Variance Of Fluctuations Research Articles

Inner and outer scales in turbulent Rayleigh–Bénard convection

As in other kinds of wall-bounded turbulence, flow and heat transport in turbulent Rayleigh–Bénard convection (RBC) can be divided into an inner layer and an outer layer. This paper refines the traditional inner scales, the Townsend inner scales, by determining the Prandtl number Pr effect, and proposes new scales for the outer layer. Major findings for the inner layer include (i) the mean modified pressure peaks in the inner layer, and the peak location scales with the Townsend inner length scale lν = ν/uinner, where ν is the kinematic viscosity and uinner is the Townsend inner velocity. (ii) The peak value of the mean modified pressure Pmax scales as ΨPρrefuinner2, where ρref is the fluid density and the coefficient ΨP is largely independent of the Reynolds number but is strongly influenced by the Prandtl number. (iii) The thickness of the thermal inner layer scales with a thermal diffusional length scale lα = Ψα α/uinner, where α is the thermal diffusivity and the coefficient Ψα is largely independent of the Reynolds number but is strongly influenced by the Prandtl number. Like passive scalar transport in a pressure-driven turbulent plane Poiseuille flow, the Prandtl number dependence of Ψα (and ΨP) can be approximated by a power law Ψα ∼ ΨP ∼ Prm, where m is a constant of about 0.5. In the outer layer, the vertical component of velocity fluctuation variance at the RBC midplane ⟨ww⟩mp is introduced as a new governing parameter in the scaling of flow and heat transfer. The new outer velocity and temperature scales for turbulent RBC are different from the Deardorff scales, which were developed for convective atmospheric boundary layers. The new outer scales are compared with direct numerical simulation data and experimental measurements.

Performance analysis of data fusion schemes in cooperative spectrum sensing for cognitive radio networks

In the actual communication environment, the accuracy of spectrum detection is easily affected by the uncertainty factors such as multipath fading, shadow effect, hidden terminal, channel signal-to-noise ratio, and noise variance fluctuation. Cooperative spectrum sensing technology makes full use of the spatial gain generated by sensor nodes in different geographical locations, and obtains more accurate combination decision results than single node decision. In cooperative sensing, fusion center (FC) will analyze and process the collected local detection statistics or sensing results according to a certain data fusion rule, and make the final decision on the current channel state according to the fusion results. Data fusion strategy plays an important role in perception results and system reliability. In this paper, we summarize several conventional data fusion schemes in cooperative spectrum sensing for cognitive radio networks and conduct performance analysis.

Analysis of quantum noise of a gain-saturated fiber-based optical parametric amplifier based on an equivalent input noise model

A theoretical approach to evaluate quantum noise in gain-saturated fiber-based optical parametric amplifiers (OPAs) is presented. An equivalent input noise model that considers quantum noise is introduced, and an approximate expression of the saturated gain is presented to obtain the analytical formulas of the probability density function and the variance of signal fluctuations. Using this approach, the noise figure of gain-saturated OPAs can be analytically evaluated.

Numerical assessment of the effect of inflow turbulators on the thermal behavior of a combustion chamber

This work numerically investigates the effects of turbulators at the air and fuel (methane) inlets on the thermal behavior of a combustion chamber. Conservation equations for mass, momentum, energy, gaseous chemical species, soot, and temperature fluctuation variance in cylindrical axysimmetric co-ordinates were solved using the finite volume method. Chemical reaction rates were computed through the Arrhenius-Magnussen model, with two-step combustion reaction. The turbulence closure model, to compute the turbulent viscosity, was the standard k-?. The modelling of turbulence-radiation interactions considered the absorption coefficient-temperature correlation and the temperature self-correlation. The radiative heat source was calculated using the discrete ordinates method, considering the weighted-sum-of-gray-gases model with the superposition method to compute the radiation from the gaseous species and soot. The effect of inlet turbulators was studied by varying the turbulence intensity (TI) of both inlet streams (air and fuel), encompassing mild to severe turbulators (TI = 3%, 6%, 15%, and 20%). The results showed that temperature and radiative heat source fields, and heat transfer rates on the chamber wall and radiative fraction were importantly affected by the different turbulators intensities (e. g. radiative fraction was increased from 20.6% to 32.8% when the TI was varied from 3% to 20%). Comparisons of results obtained when turbulence-radiation interactions modelling was neglected in relation to results obtained when turbulence-radiation interactions modelling was computed showed that turbulence-radiation interactions influenced the thermal field (temperature and radiative exchange) in a similar way independently of the turbulator intensity (e. g. radiative fraction decreased 20% when turbulence-radiation interactions modelling was neglected, for both turbulators intensities).

