Variance Of Fluctuations Research Articles

Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer

AbstractThe impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists of combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. This scheme is shown to converge as the power $3/ 2$ of the spatial resolution. This behaviour is explained by the ${L}_{2} $ convergence of the Fourier representation of a velocity field displaying discontinuities of its derivative. Benchmarking of the code is performed by measuring the drag and lift coefficients and the torque-free rotation rate of a spherical particle in various configurations of an upstream-laminar carrier flow. Such studies show a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream of the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of ‘permanence of large eddies’ that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small-scale turbulent fluctuations. It is demonstrated that the variance of the drag force fluctuations can be modelled by means of standard drag correlations. Temporal correlations of the drag and lift forces are also presented.

Features of optical image jitter in a random medium with a finite outer scale

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations is significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.

Dissecting the dynamics of the US trade balance in an estimated equilibrium model

In an estimated two-country DSGE model, we find that shocks to the marginal efficiency of investment account for more than half of the forecast variance of cyclical fluctuations in the US trade balance. Both domestic and foreign marginal efficiency shocks generate a strong effect on the variability of the imbalance, through shifts in international relative absorption. On the other hand, shocks to uncovered interest parity and foreign export prices, which transmit mainly via the terms of trade and exchange rate, have a strong influence at short forecast-horizons, before the investment disturbances begin their dominance.

Impact of lunisolar tides on the iceberg runoff in Antarctica

Regular variation in the solid runoff of Antarctic glaciers with the period of 18.6 years is revealed as a result of long-term observations. It is demonstrated that the periodicity of the solid runoff correlates with the 18.6-year periodicity of the Earth’s angular velocity variations caused by the 18.6-year cyclicity of the variability of lunisolar tides. It is revealed that the vibratory gravitational sliding of glaciers to the sea is registered due to the tidal fluctuations along with many climate processes. The iceberg runoff lags as compared with the course of the variance of tidal fluctuations of the angular velocity approximately by six years.

Vibrational anomalies and marginal stability of glasses

The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye’s elasticity theory: The density of states deviates from Debye’s ω2 law (“boson peak”), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω1+a is predicted with a ≲ 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation.

Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in the convective boundary layer of the atmosphere

Using a high-resolution LES numerical model, we calculated the turbulent thermal convection for high ratios of horizontal and vertical sizes of the computational domain (26: 26: 1). The natural analog of the simulated process is a planetary boundary layer (PBL) of the atmosphere growing with height in the background of stably stratified overlying air layers over a horizontally homogeneous heated surface under a weak average wind. We obtained the spectral distributions of variances of fluctuations in potential temperature and velocity components in ranges corresponding to scales from a few tens of meters to a few tens of kilometers. We found energetically significant segments of the spectrum of large-scale fluctuations in the potential temperature for which the power dependences S ∼ k−1/3 and S ∼ k−4/3 are satisfied with good accuracy. We calculated the characteristic spatial scales of horizontal fluctuations in velocity and temperature. We obtained a dependence of these scales on the height of the growing convective PBL. We discuss the characteristic features of large-scale distributions in terms of the self-similarity of the growing boundary layer behavior.

Virtual potentials for feedback traps

The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time scales: There is a delay between the measurement of a particle's position and the feedback response, the feedback response is applied for a finite update time, and a finite camera exposure integrates motion. We show how to incorporate such timing effects into the description of particle motion. For the test case of a virtual quadratic potential, we give the first accurate description of particle dynamics, calculating the power spectrum and variance of fluctuations as a function of feedback gain, testing against simulations. We show that for small feedback gains, the motion approximates that of a particle in an ordinary harmonic potential. Moreover, if the potential is varied in time, for example by varying its stiffness, the work that is calculated approximates that done in an ordinary changing potential. The quality of the approximation is set by the ratio of the update time of the feedback loop to the relaxation time of motion in the virtual potential.

