Temporal Correlation Function Research Articles

Collective group drift in a partial-differential-equation-based opinion dynamics model with biased perception kernels.

In the age of technology, individuals accelerate their biased gathering of information, which in turn leads to a population becoming extreme and more polarized. Here we study a partial-differential-equationmodel for opinion dynamics that exhibits collective behavior subject to nonlocal interactions. We developed an interaction kernel function to represent biased information gathering. Through a linear stability analysis, we show that biased populations can still form opinionated groups. However, a population that is too heavily biased can no longer come to a consensus, that is, the initial homogeneous mixed state becomes stable. Numerical simulations with biased information gathering show the ability for groups to collectively drift towards one end of the opinion space. This means that a small bias in each individual will collectively lead to groups of individuals becoming extreme together. The characteristic time scale for a group's existence is captured from numerical experiments using the temporal correlation function. Supplementing this, we included a measure of how different each population is after regular time intervals using a form of the Manhattan and Euclidean distance metrics. We conclude by exploring how wall boundary conditions induce pattern formation initially on the most extreme sides of the domain.

A three‐dimensional wideband mmWave multiple‐input multiple‐output channel model for aerial reconfigurable intelligent surface‐assisted communication systems

SummaryThis paper presents a wideband millimeter wave (mmWave) channel model for aerial reconfigurable intelligent surface (ARIS) communications, in which the reconfigurable intelligent surface (RIS) is attached to an unmanned aerial vehicle (UAV) to enable intelligent signal reflections in the air. The model is established according to standard 3GPP channel models and considers important propagation factors, for example, large‐scale fading, small‐scale fading, and radiation pattern of reflection units (RUs). In addition, the model assumes three‐dimensional (3D) rotations of RIS and can capture its effects on channel characteristics. Based on the model, we propose a design method for RIS reflection phases. Statistics including channel amplitude, spatial, temporal, and frequency correlation functions (CFs), and space‐Doppler power spectral density (SD‐PSD) are obtained. The impacts of RU number, UAV height and speed, and RIS rotation on channel statistics are investigated. Results suggest that the designed reflection phases can effectively mitigate multipath fading and Doppler effect. Compared to the yaw angle of the UAV platform, channel characteristics are more sensitive to the roll and pitch angles.

Second-Order Temporal Coherence of Polariton Lasers Based on an Atomically Thin Crystal in a Microcavity.

Bosonic condensation and lasing of exciton polaritons in microcavities is a fascinating solid-state phenomenon. It provides a versatile platform to study out-of-equilibrium many-body physics and has recently appeared at the forefront of quantum technologies. Here, we study the photon statistics via the second-order temporal correlation function of polariton lasing emerging from an optical microcavity with an embedded atomically thin MoSe_{2} crystal. Furthermore, we investigate the macroscopic polariton phase transition for varying excitation powers and temperatures. The lower-polariton exhibits photon bunching below the threshold, implying a dominant thermal distribution of the emission, while above the threshold, the second-order correlation transits towards unity, which evidences the formation of a coherent state. Our findings are in agreement with a microscopic numerical model, which explicitly includes scattering with phonons on the quantum level.

Temporal Correlation Characteristics of Air-to-Ground Wireless Channel With UAV Wobble

Air-to-ground (A2G) communication based on Unmanned aerial vehicle (UAV) is an important part of the future communication system. In this paper, an A2G channel model with UAV three-dimensional (3D) wobbles (pitch, roll, and yaw) based on the geometry-based stochastic model (GBSM) is proposed. On this basis, the UAV’s internal vibration is modeled as a sinusoidal random process, and the UAV wobble caused by the atmospheric flow is modeled as the uniform distribution random process. We derive the channel temporal correlation function (CF) with UAV 3D wobbles, analyze the variation of the temporal CF with different carrier frequencies, and amplitudes of the wobble angles. It is found that, even if the UAV wobbles slightly, the channel temporal correlation will be significantly affected. Numerical results show that the channel CF will decrease rapidly with the increase of the amplitudes of wobble angles and the carrier frequency. Therefore, the coherence time of millimeter wave (mmWave) band is significantly less than that of sub-6 GHz band. The consistency of simulation results and measurement results in published papers ensures the availability of the proposed model. For the MUAVs scenario, when the distance between different UAVs is much greater than the wavelength, the A2G channels between different UAVs and user equipment (UE) on the ground are not correlated to each other, and the temporal auto-correlation function (ACF) of each UAV is the same as that of the SUAV scenario. This work contributes to the theoretical exploration and system design of A2G communication based on UAV.

