Space-time Correlation Function Research Articles

Inclusive reactions from finite Minkowski spacetime correlation functions

The need to determine scattering amplitudes of few-hadron systems for arbitrary kinematics expands a broad set of subfields of modern-day nuclear and hadronic physics. In this work, we expand upon previous explorations on the use of real-time methods, like quantum computing or tensor networks, to determine few-body scattering amplitudes. Such calculations must be performed in a finite Minkowski spacetime, where scattering amplitudes are not well defined. Our previous work presented a conjecture of a systematically improvable estimator for scattering amplitudes constructed from finite-volume correlation functions. Here we provide further evidence that the prescription works for larger kinematic regions than previously explored as well as a broader class of scattering amplitudes. Finally, we devise a new method for estimating the order of magnitude of the error associated with finite time separations needed for such calculations. In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within O(10%), the spacetime volumes must satisfy mL∼O(10–102)) and mT∼O(102–104). Published by the American Physical Society 2024

A Non-Stationary Cluster-Based Channel Model for Low-Altitude Unmanned-Aerial-Vehicle-to-Vehicle Communications

Under the framework of sixth-generation (6G) wireless communications, the unmanned aerial vehicle (UAV) plays an irreplaceable role in a number of communication systems. In this paper, a novel cluster-based low-altitude UAV-to-vehicle (U2V) non-stationary channel model with uniform planar antenna arrays (UPAs) is proposed. In order to comprehensively model the scattering environment, both single and twin clusters are taken into account. A novel continuous cluster evolution algorithm that integrates time evolution and array evolution is developed to capture channel non-stationarity. In the proposed algorithm, the link between the time evolution of twin clusters and that of single clusters is established to regulate the temporal evolution trend. Moreover, an improved observable radius method is applied to UPAs for the first time to describe array evolution. Based on the combination of cluster evolution and time-variant channel parameters, some vital statistical properties are derived and analyzed, including space–time correlation function (ST-CF), angular power spectrum density (PSD), Doppler PSD, Doppler spread (DS), frequency correlation function (FCF), and delay spread (RS). The non-stationarity in the time, space, and frequency domain is captured. It demonstrates that the airspeed, density of scatterers within clusters, and carrier frequency have an impact on statistical properties. Furthermore, twin clusters have more flexible spatial characteristics with lower power than single clusters. These conclusions can provide assistance and reference for the design and deployment of 6G UAV communication systems.

Divergent Stiffness of One-Dimensional Growing Interfaces.

When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness.

A consistent approach to characterize random vibrations of nanobeams

While there is a numerous amount of research on the random vibrations of classical structures in the literature, merely some limited attempts exist to formulate the random vibrations of nano-sized structures. This study deals with the random vibration of elastic beams at the ultra-small scale. The mixture unified gradient theory of elasticity is invoked to appropriately take into consideration the size-effect. Within the introduced augmented elasticity framework, the nanoscopic effects associated with the strain gradient theory and the stress gradient theory are consistently integrated into the classical elasticity theory. The corresponding boundary-value problem of dynamic equilibrium is, accordingly, established. The exact closed-form solution of the space-time correlation function and the mean-square of the transverse displacements of the mixture unified gradient elastic beam with simply supported ends is obtained for the space-time white noise excitation. The spatial variation of the mean-square value of the transverse displacements of the elastic nanobeam in terms of gradient length-scale parameters is graphically illustrated and thoroughly discussed. A consistent approach to characterize random vibrations of elastic nanobeams within the context of the mixture unified gradient elasticity theory is presented providing important insight into the random vibration analysis of nanostructures.

Propagation characteristics of longitudinal modes in dusty plasmas

The space-time correlation function has been obtained in strongly coupled dusty plasmas (SCDPs) using equilibrium molecular dynamics (EMD) simulations. The simulated results for three-dimensional (3D) SCDPs with suitable normalization are computed over a wide domain of plasma parameters (Γ, κ) in a microcanonical ensemble. The EMD simulations indicate that different modes of propagated wave in SCDPs are analyzed for four different values of wave number (k). New investigations of normalized longitudinal current correlation function CL(k, t) show that the amplitude of oscillation and frequency of propagated modes increase with an increase in k. The obtained results for longitudinal modes of oscillation indicate that the dust particles remain in damping behavior at the low Γ, damped oscillation with decreasing amplitude inside decaying exponential envelope at intermediate Г, and sinusoidal oscillation at high Г, depending on κ. The system size (N) does not significantly affect the propagated modes of oscillation, while the periodic oscillation shifts toward higher Γ with increasing N and κ. The computations show that normalized longitudinal CL(k, t) current correlation particularly depend on Coulomb coupling (Γ), Debye screening (κ), and wave number (k). In our simulations, the frequency and the amplitude of oscillation of the dust particles decrease with an increment of κ and system size (N), but the frequency increases and the amplitude decreases with increasing Γ, as expected. It has been demonstrated that the EMD method is used to study the different propagated modes in dusty plasma systems and can be used to predict the damping behavior, damped oscillation, and periodic phenomena in 3D strongly coupled SCDPs.

