Correlation Function Of Fluctuations Research Articles

Nanoclustering in non-ideal ethanol/heptane solutions alters solvation dynamics.

Alcohol/alkane solutions widely used in chemical synthesis and as transportation fuels are highly non-ideal due to the nanoscale clustering of the amphiphilic alcohol molecules within the nonpolar alkanes. Besides impacting reactivity, such as combustion, non-ideal solutions are likely to exhibit unusual solvation dynamics on ultrafast time scales arising from the structurally heterogeneous nature of molecular-scale association. Using a convenient transition metal carbonyl vibrational probe [(C5H5)Mn(CO)3, CMT], linear absorption and nonlinear two-dimensional infrared (2D-IR) spectroscopy reveal composition-dependent solvation dynamics as reported by the frequency fluctuation correlation function in a series of ethanol/heptane solutions. Slow spectral diffusion with dilute ethanol indicates preferential solvation of the polar solute by the alcohol with a mechanism largely dominated by solvent exchange. Comparison with an ethanol/acetonitrile solution series yields no substantial preferential solvation or solvent exchange signatures in the linear or 2D-IR spectra. In ethanol/heptane solutions, increasing the ethanol concentration speeds up the solvation dynamics, which is largely consistent with a model that includes solvent exchange and single-solvent spectral diffusion. Detailed analysis of the deviation from the experimental time constants from the model's optimal parameters yields a remarkable resemblance of the concentration-weighted Kirkwood-Buff integrals for ethanol/heptane solutions. This trend indicates that solution non-ideality alters the spectral diffusion dynamics of the probe solute. Given that nanoscale clustering drives the non-ideality, these experiments reveal a dynamical consequence of nanoscale heterogeneity on the ultrafast dynamics of the solution. Refined understanding of the structural and dynamical aspects of mixed solvents will be necessary for predictive solution strategies in chemistry.

Scintillation Level of Scattered Radio Waves in the Equatorial Ionosphere

Scintillation effects of propagating and scattered radio waves (RWs) are considered analytically and numerically in the equatorial terrestrial ionosphere applying the statistical characteristics. Analytical calculations of the second-order statistical moments of the phase fluctuations of the ordinary and extraordinary RWs in the conductive collision ionospheric magnetoplasma (COCOIMA) are carried out for the first time using the Wentzel-Kramers-Brilluen method and the modified smooth perturbation method in consideration of the diffraction effects. Polarization coefficients of these waves in the equatorial ionosphere have been derived for the first time. The scintillation level includes the variance and the correlation functions of scattered RWs. Statistical moments contain complex refractive index, anisotropy coefficient characterizing irregular plasmonic structures, tilt angle of prolate irregularities concerning to the external magnetic field, permittivity components of the equatorial ionosphere, Hall's, Pedersen and longitudinal conductivities. A new feature of the "Fountain Effect" has been discovered in the equatorial ionosphere at weak and moderate scintillations caused due to anisotropy parameters of electron density fluctuations. Anisotropy parameters of electron density inhomogeneities influence the scintillation index of both the ordinary and extraordinary radio waves shifting maximums of the curves in the opposite directions at weak and moderate scintillations. Numerical calculations are carried out using the hybrid anisotropic correlation function of electron density fluctuations containing both exponential and power-law spectral functions having arbitrary spectral index, applying the experimental data.

Hydrodynamic fluctuations, diffusion and correlation functions in systems of particles adsorbed on solid surfaces

We present the detailed derivation of the equations describing the evolution of the hydrodynamic fluctuations of the coverage of particles adsorbed on homogeneous lattices. Using the method of the non-equilibrium statistical operator, we reduce the balance equation governing the behavior of the individual particles to the diffusion equation. On a macroscopic level, this equation describes the approach to equilibrium of the hydrodynamic coverage fluctuations. We obtain the analytical expressions for the Fickian diffusivity and Onsager phenomenological coefficient. These expressions are derived with account of the lateral interaction between the particles. They are simple functions of the thermodynamic quantities — derivatives of the thermodynamic potential over its arguments. The transport coefficients accurately describe the development of fluctuations in the entire coverage region and in the wide range of lateral interactions. We presented an elementary introduction to the theory of fluctuations in the lattice gas systems. For calculations of the correlation function and spectral density of fluctuations, we use the Langevin approach and the method of moments. The exact coincidence of the analytical expressions for the diffusion coefficients obtained by the two independent calculations is the direct proof of the accuracy of the approach developed in Chumak and Tarasenko (1980).

Correlations in a weakly interacting two-dimensional random flow.