Bragg grating based entangled biphoton dispersion management

In the realm of quantum information processing and precision measurements, a range of non-classical effects based on entangled photon pairs are employed. Non-local dispersion cancellation is one of these properties, in which the second photon (idler) can be manipulated to cancel the effects of dispersion on the first photon (signal). In the present study, a thorough investigation is conducted into non-local dispersion cancellation by using excitation modes within a Bragg grating slab waveguide. We present a complete theoretical analysis of non-local dispersion cancellation for frequency-limited entangled photon pairs. For the analysis of the effect of dispersion cancellation, we use a spontaneous parametric down-conversion (SPDC) photon pair source with frequency correlation and anti-correlation as the entangled source. To evaluate the dispersion cancellation effect for information processing applications, the second correlation function is used and calculated as a practical and tangible metric. Considering different cases for Bragg Grating waveguide the results on both photons are extracted and discussed. Moreover, we will show that the physical parameters of the waveguide that the second photon is propagated inside will be effective in minimizing the width of the temporal correlation function. Hence, this study underscores the feasibility of achieving non-local dispersion cancellation through strategic optimization of optical and geometric parameters in the Bragg Grating waveguide, with potential implications for quantum information processing and high-resolution sensing endeavors.

3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion

AbstractUnmanned aerial vehicles (UAVs) play a vital role in the beyond fifth‐generation (B5G) and sixth‐generation (6G) wireless communication scenarios. This paper proposes a non‐stationary three‐dimensional (3D) geometry‐based multiple‐input multiple‐output channel model for UAV to vehicle (U2V) communications considering UAV heaving motion. The proposed model incorporates the effects of UAV heaving along with the rotation, acceleration, and 3D velocity variation for matching the realistic U2V communication scenarios. The computation methods for time variant channel parameters such as Doppler frequencies, angle of arrival, and angle of departure are given and analysed. The theoretical and statistical properties, including spatial temporal correlation function, TCF, level crossing rate, average fade duration, and Doppler power spectral density are derived and analysed aiming to evaluate the proposed model. Simulation results show that the output statistical characteristics agree with the hypothetical and simulated outcomes, which shows the validity of both the channel model and theoretical derivations.The cover image is based on the Research Article 3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion by Naeem Ahmed et al., https://doi.org/10.1049/mia2.12393

Correcting Deviations of Emulated Spatial Correlation for Prefaded Signal Synthesis Method With Limited Number of Random Drops in MIMO OTA Testing

The prefaded signals synthesis (PFS) is a well-established over-the-air (OTA) testing solution, which can reconstruct the desired spatial profiles of the target channel by adjusting the power weights of the multiple probes. However, practical channel emulation campaigns tend to use a limited number of random drops due to limited time budget and hardware capacity constraint, which may cause the emulated spatial correlation to be deviated from the expected one due to the loss of ergodicity. In this article, the properties of the emulated channel under the PFS method are reexamined for a given set of initial subpath phases that are randomly configured at different probes. The analytical expressions of the spatial–temporal correlation function (STCF) are thus derived by averaging over time, compared with the general manipulations of ensemble averaging in the literature. Our derivations indicate that the spatial correlation function (SCF) of the emulated channel may deviate from the expected form for a given set of initial subpath phases in the classic PFS method. An improved configuration method for initial subpath phases is proposed. Simulation results show that the proposed method can reproduce the exact SCF in any random drop while unaffecting other important channel properties, for example, the temporal correlation function (TCF).