Nontrivial amplification below the threshold for excitable cell signaling.

In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.

Cosmology from quantum information

We describe inflation in terms of a time dependent quantum density matrix with time playing the role of a stochastic variable. Using a quasi-de Sitter model we compute the corresponding quantum Fisher information function as the second derivative of the relative entanglement entropy for the density matrix at two different times. Employing standard quantum estimation theory we evaluate the minimal variance of quantum scalar fluctuations that reproduces the power spectrum and the corresponding tilt in the slow roll limit. The Jeffreys prior associated with such Fisher information can be used to define the probabilities on the set of initial conditions defined by the slow roll parameter $\epsilon$ and the initial Shannon information.

Identification and early prediction of lean blowout in premixed flames

Lean premixed combustion is a state-of-the-art technology to meet the stringent emission norms, especially to reduce the NOx emission. In the present study, we focus on the transition to lean blowout of premixed flames. The main objective of the study is to explore some important measures for prediction of lean blowout as the existing methods are not always suitable in early detection of blowout in case of premixed flames. We further consider different cases through which lean condition can be attained. For such cases, we first discuss the flame dynamics prior to blowout. Among different statistical measures, mean, median, root mean square and coefficient of variance of heat release rate fluctuations are found to be useful in blowout prediction. On the other hand, skewness and excess of kurtosis do not show any predictive quality. We also observe that the flickering frequency defined in a specific manner also shows a significant variation near lean blowout. Further, the mean frequency evaluated using Hilbert transform is found to show indication of LBO well before its occurrence. Therefore, the frequency analysis along with statistical analysis of the heat release rate oscillations is found to be very relevant in the context of blowout prediction and can be applied in the practical combustors.

A differential homogenization method for estimating the macroscopic response and field statistics of particulate viscoelastic composites

This work provides an analytical method for determining the time-dependent effective constitutive response of linear viscoelastic composites with particulate microstructures by means of a differential-algebraic system (DAS) of equations. By making use of differential equations instead of difference equations and utilizing, as primary variables, the variances of the field fluctuations instead of the properties of fictitious linear comparison composites, the new formulation is found to be more robust and to alleviate some of the issues associated with earlier incremental approaches. Remarkably, the new formulation can be shown to recover the exact results of the correspondence principle for isotropic incompressible composites subjected to proportional loading, as well as for isotropic compressible composites subjected to purely hydrostatic loading. More generally, the proposed formulation is not exact but still delivers reasonably accurate estimates in most cases. Lastly, a generalization of the DAS formulation is provided for nonlinear viscoelastic composites with incompressible phases and also found to be more robust than earlier approaches.

Atmospheric Turbulence Suppression Algorithm Based on APD Adaptive Gain Control for FSO Links of 5G Floating Base Stations

The data transmission between 5G floating base stations will be an important application area of the free space optical (FSO) link, but the problem of atmospheric disturbance will directly affect the application effect. An atmospheric turbulence suppression algorithm based on avalanche photodiode adaptive gain control (APDAGC) for the laser transmission terminal was proposed to suppress atmospheric turbulence. The given design mechanism and experimental results demonstrate its function to improve the performance of FSO. When APDAGC is over 1 km FSO, the variance of intensity fluctuation is lowered from 0.046 to 0.009, with the bit error rate reduced from 4.82E-6 to 1E-12. Comparatively, as APDAGC is over 6.5 km FSO, the variance of intensity fluctuation is decreased from 1.767 to 0.376, with the bit error rate varying from 4.6E-2 to 2.4E-4. Moreover, it was used for the first FSO transmission of 5G floating base station signals on an airship platform.

Infrared Thermography Approach for Pipelines and Cylindrical Based Geometries.

Infrared thermography (IRT) is a competitive method for nondestructive testing; yet it is susceptible to errors when testing objects with complex geometries. This work investigates the effects of regulating different thermographic testing parameters to optimize the IRT outcomes when testing complex shaped geometries, particularly cylindrical coupons. These parameters include the scanning routine, feed-rate, and heat intensity. Fine-tuning these parameters will be performed with respect to three different variables consisting of workpiece density, defect size, and defect depth. The experimental work is designed around 3D-printed cylindrical coupons, then the obtained thermal images are stitched via image processing tool to expose defects from different scans. The analysis employs a Signal-to-Noise Ratio (SNR) metric in an orthogonal tabulation following a Taguchi Design of Experiment. Moreover, test sensitivity and the best combination of factor levels are determined using Analysis of Means (ANOM) and Analysis of Variance (ANOVA). The outcomes show that the heating intensity factor is the most dominant in exposing flaws with close to 40% mean shift and up to 47% variance fluctuation. The paper introduces the tools employed in the study, and then explains the methodology followed to test one sample quadrant. The results for running the testing on all the scenarios are presented, interpreted, and their implications are recommended.