A Mobility Model for a 3D Non-Stationary Geometry Cluster-Based Channel Model for High Speed Trains in MIMO Wireless Channels.

During channel modeling for high-mobility channels, such as high-speed train (HST) channels, the velocity of the mobile radio station is assumed to be constant. However, this might not be realistic due to the dynamic movement of the train along the track. Therefore, in this paper, an enhanced Gauss-Markov mobility model with a 3D non-stationary geometry based stochastic model (GBSM) for HST in MIMO Wireless Channels is proposed. The non-isotropic scatterers within a cluster are assumed to be around the sphere in which the mobile relay station (MRS) is located. The multi-path components (MPCs) are modeled with varying velocities, whereas the mobility model is a function of time. The MPCs are represented in a death-birth cluster using the Markov process. Furthermore, the channel statistics, i.e., the space-time correlation function, the root-mean-square Doppler shift, and the quasi-stationary interval, are derived from the non-stationary model. The model shows how the quasi-stationary time increases from 0.21 to 0.451 s with a decreasing acceleration of 0.6 to 0.2 m/s2 of the HST. In addition, the impact of the distribution of the angles on the channel statistics is presented. Finally, the simulated results are compared with the measured results. Therefore, there is a close relationship between the proposed model and the measured results, and the model can be used to characterize the channel's properties.

Modeling and Analysis of MIMO Multipath Channels With Aerial Intelligent Reflecting Surface

Recently, intelligent reflecting surface (IRS) has become a research focus for its capability of controlling the radio propagation environments. Compared to the conventional terrestrial IRS, aerial IRS (AIRS) exploiting unmanned aerial vehicle (UAV)/high-altitude platform (HAP) can provide better deployment flexibility. To this end, a three-dimensional (3D) one-cylinder model is first developed for AIRS-assisted multiple-input multiple-output (MIMO) narrowband channels. In order to change the wireless channel with AIRS and create a favorable propagation environment, we propose a novel method of designing the phase-shifts for the IRS elements. Based on the model, channel impulse response (CIR), space-time correlation function, and channel capacity are derived and thoroughly investigated. A key observation in this paper is that multipath and Doppler effects in radio propagation environments can be effectively mitigated via adjusting the phase-shifts of IRS. More specifically, for the special propagation environments in the absence of any scatterers, it is found that the effects of multipath fading can be completely eliminated by IRSs. While for the general propagation environments with multiple scatterers, a small number of IRS elements can also significantly reduce the Doppler spread and the deep fades of the channels. Based on the numerical investigation of channel correlations, it is shown that channel non-stationarity is not introduced into the time domain when the phase shift of IRS is linear related to the time. Moreover, the channel capacity can also be improved by the proposed methods. Finally, the model with non-ideal IRSs is considered and it is found that using non-ideal IRSs results in poor performances compared with using ideal IRSs. These conclusions will provide a fundamental support for developing intelligent and controllable propagation environments of the future sixth-generation (6G) wireless networks.

Decoding polymer self-dynamics using a two-step approach.

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

A 3-D Dynamic Non-WSS Cluster Geometrical-Based Stochastic Model for UAV MIMO Channels

The unmanned aerial vehicle (UAV) channel models are very important and useful for the design and evaluation of UAV communications. In existing works, the terrestrial scatterers are widely stationary or moving all the time, and the UAV is assumed to move at a constant speed. However, these modeling assumptions may not be appropriate in realistic scenarios. In this work, we propose a new 3-dimensional (3-D) dynamic non-wide-sense stationary (non-WSS) cluster-based geometric model for UAV multiple-input multiple-output (MIMO) channels. We assume that a few non-isotropic scatterers are distributed around the terrestrial receiver and have a probabilistic movement behavior. Meanwhile, we consider that the UAV flies at a varying speed, and we design a non-stationary mobility model with acceleration. The proposed channel model performs the birth-death evolutionary process of clusters based on a Markov model, and the time-variant multipath component (MPC) parameters (e.g., angle of arrival/departure (AoA/AoD), power, and delay) are obtained. In addition, we derive the space-time correlation function, mean Doppler spread, and root-mean-square doppler shift spread of the UAV MIMO channels, and provide the quasi-stationary interval. We also investigate the impact of some key model factors on the statistical properties by numerical simulations. Finally, we compare the space-time correlation functions and the second-order statistical properties between the proposed model and the UAV channel measurement results. The close agreements between the numerical simulations and field measurements have validated the proposed model.

