Density Autocorrelation Function Research Articles

Experimental validation of the analytic model for the temporal decay of the density auto-correlation function in a strongly coupled dusty plasma

In a recent theoretical work [Dhaka et al. Sci. Rep. 12, 21883 (2022)], the method of determining the transport coefficients of a system from the time dynamics of the density auto-correlation function (DAF) was extended to complex plasma systems using the framework of a generalized hydrodynamics model. An exact analytical form of the density auto-correlation function of the thermal level spontaneous fluctuations of a Yukawa system was obtained. In the present work, we provide the first experimental validation of this analytical model for a strongly coupled dusty plasma system. The dusty plasma is produced by introducing micron-sized melamine formaldehyde particles in radio frequency argon discharges, and the DAF of the spontaneous dust density fluctuations is determined by optically tracking the trajectories of the dust particles. The experimentally obtained DAF is found to show a trend that is consistent with our earlier theoretical and numerical predictions. It is further used to determine the microscopic rate of heat diffusion for various values of the fluctuation wave-number k and obtain an extrapolated value of the macroscopic heat diffusion rate in the limit k →0. The experimental validation lends strong support to our generalized theoretical model, which can be usefully employed now in a variety of strongly coupled systems.

Growth Kinetics of Random Sequential Adsorption Packings Built of Two-Dimensional Shapes with Discrete Orientations

We studied random sequential adsorption packings constructed from rectangles, ellipses, and discorectangles, where the orientations of constituent shapes were picked from discrete sets of values with varying spacing. It allowed us to monitor the transition between the two edge cases: the parallel alignment and the arbitrary, continuous orientation of the shapes within the packing. The packings were generated numerically. Apart from determining the kinetics of packing growth in low- and high-density regimes, we analyzed the results in terms of packing density and probed the microstructural properties using the density autocorrelation function.

Random sequential adsorption of aligned regular polygons and rounded squares: Transition in the kinetics of packing growth.

We study two-dimensional random sequential adsorption (RSA) of flat polygons and rounded squares aligned in parallel to find a transition in the asymptotic behavior of the kinetics of packing growth. Differences in the kinetics for RSA of disks and parallel squares were confirmed in previous analytical and numerical reports. Here, by analyzing the two classes of shapes in question we can precisely control the shape of the packed figuresand thus localize the transition. Additionally, we study how the asymptotic properties of the kinetics depend on the packing size. We also provide accurate estimations of saturated packing fractions. The microstructural properties of generated packings are analyzed in terms of the density autocorrelation function.

Turbulence structure in an experimental compound channel with varying coverage of riparian vegetation on the floodplain

Aquatic plants can alter flow structure, affect sediment transport and contaminants diffusion, and is noteworthy for channel restoration and navigation. In the present work, experiments are conducted to investigate the velocity and turbulence structures in a compound channel with varying coverage of riparian vegetation. Lateral profile of velocity may change from a traditional single sharply increasing segment to two sharply increasing segments, the shear layer (SL) and the mixing layer (ML), which are influenced by bed morphology and vegetation. Lateral profile of Reynolds stress is bimodal, with a crest value that decreases with increasing ratio of the width of nonvegetated floodplain to the bankfull height (BNV/h). Quasi-two-dimensional (Quasi-2-D) coherent structures can be found in both SL and ML when BNV/h is small according to power spectral density and temporal autocorrelation function, which have a significant influence on Reynolds stress. Brief and intense ejections and sweeps events dominate the contribution to Reynolds stress, and according to quadrant analysis, an ejections event of the SL may occur simultaneously with each event of the ML.

Auto-correlations of microscopic density fluctuations for Yukawa fluids in the generalized hydrodynamics framework with viscoelastic effects

The present work develops a theoretical procedure for obtaining transport coefficients of Yukawa systems from density fluctuations. The dynamics of Yukawa systems are described in the framework of the generalized hydrodynamic (GH) model that incorporates strong coupling and visco-elastic memory effects by using an exponentially decaying memory function in time. A hydrodynamic matrix for such a system is exactly derived and then used to obtain an analytic expression for the density autocorrelation function (DAF)—a marker of the time dynamics of density fluctuations. The present approach is validated against a DAF obtained from numerical data of Molecular Dynamics (MD) simulations of a dusty plasma system that is a practical example of a Yukawa system. The MD results and analytic expressions derived from the model equations are then used to obtain various transport coefficients and the latter are compared with values available in the literature from other models. The influence of strong coupling and visco-elastic effects on the transport parameters are discussed. Finally, the utility of our calculations for obtaining reliable estimates of transport coefficients from experimentally determined DAF is pointed out.