New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

We use the Lie symmetry theory to derive new scaling laws for passive scalar dynamics under the influence of a constant mean gradient of the scalar in decaying homogeneous isotropic turbulence. For this purpose, we apply symmetry analysis to the equations for two-point correlation of the scalar and velocity fluctuations. It is shown that, in contrast to the classical self-similarity approach, the general invariant solutions, respectively scaling laws, of the two-point functions are constructed using the symmetry approach, without requiring an a priori set of similarity scales to carry on the analysis. In the context of the current analysis also, scaling laws for one-point quantities of the scalar variance , the transverse scalar flux and the variance of the turbulent velocity fluctuations are established, which are essentially related to the scaling symmetries. A key step to derive the scaling laws is the symmetry breaking induced by the constant mean scalar gradient. We use the results of a highly resolved direct numerical simulation of Gauding et al. (Comput. Fluids, vol. 180, 2019, pp. 206–217) to verify the scaling laws and the self-similarity of the two-point correlation functions. It is shown that the general symmetry solutions obtained from symmetry results provide a very good similarity to these functions.

Modulatory effects of magnetic vestibular stimulation on resting-state networks can be explained by subject-specific orientation of inner-ear anatomy in the MR static magnetic field

Strong static magnetic fields, as used in magnetic resonance imaging (MRI), stimulate the vestibular inner ear leading to a state of imbalance within the vestibular system that causes nystagmus. This magnetic vestibular stimulation (MVS) also modulates fluctuations of resting-state functional MRI (RS-fMRI) networks. MVS can be explained by a Lorentz force model, indicating that MVS is the result of the interaction of the static magnetic field strength and direction (called “B0 magnetic field” in MRI) with the inner ear’s continuous endolymphatic ionic current. However, the high variability between subjects receiving MVS (measured as nystagmus slow-phase velocity and RS-fMRI amplitude modulations) despite matching head position, remains to be explained. Furthermore, within the imaging community, an “easy-to-acquire-and-use” proxy accounting for modulatory MVS effects in RS-fMRI fluctuations is needed. The present study uses MRI data of 60 healthy volunteers to examine the relationship between RS-fMRI fluctuations and the individual orientation of inner-ear anatomy within the static magnetic field of the MRI. The individual inner-ear anatomy and orientation were assessed via high-resolution anatomical CISS images and related to fluctuations of RS-fMRI networks previously associated with MVS. More specifically, we used a subject-specific proxy for MVS (pMVS) that corresponds to the orientation of the individual inner-ear anatomy within the static magnetic field direction (also called “z-direction” in MR imaging). We found that pMVS explained a considerable fraction of the total variance in RS-fMRI fluctuations (for instance, from 11% in the right cerebellum up to 36% in the cerebellar vermis). In addition to pMVS, we examined the angle of Reid’s plane, as determined from anatomical imaging as an alternative and found that this angle (with the same sinus transformation as for pMVS) explained considerably less variance, e.g., from 2 to 16%. In our opinion, an excess variability due to MVS should generally be addressed in fMRI research analogous to nuisance regression for movement, pulsation, and respiration effects. We suggest using the pMVS parameter to deal with modulations of RS-fMRI fluctuations due to MVS. MVS-induced variance can easily be accounted by using high-resolution anatomical imaging of the inner ear and including the proposed pMVS parameter in fMRI group-level analysis.

Novel estimation method of utility harmonic impedance based on short‐term impedance minimum variance criterion

For harmonic control of a power grid, it is prerequisite to accurately estimate and follow the utility harmonic impedance at the point of common coupling (PCC). The existing estimation methods generally consider that the utility harmonic impedance is constant, which causes the estimation error and fail in tracking of impedance fluctuations, since the utility harmonic impedance is fluctuant in practice. Actually, the harmonic impedance fluctuations will lead to the transient variation of the harmonic voltage and current which is bad for harmonic control. In this study, to follow the harmonic impedance fluctuations, a longer observation period is divided into a series of shorter period, and the fluctuations of the utility harmonic impedance over a short period are regarded as a stationary random process. Then, for each short period, the utility harmonic impedance is estimated by minimizing the fluctuation variance of the utility harmonic impedance. Besides the high estimation precision and good tracking performance of impedance fluctuations, other advantages of the proposed method are not limited by the traditional assumptions, such as the background harmonics are stable and small, the customer harmonic impedance is much larger than the utility, and the harmonic sources of both sides are independent, and so on.