Turbulent Flame Propagation in Hydrogen-Air and Methane-Air Mixtures in the Field of Synthetic Turbulence: Direct Numerical Simulation

A technique alternative to the direct numerical simulation of turbulent combustion of gas mixtures is proposed. It is based on the solution of the three-dimensional transport equations for species concentrations and the energy conservation equation in the “synthetic” field of constant-pressure homogeneous, isotropic and statistically stationary (forced) turbulence using the detailed reaction mechanism. The synthetic turbulence with given spatial and temporal correlation functions is generated using the Monte Carlo method, assuming that the components of the vector of fluctuation velocity obey the normal Gaussian distribution. The technique is applied to the problem of turbulent combustion of fuel-lean and stoichiometric mixtures of hydrogen and methane with air at a turbulence intensity up to 10 m/s. The calculated turbulent flame propagation velocities agree satisfactorily with the values measured in the fan-stirred bomb. The predicted volume fractions of active reaction centers H, O, and OH in a turbulent flame are shown to be less than in a laminar flame up to an order of magnitude, which also agrees with the experiment. In general, calculations indicate that the “wrinkled flame” model is applicable to fuel-lean and stoichiometric mixtures of hydrogen and methane with air at turbulence intensities up to 10 m/s

Low-False-Alarm-Rate Timing and Duration Estimation of Noisy Frequency Agile Signal by Image Homogeneous Detection and Morphological Signature Matching Schemes.

Frequency hopping spread spectrum (FHSS) applies widely to communication and radar systems to ensure communication information and channel signal quality by tuning frequency within a wide frequency range in a random sequence. An efficient signal processing scheme to resolve the timing and duration signature from an FHSS signal provides crucial information for signal detection and radio band management purposes. In this research, hopping time was first identified by a two-dimensional temporal correlation function (TCF). The timing information was shown at TCF phase discontinuities. To enhance and resolve the timing signature of TCF in a noisy environment, three stages of signature enhancement and morphological matching processes were applied: first, computing the TCF of the FHSS signal and enhancing discontinuities via wavelet transform; second, a dual-diagonal edge finding scheme to extract the timing pattern signature and eliminate mismatching distortion morphologically; finally, Hough transform resolved the agile frequency timing from purified line segments. A grand-scale Monte Carlo simulation of the FHSS signals with additive white Gaussian noise was carried out in the research. The results demonstrated reliable hopping time estimation obtained in SNR at 0 dB and above, with a minimal false detection rate of 1.79%, while the prior related research had an unattended false detection rate of up to 35.29% in such a noisy environment.

Application of Optimal Interpolation to Spatially and Temporally Sparse Observations of Aerosol Optical Depth

Aerosol optical depth (AOD) is one of the basic characteristics of atmospheric aerosol. A global ground-based network of sun and sky photometers, the Aerosol Robotic Network (AERONET) provides AOD data with low uncertainty. However, AERONET observations are sparse in space and time. To improve data density, we merged AERONET observations with a GEOS-Chem chemical transport model prediction using an optimal interpolation (OI) method. According to OI, we estimated AOD as a linear combination of observational data and a model forecast, with weighting coefficients chosen to minimize a mean-square error in the calculation, assuming a negligible error of AERONET AOD observations. To obtain weight coefficients, we used correlations between model errors in different grid points. In contrast with classical OI, where only spatial correlations are considered, we developed the spatial-temporal optimal interpolation (STOI) technique for atmospheric applications with the use of spatial and temporal correlation functions. Using STOI, we obtained estimates of the daily mean AOD distribution over Europe. To validate the results, we compared daily mean AOD estimated by STOI with independent AERONET observations for two months and three sites. Compared with the GEOS-Chem model results, the averaged reduction of the root-mean-square error of the AOD estimate based on the STOI method is about 25%. The study shows that STOI provides a significant improvement in AOD estimates.