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us to establish the criterion of validity of the perturbation theory for different ratios of viscosity and bottom friction. We find that the corrections to the second moment are anomalously weak in the cases of small bottom friction and small viscosity and relate the weakness to the energy and enstrophy balances. We demonstrate that at small bottom friction the triple correlation function is characterized by universal scaling behavior in some region of lengths. The developed perturbation method was verified and confirmed by direct numerical simulations.

On the testability of the Károlyházy model

Károlyházy’s original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated Károlyházy’s assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal.

A new computational methodology for the characterization of complex molecular environments using IR spectroscopy: bridging the gap between experiments and computations.

The molecular interactions and dynamics of complex liquid solutions are now routinely measured using IR and 2DIR spectroscopy. In particular, the use of the latter allows the determination of the frequency fluctuation correlation function (FFCF), while the former provides us with the average frequency. In turn, the FFCF can be used to quantify the vibrational dynamics of a molecule in a solution, and the center frequency provides details about the chemical environment, solvatochromism, of the vibrational mode. In simple solutions, the IR methodology can be used to unambiguously assign the interactions and dynamics observed by a molecule in solution. However, in complex environments with molecular heterogeneities, this assignment is not simple. Therefore, a method that allows for such an assignment is essential. Here, a parametrization free method, called Instantaneous Frequencies of Molecules or IFM, is presented. The IFM method, when coupled to classical molecular simulations, can predict the FFCF of a molecule in solutions. Here, N-methylacetamide (NMA) in seven different chemical environments, both simple and complex, is used to test this new method. The results show good agreement with experiments for the NMA solvatochromism and FFCF dynamics, including characteristic times and amplitudes of fluctuations. In addition, the new method shows equivalent or improved results when compared to conventional frequency maps. Overall, the use of the new method in conjunction with molecular dynamics simulations allows unlocking the full potential of IR spectroscopy to generate molecular maps from vibrational observables, capable of describing the interaction landscape of complex molecular systems.

Shapes of the cosmological low-speed collider

Abstract Massive particles produced during inflation leave specific signatures in soft limits of correlation functions of primordial fluctuations. When the Goldstone boson of broken time translations acquires a reduced speed of sound, implying that de Sitter boosts are strongly broken, we introduce a novel discovery channel to detect new physics during inflation, called the cosmological low-speed collider signal. This signal is characterised by a distinctive resonance lying in mildly-soft kinematic configurations of cosmological correlators, indicating the presence of a heavy particle, whose position enables to reconstruct its mass. We show that this resonance can be understood in terms of a non-local single-field effective field theory, in which the heavy field becomes effectively non-dynamical. This theory accurately describes the full dynamics of the Goldstone boson and captures all multi-field physical effects distinct from the non-perturbative particle production leading to the conventional cosmological collider signal. As such, this theory provides a systematic and tractable way to study the imprint of massive fields on cosmological correlators. We conduct a thorough study of the low-speed collider phenomenology in the scalar bispectrum, showing that large non-Gaussianities with new shapes can be generated, in particular beyond weak mixing. We also provide a low-speed collider template for future cosmological surveys.

Flickering of a radio-signal due to an atmospheric turbulence

Background. Turbulent fluctuations of the refractive index in the atmosphere lead to distortions during the passage of the radio signal. This can lead to distortion of the transmitted information due to the resulting fluctuations of the amplitude, phase and intensity of the electromagnetic wave that transmits the radio signal. Fluctuations in the intensity of the radio signal lead to flickering of the radio signal on the receiving antenna due to turbulent phenomena in the atmosphere, which are a complex multifunctional physical phenomenon. Aim. The problem of fluctuation of the intensity of the radio signal at the receiving antenna due to atmospheric turbulence is considered the flicker of the radio signal. This problem is currently extremely actual, because there is a tendency of active, negative interference in the process of high-quality transmission of the radio signal on the background of naturally caused turbulent fluctuations. Methods. A theoretical analysis of the passage of a radio signal through a turbulent atmosphere is carried out. The spatial correlation function of fluctuations in the intensity of the received radio signal due to atmospheric turbulence is investigated. Results. The concept of the radio signal flicker characteristic is introduced as the average value of a random variable over the cross section of the receiving antenna the dispersion of the logarithm of the radio signal power. A model of the occurrence of fluctuations in the case of two regions in the cross section of the receiving antenna with different levels of radio signal intensity is calculated. The correlation function for this model is found. Conclusion. Based on the Fourier-spectrum expansion of the two-point spatial correlation function of turbulent fluctuations of the refractive index, the dependence of the flicker characteristic of the radio signal on the wave number of turbulent fluctuations of the atmosphere is found. It is shown that the turbulence of the atmosphere has the greatest effect on the radio signal when the length of the electromagnetic wave is comparable to the scale of turbulent fluctuations.

