Length Scale Of Fluctuations Research Articles

Effect of Manufacturing Inaccuracies on the Wake Past Asymmetric Airfoil by PIV

The effect of manufacturing geometry deviations on the flow past a NACA 64(3)-618 asymmetric airfoil is studied. This airfoil is 3D printed according to the coordinates from a public database. An optical high-precision 3D scanner, GOM Atos, measures the difference from the idealized model. Based on this difference, another model is prepared with a physical output closer to the ideal model. The velocity in the near wake (0–0.4 chord) is measured by using the Particle Image Velocimetry (PIV) technique. This work compares the wakes past three airfoil realizations, which differ in their similarity to the original design (none of the realizations is identical to the original design). The chord-based Reynolds number ranges from 1.6×104 to 1.6×105. The ensemble average velocity is used for the determination of the wake width and for the rough estimation of the drag coefficient. The lift coefficient is measured directly by using force balance. We discuss the origin of turbulent kinetic energy in terms of anisotropy (at least in 2D) and the length-scales of fluctuations across the wake. The spatial power spectral density is shown. The autocorrelation function of the cross-stream velocity detects the regime of the von Karmán vortex street at lower velocities.

Dynamic length scales in athermal, shear-driven jamming of frictionless disks in two dimensions.

We carry out numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, ξ and ℓ, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function and argue that the more divergent length ℓ is a consequence of a dangerous irrelevant scaling variable and that it is ξ, which is the correlation length that determines the divergence of the system viscosity as jamming is approached from below in the liquid phase. We find that ξ∼(ϕ_{J}-ϕ)^{-ν} diverges with the critical exponent ν=1. We provide evidence that ξ measures the length scale of fluctuations in the rotation of the particle velocity field, while ℓ measures the length scale of fluctuations in the divergence of the velocity field.

Quantum interference in a macroscopic van der Waals conductor

Quantum corrections to charge transport can give rise to an oscillatory magnetoconductance, typically observed in mesoscopic samples with a length shorter than or comparable with the phase coherence length. Here, we report the observation of magnetoconductance oscillations periodic in magnetic field with an amplitude of the order of $e^2/h$ in macroscopic samples of Highly Oriented Pyrolytic Graphite (HOPG). The observed effect emerges when all carriers are confined to their lowest Landau levels. We argue that this quantum interference phenomenon can be explained by invoking moir\'e superlattices with a discrete distribution in periodicity. According to our results, when the magnetic length $\ell_B$, the Fermi wave length $\lambda_F$ and the length scale of fluctuations in local chemical potential are comparable in a layered conductor, quantum corrections can be detected over centimetric length scales.

Power spectrum of flow fluctuations in relativistic heavy-ion collisions

We carry out hydrodynamical simulation of the evolution of fluid in relativistic heavy-ion collisions with random initial fluctuations. The time evolution of power spectrum of momentum anisotropies shows very strong correspondence with the physics of cosmic microwave anisotropies as was earlier predicted by us. In particular, our results demonstrate suppression of superhorizon fluctuations and the correspondence between the location of the first peak in the power spectrum of momentum anisotropies and the length scale of fluctuations and expected freeze-out time-scale (more precisely, the sound horizon size at freeze-out).

Cation ratio fluctuations in Cu2ZnSnS4 at the 20 nm length scale investigated by analytical electron microscopy

Kesterite Cu2ZnSn(S,Se)4 (CZTSSe) is a sustainable material for thin‐film photovoltaics with device efficiencies greater than 12% have been demonstrated. Despite similar crystal structure and polycrystalline film microstructures, there is widespread evidence for larger‐amplitude potential and bandgap fluctuations in CZTS than in the analogous Cu(In,Ga)Se2 (CIGSe) chalcopyrite material. This disorder is believed to account for a sizable part of the larger open‐circuit voltage (VOC) deficit in CZTS devices, yet the detailed origins and length scales of these fluctuations have not been fully elucidated. Herein, we present a transmission electron microscopy study focusing on composition variation within bulk multicrystals of CZTS grown by the travelling heater method (THM). In these slow‐cooled, solution grown crystals we find direct evidence for spatial composition fluctuations of amplitude <1 at.% (∼5 × 1020 cm−3) and thus, explainable by point defects. However, rather than being homogeneously‐distributed we find a characteristic 20 nm length scale for these fluctuations, which sets a definite length scale for band gap and potential fluctuations. At Σ3 grain boundaries, we find no evidence of composition variation compared to the bulk. The finding highlights such variations reported at grain boundaries in polycrystalline thin‐films are direct consequences of processing methods and not intrinsic properties of CZTS itself.