The temporal correlation of fluctuation–variation in the non-stationary complex climate system

In this article we mainly focus on the temporal correlation between the past dynamic fluctuations and the future motion of the dynamic variables in the climate system by means of a new temporal correlation function. When the complex climate system is assumed to be in the stationary states, that is, the dynamic effects of the non-stationary states are not considered, the above correlation is weak or even non-existent. Unexpectedly, a good correlation is shown when the dynamic effects of the non-stationary states are taken into account. Subsequently, we analyze the main factors contributing to these results and conclude that the small fluctuations make a major contribution to this. At the same time, we also find that this correlation function is somewhat stable over time scales. Finally, we extend our analysis by using the persistence probabilities. Knowing these is of key importance for the study of climate analysis and prediction.

New theory tremendously improves data evaluation of fluorescence correlation spectroscopy

Since its invention by Magde, Elson, and Webb (1) in the seventies of the last century, fluorescence correlation spectroscopy (FCS) has become a widely used and powerful technique in biophysical research (2). It is most often used for studying the mobility of molecules (diffusion, directed transport) (3) but also for looking at the kinetics of photophysical transitions (4,5), the temporal dynamics of conformation fluctuations (6), or the speed of rotational diffusion (7,8). The core idea is to record long time traces of the fluorescence intensity that is excited in and detected from the picoliter-sized detection volume of a confocal microscope and then to calculate the temporal correlation function of the observed intensity fluctuations.

Linear response for pseudo-Hermitian Hamiltonian systems: Application to PT -symmetric qubits

Motivated by the recent advances in modelling the pseudo-Hermitian Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum dynamics subject to a small time-dependent perturbation. In particular, We develop the linear response theory formulation suitable for application to various pHH systems and compare it to the ones available in the literature. We derive analytical expressions for the generalized temporal quantum-mechanical correlation function $C(t)$ and the time-dependent dynamic susceptibility $\chi(t) \propto \text{Im} ~C(t)$. We apply our results to two \textit{PT}-symmetric non-Hermitian quantum systems: a single qubit and two unbiased/biased qubits coupled by the exchange interaction. For both systems we obtain the eigenvalues and eigenfunctions of the Hamiltonian, identify \textit{PT}-symmetry unbroken and broken quantum phases and quantum phase transitions between them. The temporal oscillations of the dynamic susceptibility of the qubits polarization ($z$-projection of the total spin), $\chi(t)$, relate to {\it ac} induced transitions between different eigenstates and we analyze the dependencies of the oscillations frequency and the amplitude on the gain/loss parameter $\gamma$ and the interaction strength $g$. Studying the time dependence of $\chi(t)$ we observe different types of oscillations, i.e. undamped, heavily damped and amplified ones, related to the transitions between eigenstates with broken (unbroken) $PT$-symmetry. These predictions can be verified in the microwave transmission experiments allowing controlled simulation of the pHH systems.

Fully nonseparable Gneiting covariance functions for multivariate space–time data

We broaden the well-known Gneiting class of space–time covariance functions by introducing a very general parametric class of fully nonseparable direct and cross-covariance functions for multivariate random fields, where each component has a spatial covariance function from the Matérn family with its own smoothness and scale parameters and, unlike most of currently available models, its own correlation function in time. We present sufficient conditions that result in valid models with varying degrees of complexity and we discuss the parameterization of those. Continuous-in-space and discrete-in-time simulation algorithms are also given, which are not limited by the number of target spatial coordinates and allow tens of thousands of time coordinates. The application of the proposed model is illustrated on a weather trivariate dataset over France. Our new model yields better fitting and better predictive scores in time compared to a more parsimonious model with a common temporal correlation function.

Time-domain Hong-Ou-Mandel interference of quasi-thermal fields and its application in linear optical circuit characterization.

We study temporal correlations of interfering quasi-thermal fields, obtained by scattering laser radiation on a rotating ground glass disk. We show that the Doppler effect causes oscillations in the temporal cross correlation function. Furthermore, we propose how to use Hong-Ou-Mandel interference of quasi-thermal fields in the time domain to characterize linear optical circuits.

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.