Probing the initial state of inflation: analytical structure of cosmological correlators

We study the analytic structure of in-in correlation functions in a deSitter background. The aim of this study is to probe the initial conditions for inflation through the features of correlation functions of the field fluctuations, and understand precisely how an in-in correlator responds to particles in the initial state. We emphasize that the choice of vacuua and the corresponding particle interpretation for these fluctuations is flexible, and we clarify the role of this choice at the level of calculations and their diagrammatic interpretation. We consider several possibilities aside from the standard Bunch Davies (BD) vacuum prescription for the initial state, and trace the change in pole structure as one begins adding excitations; starting from just a single particle, to highly excited states and special cases such as a coherent state. We also go beyond the pole structure of the bispectrum, and calculate the 4 point classical and quantum correlators.We illustrate — with the example of coherent states — the subtleties in concluding a Bunch Davies initial state from the absence of physical poles in the bispectrum, which is interesting in light of some recent literature.Initial states with a finite number of excitations are plagued with disconnected diagrams isolated in phase space, and we highlight their implications on the observation of these signals, and how the situation changes as one begins to excite more and more particles. We also comment about the implications of various initial conditions on the squeezed limit of the bispectrum.These new pole structures are a direct consequence of mixing of positive and negative frequency modes which is a characteristic of curved spacetimes; in particular, we see in detail how particles in an initial state replicate mode mixing structures. This study aims to clarify the missing details that link quantum and classical initial conditions, and sharpen our understanding of in-in correlators in inflation.

Horizontal Correlation Functions of Wind Fluctuations in the Mesosphere and Lower Thermosphere

AbstractMeasurements of kinetic energy in vortical and divergent fluctuations in the mesosphere and lower thermosphere can be used to study stratified turbulence (ST) and gravity waves. This can be done using horizontal correlation functions of the fluctuating component of velocity. This study introduces a novel method for estimating these correlation functions using radars that observe Doppler shifts of ionized specular meteor trails. The technique solves the correlation functions directly on a longitudinal‐transverse‐up coordinate system, assuming axial symmetry. This procedure is more efficient and leads to smaller uncertainties than a previous approach. The new technique is applied to a year‐long data set from a multistatic specular meteor radar network in Germany, to study the annual variability of kinetic energy within turbulent fluctuations at 87–93 km of altitude. In monthly averages, the kinetic energy is found to be nearly equipartitioned between vortical and divergent modes. Turbulent fluctuations maximize during the winter months with approximately 25% more energy in these months than at other times. The horizontal correlation functions are in agreement with the inertial subrange of ST, exhibiting a 2/3 power law in the horizontal lag direction, with an outermost scale of ST to be about 380 km. This suggests that horizontal correlation functions could be used to estimate turbulent energy transfer rates.

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions.

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

FCSNet and ImFCSNet, convolutional neural network approaches to FCS data analysis.

Fluorescence Correlation Spectroscopy (FCS) is a widely used tool to analyse molecular dynamics in biological samples. It analyses the correlation function of the fluorescence fluctuations in a defined observation volume to extract information about the underlying molecular processes. However, FCS faces a number of challenges. First, it requires the use of theoretical fit models that often cannot be solved exactly and thus require approximations. Second, the measurement times for FCS are comparatively long, on the order of a minute, to obtain accurate parameter estimates. Third, the data analysis can be computationally quite time consuming. We therefore explore deep learning approaches to address these issues. For this purpose, we focus on Imaging FCS, a camera-based FCS modality, that provides correlation functions at or between any pixels on a camera, without loss of generality. We developed two convolutional neural networks (CNNs). FCSNet and ImFCSNet use either correlation functions or raw intensity traces as input, respectively. Both networks are trained on simulated, synthetic data, as it is difficult to obtain ground truth data for FCS over wide parameter ranges. More importantly, it allows us to use arbitrary experimental geometries and molecular processes, even when analytic models are not available for conventional fitting, thus solving the first problem. We demonstrate that the two CNNs perform well on synthetic and experimental data and outperform conventional nonlinear least squares (NLS) fits by a) requiring about one order of magnitude less data, b) providing higher precision for parameter estimates, and c) being two orders of magnitude faster. To demonstrate the power of CNNs we present comparisons of data evaluations by conventional NLS fitting on lipid bilayers and cells and on data recorded on total internal reflection and light sheet microscopes.

