI and WMAP in COSMOGLOBE Data Release 1. Thus, although technically possible to run already in its current state, future work should aim to reduce the effective cost per independent sample by one order of magnitude to avoid excessive runtimes, for instance through multi-grid preconditioners and/or derivative-based Markov chain sampling schemes. This work demonstrates the computational feasibility of true Bayesian cosmological parameter estimation with end-to-end error propagation for high-precision CMB experiments without likelihood approximations, but it also highlights the need for additional optimizations before it is ready for full production-level analysis.

Typical Correlation Length of Sequentially Generated Tensor Network States

Typical Correlation Length of Sequentially Generated Tensor Network States

Spatial metallicity distribution statistics at ≲100 pc scales in the AMUSING++ nearby galaxy sample

ABSTRACT We analyse the spatial statistics of the 2D gas-phase oxygen abundance distributions in a sample of 219 local galaxies. We introduce a new adaptive binning technique to enhance the signal-to-noise ratio of weak lines, which we use to produce well-filled metallicity maps for these galaxies. We show that the two-point correlation functions computed from the metallicity distributions after removing radial gradients are in most cases well-described by a simple injection–diffusion model. Fitting the data to this model yields the correlation length lcorr, which describes the characteristic interstellar medium (ISM) mixing length-scale. We find typical correlation lengths lcorr ∼ 1 kpc, with a strong correlation between lcorr and stellar mass, star formation rate (SFR), and effective radius, and a weak correlation with Hubble type. Two galaxies in the sample show significantly larger lcorr, and both prove to be interacting or merging systems. We show that the trend of lcorr with SFR can be reproduced by a simple transport + feedback model of ISM turbulence at high SFR, and plausibly also at low SFR if dwarf galaxy winds have large mass-loading factors. We also report the first measurements of the injection width that describes the initial radii over which supernova remnants deposit metals. Inside this radius the metallicity correlation function is not purely the product of a competition between injection and diffusion. We show that this size scale is generally smaller than 60 pc.

Localization properties of a discrete-time 1D quantum walk with generalized exponential correlated disorder

We study the dynamics of the 1D Hadamard quantum walk featuring generalized exponential correlated phase disorder. We report the existence of distinct dynamical regimes and discuss the prospect of a judicious tuning of the strength of localization of the walker via the degree of correlation. In particular, we unveil that when the typical correlation length is smaller than the chain size, the maximum spreading of the quantum wavepacket is achieved when the underlying disorder displays Gaussian correlations. Our work provides a framework for investigating the weakening of Anderson localization due to correlated disorder and may also find applications in the context of quantum information processing.

Fluctuation suppression in microgels by polymer electrolytes.

Structural details of thermoresponsive, cationically poly(N-iso-propylacrylamide-co-methacrylamido propyl trimethyl ammonium chloride) microgels and the influence of the anionic electrolyte polystyrene sulfonate (PSS) on the internal structure and dynamics of the cationic microgels have been studied with a combination of small angle neutron scattering (SANS) and neutron spin echo (NSE) spectroscopy. While SANS can yield information on the overall size of the particles and on the typical correlation length inside the particles, studying the segmental polymer dynamics with NSE gives access to more internal details, which only appear due to their effect on the polymer motion. The segmental dynamics of the microgels studied in this paper is to a large extent suppressed by the PSS additive. Possible scenarios of the influence of the polyanions on the microgel structure and dynamics are discussed.

Spectral Magnetic Helicity of Solar Active Regions between 2006 and 2017

Abstract We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006–2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6– , while the length scale relating the magnetic and current helicities to each other is around .