Annihilation dynamics of magnetic skyrmion lattice state under in-plane magnetic field and spontaneous recovery after field removal

Nanoscale magnetic skyrmions are potential candidates for information carriers, for which the nonvolatility under external stimuli is critical to the stability of recorded bits. Here, we present a micromagnetic study on the annihilation dynamics of a two-dimensional skyrmion lattice under a transverse magnetic field and the recoverability of the topological charge after removing the field. The temporal and spatial correlation functions and their Fourier transforms of the spin system reveal position-dependent dynamics under the transverse field. The slow modes $(<10\phantom{\rule{0.16em}{0ex}}\mathrm{GHz})$ hosted by all spins determine the spin configurations, and the fast ones $(>10\phantom{\rule{4pt}{0ex}}\mathrm{GHz})$ around the skyrmion core region control the dynamics of topological properties. A dynamic critical time ${t}_{\mathrm{cri}}$, when the field-induced ferromagnetic nuclei begin to be long-range correlated, is proved by statistical analyses of their spatial distribution over time. If turning off the transverse field before ${t}_{\mathrm{cri}}$, the collective motion of the spin system can restore the previously lost topological charge. Our results guide the realization of nonvolatile information storage in skyrmion lattice, thus widening the possibility of skyrmion-based devices for future spintronics-based nanocomputing.

Quantum dynamics of disordered arrays of interacting superconducting qubits: Signatures of quantum collective states

We study theoretically the collective quantum dynamics occurring in various interacting superconducting qubits arrays (SQAs) in the presence of a spread of individual qubit frequencies. The interaction is provided by mutual inductive coupling between adjacent qubits (short-range Ising interaction) or inductive coupling to a low-dissipative resonator (long-range exchange interaction). In the absence of interaction the Fourier transform of temporal correlation function of the total polarization ($z$-projection of the total spin), i.e. the dynamic susceptibility $C(\omega)$, demonstrates a set of sharp small magnitude resonances corresponding to the transitions of individual superconducting qubits. We show that even a weak interaction between qubits can overcome the disorder with a simultaneous formation of the collective excited states. This collective behavior manifests itself by a single large resonance in $C(\omega)$. In the presence of a weak non-resonant microwave photon field in the low-dissipative resonator, the positions of dominant resonances depend on the number of photons, i.e. the collective ac Stark effect. Coupling of an SQA to the transmission line allows a straightforward experimental access of the collective states in microwave transmission experiments and, at the same time, to employ SQAs as sensitive single-photon detectors.

Intensityg(2)correlations in random fiber lasers: A random-matrix-theory approach

We propose an approach based on random matrix theory to calculate the temporal second-order intensity correlation function ${g}^{(2)}(t)$ of the radiation emitted by random lasers and random fiber lasers. The multimode character of these systems, with a relevant degree of disorder in the active medium, and a large number of random scattering centers substantially hinder the calculation of ${g}^{(2)}(t)$. Here, we apply in a photonic system the universal statistical properties of Ginibre's non-Hermitian random matrix ensemble to obtain ${g}^{(2)}(t)$. Excellent agreement is found with time-resolved measurements for several excitation powers of an erbium-based random fiber laser. We also discuss the extension of the random matrix approach to address the statistical properties of general disordered photonic systems with various Hamiltonian symmetries.

OPTIMAL INTERPOLATION OF AERONET RADIOMETRIC NETWORK OBSERVATIONS FOR THE EVALUATION OF THE AEROSOL OPTICAL DEPTH DISTRIBUTION IN THE EASTERN EUROPEAN REGION

The application of the optimal interpolation method for the assimilation of the observational data of aerosol optical thickness (AOT), which are sparse in space and time, in the chemical transport model is herein validated. Assuming the negligible error of AOT observations in the AERONET ground-based radiometric network, spatial and temporal correlation functions of the errors in the results of the AOT simulated by the GEOS-Chem chemical transport model are obtained. The optimal interpolation method is applied to the AERONET data using the GEOS-Chem results as a background field for the Eastern European region for 2015–2016. It is shown that the use of the optimal interpolation method permits to reduce the root-mean-square error of the AOT estimation by more than a third in places where there are no AERONET stations in comparison with the model results.