Principle of subtraction ghost imaging in scattering medium

Scattering medium in light path will cause distortion of the light field, resulting in poor signal-to-noise ratio (SNR) of ghost imaging. The disturbance is usually eliminated by the method of pre-compensation. We deduce the intensity fluctuation correlation function of the ghost imaging with the disturbance of the scattering medium, which proves that the ghost image consists of two correlated results: the image of scattering medium and the target object. The effect of the scattering medium can be eliminated by subtracting the correlated result between the light field after the scattering medium and the reference light from ghost image, which verifies the theoretical results. Our research may provide a new idea of ghost imaging in harsh environment.

Structure of groups of eigenfrequencies in spectra of geomagnetic pulsations in the nightside magnetosphere

Using a new method of correlation function for amplitude and phase fluctuations (APCF), records of geomagnetic field component fluctuations (observatories Mondy and Borok) have been processed for a number of hour zones of the nightside magnetosphere. This method is meant to detect groups of equidistant frequencies inside the spectrum of source signal and also to measure a difference between two neighbor frequencies in each of these groups.

Структура групп собственных частот в спектрах геомагнитных пульсаций ночной стороны магнитосферы

Using a new method of correlation function for amplitude and phase fluctuations (APCF), records of geomagnetic field component fluctuations (observatories Mondy and Borok) have been processed for a number of hour zones of the nightside magnetosphere. This method is meant to detect groups of equidistant frequencies inside the spectrum of source signal and also to measure a difference between two neighbor frequencies in each of these groups.
 The groups of equidistant frequencies in broadband spectra of these fluctuations are shown to depend on eigenfrequencies of the 2D Alfvén wave resonator, just as for dayside fluctuations [Polyakov, 2018]. An empirical relation has been found between a combination of parameters of this resonator and local time. The similarity between structural elements in the final products of processing of Alfvén fluctuation N-S and E-W components for almost all hour zones clearly indicates the reliability of the results of the APCF method in processing any broadband signals.

Horizontal Wavenumber Spectra of Vertical Vorticity and Horizontal Divergence of Mesoscale Dynamics in the Mesosphere and Lower Thermosphere Using Multistatic Specular Meteor Radar Observations

AbstractSpecular meteor radars (SMRs) have significantly contributed to the understanding of wind dynamics in the mesosphere and lower thermosphere (MLT). We present a method to estimate horizontal correlations of vertical vorticity (Qzz) and horizontal divergence (P) in the MLT, using line‐of‐sight multistatic SMRs velocities, that consists of three steps. First, we estimate 2D, zonal, and meridional correlation functions of wind fluctuations (with periods less than 4 hr and vertical wavelengths smaller than 4 km) using the wind field correlation function inversion (WCFI) technique. Then, the WCFI's statistical estimates are converted into longitudinal and transverse components. The conversion relation is obtained by considering the rotation about the vertical direction of two velocity vectors, from an east‐north‐up system to a meteor‐pair‐dependent cylindrical system. Finally, following a procedure previously applied in the upper troposphere and lower stratosphere to airborne wind measurements, the longitudinal and transverse spatial correlations are fitted, from which Qzz, P, and their spectra are directly estimated. The method is applied to a special Spread spectrum Interferometric Multistatic meteor radar Observing Network data set, obtained over northern Germany for seven days in November 2018. The results show that in a quasi‐axisymmetric scenario, P was more than five times larger than Qzz for the horizontal wavelengths range given by ∼50–400 km, indicating a predominance of internal gravity waves over vortical modes of motion as a possible explanation for the MLT mesoscale dynamics during this campaign.

Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

Electrolyte solutions play an important role in energy storage devices, whose performance relies heavily on the electrokinetic processes at sub-micron scales. Although fluctuations and stochastic features become more critical at small scales, the long-range Coulomb interactions pose a particular challenge for both theoretical analysis and simulation of fluid systems with fluctuating hydrodynamic and electrostatic interactions. Here, we present a theoretical framework based on the Landau–Lifshitz theory to derive closed-form expressions for fluctuation correlations in electrolyte solutions, indicating significantly different decorrelation processes of ionic concentration fluctuations from hydrodynamic fluctuations, which provides insights for understanding transport phenomena of coupled fluctuating hydrodynamics and electrokinetics. Furthermore, we simulate fluctuating electrokinetic systems using both molecular dynamics (MD) with explicit ions and mesoscopic charged dissipative particle dynamics (cDPD) with semi-implicit ions, from which we identify that the spatial probability density functions of local charge density follow a gamma distribution at sub-nanometre scale (i.e. $0.3\,{\rm nm}$ ) and converge to a Gaussian distribution above nanometre scales (i.e. $1.55\,{\rm nm}$ ), indicating the existence of a lower limit of length scale for mesoscale models using Gaussian fluctuations. The temporal correlation functions of both hydrodynamic and electrokinetic fluctuations are computed from all-atom MD and mesoscale cDPD simulations, showing good agreement with the theoretical predictions based on the linearized fluctuating hydrodynamics theory.