Neutron transport in anisotropic random media

Assessing the impact of random media for eigenvalue problems plays a central role in nuclear reactor physics and criticality safety. In a recent work (Larmier et al., 2018a), we have applied a probabilistic model based on stochastic tessellations in order to describe fuel degradation following severe accidents with partial melting and re-arrangement of the resulting debris. The distribution of the multiplication factor and of the kinetics parameters as a function of the mixing statistics model and of the typical correlation length of the tessellation were examined in detail for a benchmark configuration consisting in a fuel assembly with UOX or MOX fuel pins. In this paper, we extend our previous findings by including in the stochastic tessellation model the effects of anisotropy that might result from gravity and material stratification: for this purpose, we adopt the broad class of anisotropic Poisson geometries. We discuss the behaviour of the key observables of interest for eigenvalue problems in anisotropic tessellations by revisiting the fuel assembly benchmark calculations proposed in (Larmier et al., 2018a). The effects of anisotropic random media on the multiplication factor, on the kinetics parameters and on the flux spectrum will be carefully examined.

Matter wave speckle observed in an out-of-equilibrium quantum fluid

We report the results of the direct comparison of a freely expanding turbulent Bose-Einstein condensate and a propagating optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. The calculated second-order correlation together with the typical correlation length of each system is used to compare and substantiate our observations. We believe that the close analogy existing between an expanding turbulent quantum gas and a traveling optical speckle might burgeon into an exciting research field investigating disordered quantum matter.

Structural deformation of the S=1 kagome-lattice compound KV3Ge2O9

The dielectric and structural properties of the $S=1$ kagome antiferromagnet ${\mathrm{KV}}_{3}{\mathrm{Ge}}_{2}{\mathrm{O}}_{9}$ are examined. The low-temperature structure below 50 K is orthorhombic with a typical correlation length of 8 nm. While the high-temperature hexagonal phase can be considered $C$-centered orthorhombic, the $C$-centered symmetry is broken below 50 K. The low-temperature symmetry does not support the simplex solid state, which is the theoretically expected ground state for the $S=1$ kagome lattice. Above 60 K, incommensurate lattice modulation is observed. The lock-in transition suggests that the origin of the orthorhombic deformation is the development of a short-range magnetic ordering.

Directed collective motion of bacteria under channel confinement

Dense suspensions of swimming bacteria are known to exhibit collective behaviour arising from the interplay of steric and hydrodynamic interactions. Unconfined suspensions exhibit transient, recurring vortices and jets, whereas those confined in circular domains may exhibit order in the form of a spiral vortex. Here we show that confinement into a long and narrow macroscopic ‘racetrack’ geometry stabilises bacterial motion to form a steady unidirectional circulation. This motion is reproduced in simulations of discrete swimmers that reveal the crucial role that bacteria-driven fluid flows play in the dynamics. In particular, cells close to the channel wall produce strong flows which advect cells in the bulk against their swimming direction. We examine in detail the transition from a disordered state to persistent directed motion as a function of the channel width, and show that the width at the crossover point is comparable to the typical correlation length of swirls seen in the unbounded system. Our results shed light on the mechanisms driving the collective behaviour of bacteria and other active matter systems, and stress the importance of the ubiquitous boundaries found in natural habitats.

A circulation-based method for detecting vortices in granular materials

Dense granular flows exhibit large clusters of grains rotating in correlated fashions. We present a method to identify and quantify such granular vortices, based on the circulation of velocity fluctuations around closed curves. Here, the method is applied on physical experiments of two-dimensional granular flows in the Stadium Shear Device geometry. Results illustrate how the method is capable to capture the positions, sizes, velocities and life-times of individual vortices. The method should be useful for many purposes, including: (1) complementing existing ways for defining typical correlation lengths in granular systems; (2) studying the kinematics behind the superior efficiency of granular systems to transfer of mass, heat and momentum when compared with other fluids; and (3) characterising vortices in other particulate fluid systems such as suspensions, emulsions and foams, which exhibit similar velocity patterns.