Statistical Characterization of the Magnetic Field in Space during Magnetic Storms

Magnetic storms are an important type of space weather and are usually caused by large streams of charged elementary particles (ions, for example) generated during solar wind production. The occurrence of magnetic storms can pose a threat to the internal electronics of satellites, communication, navigation, remote sensing, etc. Additionally, ground-based electrical facilities may be impacted. In this paper, we focus on the statistical characteristics of the space channel during the occurrence of magnetic storms. By analyzing the observed data for each component of the magnetic field during a magnetic storm and applying the relevant cognitive radio theory, we obtain the probability density function, autocorrelation function, and power spectrum of the magnitude of each component of the magnetic field. The results show that the probability density of the magnitude of each component of the magnetic field gradually deviates from the Gaussian distribution as the Magnetic storm ring current index (Dst index) increases during a magnetic storm, and the autocorrelation function exhibits nonstationary characteristics, which further leads to the time-varying characteristics of the power spectrum.

Time-correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrödinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, and quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of the density function, with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.

Random sequential adsorption of rounded rectangles, isosceles and right triangles

We studied random sequential adsorption (RSA) of three classes of polygons with rounded corners: rectangles, isosceles triangles, and orthogonal triangles. Using the algorithm that enables the generation of strictly saturated RSA packing, we systematically determined the mean saturated packing fraction for RSA configurations built by these shapes. The main aim was to find the figure that forms the densest random configuration. Although for rounded rectangles the packing fractions were lower than for discorectangles, the densities reached for some rounded isosceles and right triangles exceeded the highest known two-dimensional packing fraction for configurations built of unoriented monodisperse objects. The microstructural properties of several packings were discussed in terms of the two-point density autocorrelation function.

The effect of substrate waviness on random sequential adsorption packing properties

Random sequential adsorption of spheres on a wavy surface was studied. It was determined how surface structure influences random packing properties such as the packing fraction, the kinetics of packing growth and the two-particle density correlation function. Until the substrate varies within the range one order of magnitude smaller than the particle’s diameter, the properties of the packings obtained do not differ significantly from those on a flat surface. On the other hand, for the higher amplitude of unevenness, the packing fraction, low-density growth kinetics and the density autocorrelation function change significantly, while asymptotic growth kinetics seems to be barely sensitive to surface waviness. Besides fundamental significance, the study suggests that the experimental measurement of the aforementioned basic properties of adsorption monolayers can reveal the surface’s porous structure without investigating the surface itself.

Dynamical properties of different models of elastic polymer rings: Confirming the link between deformation and fragility.

We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [N. Gnan and E. Zaccarelli, Nat. Phys. 15, 683 (2019)] where an inner Hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced by opposite forces, and (iii) a semi-flexible model where an angular potential between adjacent monomers induces strong particle deformations. By analyzing the dynamics of the three models, we find that in all cases, there exists a direct link between the system fragility and particle asphericity. Among the three, only the first model displays anomalous dynamics in the form of a super-diffusive behavior of the mean-squared displacement and of a compressed exponential relaxation of the density auto-correlation function. We show that this is due to the combination of internal elasticity and the out-of-equilibrium force self-generated by each ring, both of which are necessary ingredients to induce such a peculiar behavior often observed in experiments of colloidal gels. These findings reinforce the role of particle deformation, connected to internal elasticity, in driving the dynamical response of dense soft particles.

Diffraction pattern degradation driven by intense ultrafast X-ray pulse for [formula omitted

The drastic evolution of molecular systems exposed to ultrashort intense X-ray pulse is a fundamental obstacle for single-particle imaging (SPI) by means of X-ray free electron lasers (XFEL). Here we tackle the simplest molecule H2+ and its diffraction pattern degradations in the strong ultrashort X-ray beam. The semiclassical method of the problem solution and its advantages are described in detail. We apply the method to calculate the electron density autocorrelation functions (ACF) for a few internuclear distances and then discuss numeric simulation data.

The Structure of Climate Variability Across Scales

AbstractOne of the most intriguing facets of the climate system is that it exhibits variability across all temporal and spatial scales; pronounced examples are temperature and precipitation. The structure of this variability, however, is not arbitrary. Over certain spatial and temporal ranges, it can be described by scaling relationships in the form of power laws in probability density distributions and autocorrelation functions. These scaling relationships can be quantified by scaling exponents which measure how the variability changes across scales and how the intensity changes with frequency of occurrence. Scaling determines the relative magnitudes and persistence of natural climate fluctuations. Here, we review various scaling mechanisms and their relevance for the climate system. We show observational evidence of scaling and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate prediction.