Oil price shocks and stock market in oil‐exporting countries: evidence from Iran stock market

AbstractThis study adopts causality in mean and variance approach to investigate dynamic relationship between stock market in an oil‐exporting country (Iran) and the international oil market. The empirical results imply that in view of underlying data‐generating process of the series, the variance of oil price fluctuations does not cause the variance of Iran stock returns. This means that there is no volatility spillover effect between Iran stock market and international oil market.

Hydrologic variability in dryland regions: impacts on ecosystem dynamics and food security

Research on ecosystem and societal response to global environmental change typically considers the effects of shifts in mean climate conditions. There is, however, some evidence of ongoing changes also in the variance of hydrologic and climate fluctuations. A relatively high interannual variability is a distinctive feature of the hydrologic regime of dryland regions, particularly at the desert margins. Hydrologic variability has an important impact on ecosystem dynamics, food security and societal reliance on ecosystem services in water-limited environments. Here, we investigate some of the current patterns of hydrologic variability in drylands around the world and review the major effects of hydrologic fluctuations on ecosystem resilience, maintenance of biodiversity and food security. We show that random hydrologic fluctuations may enhance the resilience of dryland ecosystems by obliterating bistable deterministic behaviours and threshold-like responses to external drivers. Moreover, by increasing biodiversity and the associated ecosystem redundancy, hydrologic variability can indirectly enhance post-disturbance recovery, i.e. ecosystem resilience.

An alternative to the conventional micro-canonical ensemble

The usual approach to the foundations of quantum statistical physics is based on the conventional micro-canonical ensemble as a starting point for deriving the Boltzmann–Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as the quantum micro-canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems, revealing good agreement with the existing analytical results for large quantum systems. We also propose the way to introduce analytical corrections accounting for finite-size effects. With the above corrections, the agreement between the analytical and the numerical results becomes very accurate. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium.

On the Likelihood and Fluctuations of Gaussian Realizations

The likelihood of Gaussian realizations, as generated by the Cholesky simulation method, is analyzed in terms of Mahalanobis distances and fluctuations in the variogram reproduction. For random sampling, the probability to observe a Gaussian realization vector can be expressed as a function of its Mahalanobis distance, and the maximum likelihood depends only on the vector size. The Mahalanobis distances are themselves distributed as a Chi-square distribution and they can be used to describe the likelihood of Gaussian realizations. Their expected value and variance are only determined by the size of the vector of independent random normal scores used to generate the realizations. When the vector size is small, the distribution of Mahalanobis distances is highly skewed and most realizations are close to the vector mean in agreement with the multi-Gaussian density model. As the vector size increases, the realizations sample a region increasingly far out on the tail of the multi-Gaussian distribution, due to the large increase in the size of the uncertainty space largely compensating for the low probability density. For a large vector size, realizations close to the vector mean are not observed anymore. Instead, Gaussian vectors with Mahalanobis distance in the neighborhood of the expected Mahalanobis distance have the maximum probability to be observed. The distribution of Mahalanobis distances becomes Gaussian shaped and the bulk of realizations appear more equiprobable. However, the ratio of their probabilities indicates that they still remain far from being equiprobable. On the other hand, it is observed that equiprobable realizations still display important fluctuations in their variogram reproduction. The variance level that is expected in the variogram reproduction, as well as the variance of the variogram fluctuations, is dependent on the Mahalanobis distance. Realizations with smaller Mahalanobis distances are, on average, smoother than realizations with larger Mahalanobis distances. Poor ergodic conditions tend to generate higher proportions of flatter variograms relative to the variogram model. Only equiprobable realizations with a Mahalanobis distance equal to the expected Mahalanobis distance have an expected variogram matching the variogram model. For large vector sizes, Cholesky simulated Gaussian vectors cannot be used to explore uncertainty in the neighborhood of the vector mean. Instead uncertainty is explored around the n-dimensional elliptical envelop corresponding to the expected Mahalanobis distance.