Reciprocal space mapping of silver nanoparticle array re-assembly and oxidation

Self-assembled metal oxide nanoparticle layers have attracted much attention recently due to potential applications in sensors. Here we report on a UV/ozone-driven re-assembly and oxidation of a self-assembled silver nanoparticle bilayer deposited by a modified Langmuir-Schaefer technique that was probed in-situ by simultaneous measurements of the small- and wide-angle X-ray scattering at grazing incidence (GISAXS, GIWAXS). The experiments were performed at BL23A endstation of NSRRC, Taiwan. Four distinct stages of the system response to the UV/ozone treatment were identified. In the first stage 0-120 s, a gradual extinction of Bragg rods and the nanoparticle short-range order due to a gradual surfactant removal is observed in GISAXS that is connected with an array densification and order improvement obeying the paracrystal model in the shrinking self-assembled regions. In the second stage 120-360 s, the original self-assembly goes to a total extinction while the integral intensity of Ag 111 diffraction in GIWAXS starts to decrease, suggesting the total surfactant removal. No nanoparticle short-range order is observed in stage III 360-730 s where AgO monoclinic phase due to the nanoparticle surface oxidation appears and pure Ag phase disappears. The initial AgO unit cell volume corresponding to the unstrained phase gradually expands by 4.6 % to the end of stage III. In stage IV 730-2000 s (end of measurements), new Bragg rods appear in GISAXS, suggesting a nanoparticle agglomeration with a typical correlation length of approximately 240 nm that was confirmed by ex-situ atomic force microscopy. The agglomeration does not reach saturation even after 2000 s while the AgO phase remains stable. These results have direct implications for tailored preparation of advanced sensors based on metal oxide nanoparticles. The work was supported by the projects APVV-0308-11, VEGA 2/0041/11, SAS-NSC JRP 2011/05, SAS-TUBITAK JRP 2013/6, COST MP1203 and COST CM1101.

Hydrodynamic shadowing effect during precipitation of dendrites in channel flow.

A supersaturated fluid flowing over a reactive, rough surface leads to complex precipitation patterns. We study the growth and interaction between discrete precipitates along a reactive wall in a nonlaminar channel flow. We show that the competition between advective transport, diffusion, and mixing strongly influences the downstream precipitates morphology and the typical correlation length between different precipitates.

Seismic energy envelopes in volcanic media: in need of boundary conditions

Seismogram envelopes recorded at Campi Flegrei caldera show diffusive characteristics as well as steep amplitude increases in the intermediate and late coda, which can be related to the presence of a non-uniformly scattering medium. In this paper, we first show the results of a simulation with a statistical model considering anisotropic scattering interactions, in order to match coda-envelope duration and shape. We consider as realistic parameters for a volcanic caldera the presence of large square root velocity fluctuations (10 per cent) and two typical correlation lengths for such an heterogeneous crust, a = 0.1 and 1 km. Then, we propose the inclusion of a diffusive boundary condition in the stochastic description of multiple scattering, in order to model intermediate and late coda intensities, and particularly the sharp intensity peaks at some stations in the caldera. Finally, we show that a reliable 2-D synthetic model of the envelopes produced by earthquakes vertically sampling a small region can be obtained including a single drastic change of the scattering properties of the volcano, that is, a caldera rim of radius 3 km, and sections varying between 2 and 3 km. These boundary conditions are diffusive, which signifies that the rim must have more scattering potential than the rest of the medium, with its diffusivity 2–3 orders of magnitude lower than the one of the background medium, so that the secondary sources on its interface(s) could enhance coda intensities. We achieve a good first-order model of high-frequency (18 Hz) envelope broadening adding to the Monte Carlo solution for the incident flux the secondary source effects produced by a closed annular boundary, designed on the caldera rim signature at 1.5 km depth. At lower frequencies (3 Hz) the annular boundary controls the intermediate and late coda envelope behaviour, in a way similar to an extended diffusive source. In our interpretation, the anomalous intensities observed at several stations and predicted by the final Monte Carlo solutions are mainly due to the diffusive transmission reflection from a scattering object of increased scattering power, and are controlled by its varying thickness.