Structure of the hydrophilic phase and its impact on the conductivity of graft copolymer ionomers at low hydration level

SAXS studies indicate that the spatial distribution of ion-rich clusters is not uniform in radiation grafted polymer electrolytes based on a semi-crystalline polymer matrix. Due to the matrix microstructure, certain domains of the polymer electrolyte are rich in these hydrophilic clusters, while other domains are devoid of them. Therefore, the hydrophilic phase is not continuous on the nano-scale, which results in fluctuations in the volumetric number density of ion-rich clusters. The length-scale of fluctuations within the electrolyte is larger than the characteristic distance between ionic aggregates, and we argue that at low hydration level it has a negative impact on the percolation and connectivity of the aqueous phase. However, an increased number density of hydrophilic clusters within grafted domains or an increased volume fraction of grafted domains within the semi-crystalline polymer both have favorable impact on the conductivity at low-hydration levels. We anticipate that a polymer electrolyte with a less heterogenous distribution of hydrophilic clusters would have considerably improved proton conductivity at low-hydration levels, because a uniform distribution on the one hand decreases the percolation threshold of the aqueous phase and one the other hand increases the connectivity of the hydrophilic clusters.

Enhancement of the finite-frequency superfluid response in the pseudogap regime of strongly disordered superconducting films.

The persistence of a soft gap in the density of states above the superconducting transition temperature Tc, the pseudogap, has long been thought to be a hallmark of unconventional high-temperature superconductors. However, in the last few years this paradigm has been strongly revised by increasing experimental evidence for the emergence of a pseudogap state in strongly-disordered conventional superconductors. Nonetheless, the nature of this state, probed primarily through scanning tunneling spectroscopy (STS) measurements, remains partly elusive. Here we show that the dynamic response above Tc, obtained from the complex ac conductivity, is highly modified in the pseudogap regime of strongly disordered NbN films. Below the pseudogap temperature, T*, the superfluid stiffness acquires a strong frequency dependence associated with a marked slowing down of critical fluctuations. When translated into the length-scale of fluctuations, our results suggest a scenario of thermal phase fluctuations between superconducting domains in a strongly disordered s-wave superconductor.

Spatial scales and temporal scales in the theory of magnetohydrodynamic turbulence

In the study of incompressible magnetohydrodynamic (MHD) turbulence the correlation lengths along the directions parallel and perpendicular to the local mean magnetic field may be defined by iso-energy surfaces derived from second order structure functions. The correlation time of the turbulence may be defined in a similar manner by means of a temporal second order structure function. Moreover, there is a natural correspondence between the lengthscales of fluctuations with a given energy and the timescale of fluctuations of the same energy so that each iso-energy surface is associated with a unique pair of parallel and perpendicular correlation lengths and a unique correlation time. In the case when the magnetic Prandtl number is unity, Prm≡ν/η=1, it is shown that the correlation time τ associated with an iso-energy contour of energy E is equal to the energy cascade time of the turbulence in the sense that E/τ∼ε, where ε is the energy cascade rate. For balanced MHD turbulence, turbulence with vanishing cross-helicity, both the Goldreich and Sridhar theory and Boldyrev’s theory are shown to have this same property. An attempt is made to generalize these ideas to imbalanced MHD turbulence, turbulence with nonvanishing cross-helicity. It is shown that if the normalized cross-helicity σc is a constant in the inertial range, independent of wavenumber, then one obtains a model in which the energy cascade times of the two Elsasser fields are equal throughout the inertial range, that is, τ+/τ−=1. This result appears to be contradicted by numerical simulations and, therefore, the generalization to imbalanced turbulence discussed here requires further development; this is an important unsolved problem.