Site-selective dynamics of ligand-free and ligand-bound azidolysozyme.

Azido-modified alanine residues (AlaN3) are environment-sensitive, minimally invasive infrared probes for the site-specific investigation of protein structure and dynamics. Here, the capability of the label is investigated to query whether or not a ligand is bound to the active site of lysozyme and how the spectroscopy and dynamics change upon ligand binding. The results demonstrate specific differences for center frequencies of the asymmetric azide stretch vibration, the longtime decay, and the static offset of the frequency fluctuation correlation function (FFCF)-all of which are experimental observables-between the ligand-free and the ligand-bound N3-labeled protein. The center-frequency shifts range from 1 to 8 cm-1, which is detectable from state-of-the art experiments. Similarly, the nonvanishing static component Δ0 of the FFCF between ligand-free and ligand-bound protein can differ by up to a factor of 2.5. This makes the azide label a versatile and structurally sensitive probe to report on the dynamics of proteins in a variety of environments and for a range of different applications. Ligand-induced differences in the dynamics are also mapped onto changes in the local and through-space coupling between residues by virtue of dynamical cross correlation maps. This demonstrates that the position where the label is placed also influences the local and global protein motions.

Proton number cumulants and correlation functions in Au-Au collisions at sNN=7.7 –200 GeV from hydrodynamics

We present a dynamical description of (anti)proton number fluctuations cumulants and correlation functions in central Au-Au collisions at $\sqrt{s_{\rm NN}} = 7.7-200$ GeV by utilizing viscous hydrodynamics simulations. The cumulants of proton and baryon number are calculated in a given momentum acceptance analytically, via an appropriately extended Cooper-Frye procedure describing particlization of an interacting hadron resonance gas. The effects of global baryon number conservation are taken into account using a generalized subensemble acceptance method. The experimental data of the STAR collaboration are consistent at $\sqrt{s_{\rm NN}} \gtrsim 20$ GeV with simultaneous effects of global baryon number conservation and repulsive interactions in baryon sector, the latter being in line with the behavior of baryon number susceptibilities observed in lattice QCD. The data at lower collision energies show possible indications for sizable attractive interactions among baryons. The data also indicate sizable negative two-particle correlations between antiprotons that are not satisfactorily described by baryon conservation and excluded volume effects. We also discuss differences between cumulants and correlation functions (factorial cumulants) of (anti)proton number distribution, proton versus baryon number fluctuations, and effects of hadronic afterburner.

Quantum fluctuations approach to the nonequilibrium GW approximation

The quantum dynamics of fermionic or bosonic many-body systems following external excitation can be successfully studied using two-time nonequilibrium Green's functions (NEGF) or single-time reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle self-energy or decoupling of the BBGKY hierarchy. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. Here, we develop a different approach where, instead of equations of motion for the many-particle NEGF (or density operators), single-time equations for the correlation functions of fluctuations are analyzed. We present a derivation of the first two equations of the alternative hierarchy of fluctuations and discuss possible decoupling approximations. In particular, we derive the polarization approximation (PA) which is shown to be equivalent to the single-time version [following by applying the generalized Kadanoff-Baym ansatz (GKBA)] of the nonequilibrium GW approximation with exchange effects of NEGF theory, for weak coupling. The main advantage of the quantum fluctuations approach is that the standard ensemble average can be replaced by a semiclassical average over different initial realizations, as was demonstrated before by Lacroix and co-workers [see e.g. D. Lacroix et al., Phys. Rev. B, 2014, 90, 125112]. Here, we introduce the stochastic GW (SGW) approximation and the stochastic polarization approximation (SPA) which are demonstrated to be equivalent to the single-time GW approximation without and with exchange, respectively, in the weak coupling limit. In addition to the standard stochastic approach to sample initial configurations, we also present a deterministic approach. Our numerical tests confirm that our approach has the same favorable linear scaling with the computation time as the recently developed G1-G2 scheme [Schluenzen et al., Phys. Rev. Lett., 2020, 124, 076601]. At the same time, the SPA and SGW approaches scale more favorably with the system size than the G1-G2 scheme, allowing to extend nonequilibrium GW calculations to bigger systems.