Random sequential adsorption of particles with tetrahedral symmetry.

We study random sequential adsorption (RSA) of a class of solids that can be obtained from a cube by specific cutting of its vertices, in order to find out how the transition from tetrahedral to octahedral symmetry affects the densities of the resulting jammed packings. We find that in general solids of octahedral symmetry form less dense packing; however, the lowest density was obtained for the packing built of tetrahedra. The densest packing is formed by a solid close to a tetrahedron but with vertices and edges slightly cut. Its density is θ_{max}=0.41278±0.00059 and is higher than the mean packing fraction of spheres or cuboids but is lower than that for the densest RSA packings built of ellipsoids or spherocylinders. The density autocorrelation function of the studied packings is typical for random media and vanishes very quickly with distance.

Chaotic characteristic analysis of network traffic time series at different time scales

Abstract Characteristic analysis of network traffic time series is very meaningful for network traffic prediction. The dynamic behavior of network traffic time series is an external manifestation under the combined action of complex non-linear and multi-scale phenomena. Based on the chaotic theory, the chaotic characteristics of network traffic time series collected at different time scales are analyzed and discussed. Firstly, power spectral density analysis and autocorrelation function analysis are introduced. The results show that the power spectral density of network traffic has continuous broad spectrum, which qualitatively explains the chaotic behavior of network traffic. The value of autocorrelation function of network traffic decreases with time delay, which shows its short-term predictability. Calculations on scaling exponent show that network traffic is scale-free at different time scales. Then, Hurst index of network traffic is calculated, and the 0-1 test algorithm for chaos is used to calculate the incremental growth rate of network traffic time series. The variation of chaotic characteristics of network traffic at different time scales is discussed. Further, the phase space of network traffic time series at different time scales is reconstructed, and the correlation dimension, largest Lyapunov exponent, and Kolmogorov entropy are calculated respectively. These chaotic identification indexes are used to analyze the chaotic characteristics of network traffic and their variation with time scales. The results show that the relationship between the time scale and the non-linear characteristics of network traffic time series is not obvious. The incremental growth rate of network traffic time series has no obvious change with the increase of time scale. There is no clear relationship between the change of time scale and embedding dimension and delay time. The largest Lyapunov exponent show that the network traffic at different time scales has different maximum predictable time. At the same time, Kolmogorov entropy increase with the increase of time scale, which means that the chaotic characteristics of network traffic time series become stronger and the predictability becomes worse with the time scale.

Random sequential adsorption of unoriented rectangles at saturation

This study presents an algorithm to generate a saturated random packing built of identical, unoriented rectangles. The algorithm is based on tracing regions that are unavailable for placing subsequent shapes. If these regions cover the whole packing the algorithm stops because no more objects can be added to the packing; thus it is saturated. The algorithm is used to study packings built of rectangles of side-to-side length ratio $\ensuremath{\epsilon}\ensuremath{\in}[1.0,2.5]$. The densest packings are obtained for $\ensuremath{\epsilon}=1.49\ifmmode\pm\else\textpm\fi{}0.02$, and the packing fraction, in this case, reached $0.549641\ifmmode\pm\else\textpm\fi{}0.000017$. The microstructural properties of the obtained packings are studied in terms of density autocorrelation function and propagation of orientational ordering.

Random sequential adsorption of cubes.

Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.

Fermi liquid, clustering, and structure factor in dilute warm nuclear matter

Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structure factor. Comparing with the Landau Fermi liquid theory which is reproduced in lowest approximation, the account of bound state formation and continuum correlations gives the correct low-density result as described by the second virial coefficient and by the mass action law (nuclear statistical equilibrium). Going to higher densities, the inclusion of medium effects is more involved compared with other quantum statistical approaches, but the relation to the Landau Fermi liquid theory gives a promising approach to describe not only thermodynamic but also collective excitations and non-equilibrium properties of nuclear systems in a wide region of the phase diagram.

Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit

Spin-echo-based small-angle neutron scattering techniques like spin-echo SANS (SESANS) or spin-echo modulated SANS (SEMSANS) as well as dark-field (DF) imaging are directly sensitive to \tilde{G}(\delta), which is the projection of the scattering length density autocorrelation function \tilde{\gamma}(r). Here, a simplified transformation cycle relating the spherically symmetric correlation function \tilde{\gamma}(r), the projected correlation function \tilde{G}(\delta) and the macroscopic small-angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in theSASfitsoftware package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate \tilde{G}(0) from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally availableqrange can strongly influence the obtained results.

Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging.

We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.