Measurements of scalar dissipation in a turbulent piloted methane/air jet flame

This paper describes the first results from a new experimental facility that combines line-imaging measurementsof Raman scattering, Rayleight scattering, and laser-induced CO fluorescence. Simultaneous single-shot line measurements of major species, temperature, mixture fraction, and the radial component of scalar dissipation are obtained in partially premixed methane/air jet flames (25% CH4, 75% air, by volume). The experimental setup and methods of data analysis are described. Results from a laminar jet flame and a piloted turbulent flame (Sandia flame D) are presented. The laminar and turbulent flames both show a local minimum in the average scalar dissipation near the stoichiometric mixture fraction. In the turbulent flame, the radial component of the instantaneous scalar dissipation near the stoichiometric condition displays a log-normal distribution at high values and an exponential distribution at low values. This is attributed to variation in the orientation of the three-dimensional mixture fraction gradient relative to the one-dimensional measurement. The effect of scalar dissipation on flame structure is examined, based on average species mass fractions doubly conditioned upon mixture fraction and scalar dissipation. The length scale of fluctuations in mixture fraction in the turbulent reaction zone is derived from the measured single-shot radial profiles at each streamwise location. This macro length scale is well resolved by the present methods, shows correlation over radial distances of a few millimeters, and grows with streamwise distance as the jet flame spreads. The length scale for fluctuations in scalar dissipation is less than 1 mm at each of the measured streamwise locations in the turbulent flame.

Dynamic Light Scattering Study of Structural Changes of Cellulose Diacetate in Solution under Couette Flow

Dynamic light scattering (DLS) measurements were conducted under a simple shear flow, i.e., the Couette flow field, to cellulose diacetate (CDA; a typical polysaccharide) in semidilute N,N-dimethylacetamide (DMAc) solution. The shear rate y was varied from 0 to 5.25 s -1 . At quiescence, CDA showed three dynamic modes, which correspond to two kinds of associations and a single chain. In the weakly sheared system (0.402 s -1 ≤ γ ≤ 5.25 s -1 ), the three dynamic modes collapsed, and alternatively two completely different modes were observed. The fast mode experienced a transition around y = 0.81 s -1 , the decay rate distribution changing from a broader bimodal to a narrower unimodal shape with increasing shear. The slow mode had a unimodal decay rate distribution, but the length scale of fluctuations was larger by 3 orders of magnitude compared to those observed at y = 0 s -1 ; that is, the length distribution was extremely uniform irrespective of y, and the length ξ s was proportional to γ -1 . This ξ s γ -1 relation was interpreted by Taylor's treatment of the behavior of viscous drops. Thus, the repetition of the burst and the coalescence growth of the associations was suggested for the slow mode. The ξ s γ -1 relation implied that CDA was molecularly disperse in DMAc under the viscometric field in a capillary viscometer at γ = 920 s -1 .

Separating Intrinsic And Microlensing Variability Using Parallax Measurements

In gravitational lens systems with 3 or more resolved images of a quasar, the intrinsic variability may be unambiguously separated from the microlensing variability through parallax measurements from 3 observers when there is no relative motion of the lens masses (Refsdal 1993). In systems with fewer than 3 resolved images, however, this separation is not straightforward. For the purpose of illustration, I make the following simplifications for the one-dimensional case: The observations consist of well-sampled time series of the observed flux FA(ti) and FB(ti) at two points in the observer plane. The separation vector of the two points is parallel to the direction of the transverse motion of the source-lens-observer system, and the distance DAB between the observers is known. Furthermore, the distance DAB is small compared to the typical length scale of fluctuations in the magnification μ(x).

Properties of the disordered two-dimensional electron gas in a strong magnetic field

The authors investigate non-interacting electrons moving in a two-dimensional, disordered potential under the influence of a perpendicular magnetic field. The random potential is assumed to have a minimum length scale for fluctuations. If the magnetic field is sufficiently strong the ratio of the cyclotron length to the correlation length of the potential is a small parameter. They develop a systematic perturbation theory in this quantity for the disorder-averaged Greens functions from which physical properties are calculated. The method yields useful results for single particle quantities, including the density of states, but not for the low-frequency transport coefficients.