Random transverse field Ising model on the Cayley tree: analysis via boundary strong disorder renormalization

Strong disorder renormalization for the random transverse field Ising model leads to a complicated topology of surviving clusters as soon as d > 1. Even if one starts from a Cayley tree, the network of surviving renormalized clusters will contain loops, so that no analytical solution can be obtained. Here we introduce a modified procedure called ‘boundary strong disorder renormalization’ that preserves the tree structure, so that one can write simple recursions with respect to the number of generations. We first show that this modified procedure allows one to recover exactly most of the critical exponents for the one-dimensional chain. After this important check, we study the RG equations for the quantum Ising model on a Cayley tree with a uniform ferromagnetic coupling J and random transverse fields with support [hmin,hmax]. We find the following picture: (i) for J > hmax, only bonds are decimated, so that the whole tree is a quantum ferromagnetic cluster; (ii) for J < hmin, only sites are decimated, so that no quantum ferromagnetic cluster is formed, and the ferromagnetic coupling to the boundary coincides with the partition function of a directed polymer model in a random medium; (iii) for hmin < J < hmax, both sites and bonds can be decimated, and the quantum ferromagnetic clusters can either remain finite (the physics is then similar to (ii), with a quantitative mapping to a modified directed polymer model) or an infinite quantum ferromagnetic cluster appears. We find that the quantum transition can be of two types: (a) either the quantum transition takes place in the region where quantum ferromagnetic clusters remain finite, and the singularity of the ferromagnetic coupling to the boundary involves the typical correlation length exponent νtyp = 1; (b) or the quantum transition takes place at the point where an extensive quantum ferromagnetic cluster appears, with a correlation length exponent ν ≃ 0.75.

Search for cold gas in strong Mg II absorbers at 0.5 &lt; z &lt; 1.5: nature and evolution of 21-cm absorbers

We report 4 new detections of 21-cm absorption from a systematic search of 21-cm absorption in a sample of 17 strong (Wr(MgII 2796)>1A) intervening MgII absorbers at 0.5<z<1.5. We also present 20-cm milliarcsecond scale maps of 40 quasars having 42 intervening strong MgII absorbers for which we have searched for 21-cm absorption. Combining 21-cm absorption measurements for 50 strong MgII systems from our surveys with the measurements from literature, we obtain a sample of 85 strong MgII absorbers at 0.5<z<1 and 1.1<z<1.5. We present detailed analysis of this sample, taking into account the effect of the varying 21-cm optical depth sensitivity and covering factor associated with the different quasar sight lines. We find that the 21-cm detection rate is higher towards the quasars with flat or inverted spectral index at cm wavelengths. About 70% of 21-cm detections are towards the quasars with linear size, LS<100 pc. The 21-cm absorption lines having velocity widths, DeltaV>100 km/s are mainly seen towards the quasars with extended radio morphology at arcsecond scales. However, we do not find any correlation between the integrated 21-cm optical depth or DeltaV with the LS measured from the milliarcsecond scale images. All this can be understood if the absorbing gas is patchy with a typical correlation length of ~30-100 pc. We show that within the measurement uncertainty, the 21-cm detection rate in strong MgII systems is constant over 0.5<z<1.5, i.e., over ~30% of the total age of universe. We show that the detection rate can be underestimated by up to a factor 2 if 21-cm optical depths are not corrected for the partial coverage estimated using milliarcsecond scale maps. Since stellar feedback processes are expected to diminish the filling factor of cold neutral medium over 0.5<z<1, this lack of evolution in the 21-cm detection rate in strong MgII absorbers is intriguing. [abridged]

Random transverse field Ising model in dimension d > 1: scaling analysis in the disordered phase from the directed polymer model