Fluctuations of current in nonstationary diffusive lattice gases

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a steplike initial density profile. We analytically determine the variance of the current fluctuations for a class of diffusive processes with a density-independent diffusion coefficient. Our calculations rely on a perturbation theory around the noiseless hydrodynamic solution. We consider both quenched and annealed types of averaging (the initial condition is allowed to fluctuate in the latter situation). The general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the Kipnis-Marchioro-Presutti model [Kipnis, Marchioro, and Presutti, J. Stat. Phys. 27, 65 (1982)]. We also probe large deviations of the current for the symmetric exclusion process. This is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm.

Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in Terms of Phenotypic Variances

The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic variances of epigenetic and genetic origins is confirmed. The former is given by the variance of the phenotypic fluctuation due to noise in the developmental process; and the latter, by the variance of the phenotypic fluctuation due to genetic mutation. The relationship suggests a link between robustness to noise and to mutation, since robustness can be defined by the sharpness of the distribution of the phenotype. Next, the proportionality between the variances is demonstrated to also hold over expressions of different genes (phenotypic traits) when the system acquires robustness through the evolution. Then, evolution under environmental variation is numerically investigated and it is found that both the adaptability to a novel environment and the robustness are made compatible when a certain degree of phenotypic fluctuations exists due to noise. The highest adaptability is achieved at a certain noise level at which the gene expression dynamics are near the critical state to lose the robustness. Based on our results, we revisit Waddington's canalization and genetic assimilation with regard to the two types of phenotypic fluctuations.

THE TRANSPORT OF DENSITY FLUCTUATIONS THROUGHOUT THE HELIOSPHERE

The solar wind is recognized as a turbulent magnetofluid, for which the properties of the turbulent velocity and magnetic field fluctuations are often described by the equations of incompressible magnetohydrodynamics (MHD). However, low-frequency density turbulence is also ubiquitous. On the basis of a nearly incompressible formulation of MHD in the expanding inhomogeneous solar wind, we derive the transport equation for the variance of the density fluctuations (Rho(exp 2)). The transport equation shows that density fluctuations behave as a passive scalar in the supersonic solar wind. In the absence of sources of density turbulence, such as within 1AU, the variance (Rho(exp 2)) approximates r(exp -4). In the outer heliosphere beyond 1 AU, the shear between fast and slow streams, the propagation of shocks, and the creation of interstellar pickup ions all act as sources of density turbulence. The model density fluctuation variance evolves with heliocentric distance within approximately 300 AU as (Rho(exp 2)) approximates r(exp -3.3) after which it flattens and then slowly increases. This is precisely the radial profile for the density fluctuation variance observed by Voyager 2. Using a different analysis technique, we confirm the radial profile for Rho(exp 2) of Bellamy, Cairns, & Smith using Voyager 2 data. We conclude that a passive scalar description for density fluctuations in the supersonic solar wind can explain the density fluctuation variance observed in both the inner and the outer heliosphere.

Optical conductivity of single-layer graphene induced by temporal mass-gap fluctuations

We consider the dynamics of charge carriers in single-layer graphene that are subject to random temporal fluctuations of their mass gap. The optical conductivity is calculated by incorporating the quantum-stochastic time evolution into the standard linear-response (Kubo) theory. We find that, for an intermediate range of frequencies below the average gap size, electron transport is enhanced by fluctuations. At the same time, in the limit of high as well as low frequencies, the conductivity is suppressed as the variance of gap fluctuations increases. In particular, the dc conductivity is always suppressed by a random temporal mass with nonvanishing mean value and vanishes in the zero-temperature limit. Our results are complementary to those obtained recently for static random-gap disorder in finite-size systems.