Logarithmic and nonlogarithmic scaling laws of two-point statistics in wall turbulence.

Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point statistics or specifically two-point cumulants of those fluctuations by means of experiments in a wind tunnel. As for corresponding statistics of the rate of the energy dissipation, the scaling is found to be not logarithmic. We reproduce these scaling laws with some mathematics and also with a model of energy-containing eddies that are attached to the wall.

Spin squeezing of 1011 atoms by prediction and retrodiction measurements.

The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit1, which is proportional to [Formula: see text]. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states2. Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 1011 rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states3,4 to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments5-10, with a corresponding angular variance of the squeezed collective spin of 4.6×10-13 radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.

Variance of Atomic Coordinates as a Dynamical Metric to Distinguish Proteins and Protein-Protein Interactions in Molecular Dynamics Simulations.

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.

The Quality Amplification Challenge

In dynamic production environments, positive business outcomes often require pursuing high quality, shorter throughput time, and low cost simultaneously. This research tries to track the timing effect of having undetected defects continue to progress through the supply chain. The purpose is to demonstrate the influence of throughput time on quality variance amplification and the effect of quality loss on manufacturing performance. A time series model is developed, and numerical analyses are conducted to understand how various parameters affect the quality variance fluctuation and quality loss amplification phenomena. The results show that the variance in quality increases as materials move down a supply chain, away from a supplier. In addition, the quality loss experienced by a manufacturer is greater than that faced by a supplier. Finally, both quality variability and quality loss amplification phenomena are larger when throughput time is longer.

Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments

Bank erosion in a sinuous alluvial channel is a continuous phenomenon resulting in bank instability and migration of sediment. In this study, flume experiments were conducted in a sinuous channel to investigate its morphological changes and hydrodynamics. High-order velocity fluctuation moments are analyzed at outer and inner banks to explain the morphological variation in a sinuous river channel. The variance of streamwise velocity fluctuations on both banks of the sinuous channel follows a logarithmic law from a particular depth. In the outer bend region, the magnitude of velocity fluctuation moment is significant, indicating erosion. The trend of velocity fluctuation at higher even-order moments is similar to the variance of streamwise velocity fluctuations where the outer bend magnitude is greater than the inner bend. The premultiplied probability density functions (PDFs) and the flatness factor show greater magnitude in the outer bend of the channel as compared to the inner bend.

Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth Order and Looks Like Second Order

We report that the thermally induced Mott transition in vanadium sesquioxide shows critical slowing down and enhanced variance ("critical opalescence") of the order parameter fluctuations measured through low-frequency resistance-noise spectroscopy. Coupled with the observed increase of the phase-ordering time, these features suggest that the strong abrupt transition is controlled by a critical-like singularity in the hysteretic metastable phase. The singularity is identified with the spinodal point and is a likely consequence of the strain-induced long-range interaction.

Inner, meso, and outer scales in a differentially heated vertical channel

Reynolds shear stress and Reynolds normal stress in a differentially heated vertical channel were shown in a previous paper to scale by a mixed scale of the friction velocity uτ and the maximum mean vertical velocity Umax. This scale was empirically determined; this work presents a physical understanding of the new scaling. A new dimensional analysis is developed that involves a simple modification of the traditional inner–outer scaling. The functional dependencies in the new dimensional analysis are determined using direct numerical simulation (DNS) data. The DNS data confirm the new physical reasoning and reveal, as follows: (i) The velocity fluctuation variance at the centerline scales with an outer scale, which is the mixed scale uτUmax. (ii) The location of the maximum mean vertical velocity scales as an Obukhov-style length scale, which, in turn, scales as the geometric mean of the inner length scale and the outer length scale. (iii) The temperature fluctuation variance at the centerline scales with an outer temperature scale. (iv) The temperature fluctuation variance peaks in the inner layer, and its peak value scales with an inner temperature scale. The new outer scales obtained from the dimensional analysis are shown to be consistent with the properties of the mean momentum balance equation.