For the quantum Ising model with ferromagnetic random couplings Ji, j > 0 and random transverse fields hi > 0 at zero temperature in finite dimensions d > 1, we consider the lowest order contributions in perturbation theory in (Ji, j/hi) to obtain some information on the statistics of various observables in the disordered phase. We find that the two-point correlation scales as , where ξtyp is the typical correlation length, u is a random variable and ω coincides with the droplet exponent ωDP(D = d − 1) of the directed polymer with D = (d − 1) transverse directions. Our main conclusions are as follows. (i) Whenever ω > 0, the quantum model is governed by an infinite-disorder fixed point: there are two distinct correlation length exponents related by νtyp = (1 − ω)νav; the distribution of the local susceptibility χloc presents the power-law tail P(χloc) ∼ 1/χ1 + μloc, where μ vanishes as ξ−ωav so that the averaged local susceptibility diverges in a finite neighborhood 0 < μ < 1 before criticality (Griffiths phase); the dynamical exponent z diverges near criticality as z = d/μ ∼ ξωav. (ii) In dimensions d ⩽ 3, any infinitesimal disorder flows toward this infinite-disorder fixed point with ω(d) > 0 (for instance ω(d = 2) = 1/3 and ω(d = 3) ∼ 0.24). (iii) In finite dimensions d > 3, a finite disorder strength is necessary to flow toward the infinite-disorder fixed point with ω(d) > 0 (for instance ω(d = 4) ≃ 0.19), whereas a finite-disorder fixed point remains possible for a small enough disorder strength. For the Cayley tree of effective dimension d = ∞, where ω = 0, we discuss the similarities and differences with the case of finite dimensions.

Flux-driven gyrokinetic simulations of ion turbulent transport at low magnetic shear

Ion Temperature Gradient driven turbulence is investigated with the global full-f gyrokinetic code GYSELA for different magnetic equilibria. Reversed shear and monotonous q profile cases do not exhibit dramatic changes nor in the dynamics nor in the level of turbulence, leading to similar mean profiles. Especially, no transport barrier is observed in the vicinity of s = 0 in the general case, although the radial extent of the gap without resonant modes is larger than the typical turbulence correlation length. Conversely, a transport barrier is found to develop in the gap region if non resonant modes are artificially suppressed from the simulation. Such simulations tend to reconcile previously published contradictory results, while extending the analysis to more realistic flux-driven gyrokinetic regimes.

Simulation ofZ(3)walls and string production via bubble nucleation in a quark-hadron transition

We study the dynamics of confinement-deconfinement (C-D) phase transition in the context of relativistic heavy-ion collisions within the framework of effective models for the Polyakov loop order parameter. We study the formation of $Z(3)$ walls and associated strings in the initial transition from the confining (hadronic) phase to the deconfining (QGP) phase via the so called Kibble mechanism. Essential physics of the Kibble mechanism is contained in a sort of domain structure arising after any phase transition which represents random variation of the order parameter at distances beyond the typical correlation length. We implement this domain structure by using the Polyakov loop effective model with a first order phase transition and confine ourselves with temperature/time ranges so that the first order C-D transition proceeds via bubble nucleation, leading to a well defined domain structure. The formation of $Z(3)$ walls and associated strings results from the coalescence of QGP bubbles expanding in the confining background. We investigate the evolution of the $Z(3)$ wall and string network. We also calculate the energy density fluctuations associated with $Z(3)$ wall network and strings which decay away after the temperature drops below the quark-hadron transition temperature during the expansion of QGP. We discuss evolution of these quantities with changing temperature via Bjorken's hydrodynamical model and discuss possible experimental signatures resulting from the presence of $Z(3)$ wall network and associate strings.

Orientational Quenched Disorder of a Nematic Liquid Crystal

By means of direct imaging, we map the surface heterogeneities of the nematic director orientation on a SiOx anchoring layer. The spatial correlations of surface director orientations are well fitted with a compressed exponential with exponent of 1.5 and typical correlation length of few microns. To discuss these results a formal analogy is established between the equation governing the nematic surface torques and the Langevin equation. Based on this analogy we prove that the disorder is spatially correlated orientational quenched disorder. The measured correlation length is discussed in terms of substrate morphology and molecular adsorption.