MAGNETIC VARIANCES AND PITCH-ANGLE SCATTERING TIMES UPSTREAM OF INTERPLANETARY SHOCKS

Recent observations of power-law time profiles of energetic particles accelerated at interplanetary shocks have shown the possibility of anomalous, superdiffusive transport for energetic particles throughout the heliosphere. Those findings call for an accurate investigation of the magnetic field fluctuation properties at the resonance frequencies upstream of the shock's fronts. Normalized magnetic field variances, indeed, play a crucial role in the determination of the pitch-angle scattering times and then of the transport regime. The present analysis investigates the time behavior of the normalized variances of the magnetic field fluctuations, measured by the Ulysses spacecraft upstream of corotating interaction region (CIR) shocks, for those events which exhibit superdiffusion for energetic electrons. We find a quasi-constant value for the normalized magnetic field variances from about 10 hr to 100 hr from the shock front. This rules out the presence of a varying diffusion coefficient and confirms the possibility of superdiffusion for energetic electrons. A statistical analysis of the scattering times obtained from the magnetic fluctuations upstream of the CIR events has also been performed; the resulting power-law distributions of scattering times imply long range correlations and weak pitch-angle scattering, and the power-law slopes are in qualitative agreement with superdiffusive processes described by amore » Levy random walk.« less

Frequency stabilization of an external-cavity diode laser to metastable argon atoms in a discharge

A laser stabilization scheme using magnetic dichroism in a RF plasma discharge is presented. This method has been used to provide a frequency stable external-cavity diode laser that is locked to the 4s[3/2](2) → 4p[5/2](3) argon laser cooling transition at 811.53 nm. Using saturated absorption spectroscopy, we lock the laser to a Doppler free peak which gave a locking range of 20 MHz when the slope of the error signal was maximized. The stability of the laser was characterized by determining the square root Allan variance of laser frequency fluctuations when the laser was locked. A stability of 129 kHz was measured at 1 s averaging time for data acquired over 6000 s.

Alleviation of Power Fluctuation in Interconnected Power Systems With Wind Farm by SMES With Optimal Coil Size

The large penetration of wind power into interconnected power systems causes the severe power fluctuation in tie-lines. To alleviate power fluctuation, the superconducting magnetic energy storage (SMES) can be applied. Nevertheless, the installation of SMES is quite costly. Especially, the superconducting coil size which is the vital part of SMES, must be carefully specified. This paper proposes a new optimization technique of power controller parameters and coil sizes of multiple SMES units for alleviation of tie-line power fluctuation in interconnected power systems with wind farms. The structure of active and reactive power controllers of SMES is the proportional-integral (PI). Based on the minimization of the variance of tie-line power fluctuation and the initial stored energy of a SMES unit, the optimal PI parameters and coil size can be automatically tuned by a particle swarm optimization. Simulation study in the West Japan interconnected systems confirms that the proposed SMES with optimal coil size is able to effectively and robustly suppress power fluctuation against various wind power patterns and heavy power flow levels.

The magnitude and colour of noise in genetic negative feedback systems

The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or ‘noise’ in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier—for transcriptional autorepression, it is frequently negligible.

Phase fluctuations of optical waves in the case of cone focusing in turbulent atmosphere

Statistical parameters of phase fluctuations of optical radiation with a cone-shape wavefront propagating in turbulent atmosphere are studied. The method of smooth perturbations is used for calculation of the variance of phase fluctuations of conical optical waves formed by conical and conoidal axicons. It is found that the variance of phase fluctuations of a conical optical wave in turbulent atmosphere is less than that of a plane wave and a fundamental Bessel beam. The dependence of the variance of phase fluctuations on the parameter characterizing the cone-shape wavefront of an optical wave, is of a two-scale character for both conical and conoidal axicons. A decrease in the variance of phase fluctuations in turbulent atmosphere is more typical for the conical axicon than for the conoidal. The spatial nonuniformity of phase fluctuations, known for a fundamental Bessel beam, occurs for conic optical waves as well; however, the quantitative value of the effect differs in this case.