Sorption of Per- and Polyfluoroalkyl Substances (PFAS) using Polyethylene (PE) microplastics as adsorbent: Grand Canonical Monte Carlo and Molecular Dynamics (GCMC-MD) studies

ABSTRACT Per- and Polyfluoroalkyl Substances (PFAS) and microplastics (MPs) removal is one of the main technical measures in these emerging pollutant control and MPs can sorb PFAS acting as carriers. In order to explore the sorption process of polyethylene (PE MPs) for different PFAS, Grand Canonical Monte Carlo and molecular dynamics simulation was used. Seven commonly found PFAS compounds including PFNA (Perfluorononanoic acid), PFHxS (Perfluorohexanesulphonic acid), PFHxA (Perfluorohexanoic acid), PFDA (Perfluorodecanoic acid), PFOS (Perfluorooctanesulfonic acid), PFBS (Perfluorobutanesulfonic acid) and Perfluorooctanoic acid (PFOA) were selected. The sorption on PE MPs was based on fixed loading and the sorption (PE MPs+PFAS) average total energy for all simulation steps followed PFHxA (−29.17 kcal/mol) < PFBS (−52.71 kcal/mol) < PFOA (−57.12 kcal/mol) < PFNA (−70.58 kcal/mol) < PFDA (−78.27 kcal/mol) < PFHxS (−80.06 kcal/mol) < PFOS (−102.30 kcal/mol). However, the binding/interaction energies followed PFHxS > PFOS > PFNA > PFDA > PFOA > PFBS > PFHxA. The MD simulation was carried out under NVT ensemble at 298 K, the thermodynamic states and relaxation pretreatment procedures were then examined quantitatively by radial distribution function, X-ray scattering, relative concentration profile, mean square displacement and space time correlation function. The results show that effective sorption of PFAS molecule by PE MPs involves hydrogen or chemical bonding as well non-bond energy such as Van der Waals (VdW), electrostatic and intramolecular energies. The cell volume did not change during single and multicomponent sorption while the sorption density increased about threefold the single component (0.36 g/cm3), suggesting that as the pollutant number increased the sorption capacity increased. This study showed that PE MPs can used for single and multicomponent sorption of PFASs effectively and also provided theoretical support for our knowledge of the sorption mechanism at the molecular level, which will help in better understanding of PFAS removal by MPs.

A Novel 3D Non-Stationary Maritime Wireless Channel Model

In this paper, a novel 3-dimensional (3D) non-stationary geometry-based stochastic model (GBSM) is proposed to mimic the ship-to-ship multiple-input multiple-output (MIMO) communication channels. To reflect the realistic maritime propagation environment, the effects of rough sea surface scattering and evaporation duct propagation are investigated in the proposed channel model. The model considers the movements of transmitter (Tx), receiver (Rx), and scatterers, and is capable of capturing the channel characteristics, including non-stationary characteristics, spatial consistency, location-dependent property, etc. Through taking the array cluster evolution into account, the proposed channel model can describe massive MIMO channels and can easily switch to conventional MIMO channel model by adjusting corresponding parameters. Based on the proposed model, key statistical properties like delay/angular/Doppler power spectrum density (PSD), space-time correlation function (STCF), stationary interval, and root mean square (RMS) Doppler/delay spreads in multi-scenarios are derived. The usefulness and accuracy of the proposed model are demonstrated by comparing theoretical results, simulation results, and corresponding measurement results.

A stochastic confocal ellipsoid channel model for high speed railway MIMO communication systems

This paper investigates the channel model for multiple-input multiple-output (MIMO) communication systems in high speed railway (HSR) networks. Specially, a three-dimensional (3D) confocal stochastic geometry ellipsoid model is proposed for modeling the MIMO channels. Normalized space–time correlation function(ST CF), Spatial cross correlation function (CCF) and level crossing rate (LCR) of both theoretical and simulation model are have been derived and analyzed. As a 3D GBSM, the proposed confocal ellipsoid model has lower correlation in spatial cross-correlation function (CCF) compared with that of the corresponding two-dimensional (2D) ellipse model. Measurement data of different HSR scenarios verify the applicability of the confocal ellipsoid model.

A 3-D Nonstationary Wideband V2V GBSM With UPAs for Massive MIMO Wireless Communication Systems

This article proposes a novel 3-D nonstationary wideband vehicle-to-vehicle (V2V) geometry-based stochastic model (GBSM) with uniform planar antenna arrays (UPAs) for massive multiple-input–multiple-output (MIMO) wireless communication systems. In the proposed GBSM, a novel method, so-called birth–death (BD) process and seed algorithm-based selective cluster evolution, is developed to capture the space nonstationarity of V2V massive MIMO with UPA channels. The time nonstationarity is further mimicked by employing this novel method over the entire timeline. In addition, the proposed GBSM not only models the reflection of the ground, but also divides clusters into static clusters and dynamic clusters to sufficiently investigate the impact of vehicular traffic density (VTD) on channel statics. The channel parameters are properly calculated by 3-D vectors, resulting in the proposed GBSM with high accuracy and low complexity. Important statistical properties, such as the space-time correlation function (S-T CF), spatial cross-correlation function (CCF), temporal auto-correlation function (ACF), and Doppler power spectrum density (PSD) are derived and thoroughly investigated. Simulation results show that the space-time nonstationarity is successfully mimicked and the VTD has a significant impact on channel statistics. Finally, an excellent agreement is achieved between simulation results and measurements, validating the accuracy of the proposed GBSM.

Formation of a quasi-equilibrium domain structure of crystals of the TGS group near TC

In the temperature range ΔT ≈ 321 K ÷ 322 K, the kinetics of the nonequilibrium domain structure of triglycine sulphate crystals, both pure and with specially introduced defects, has been studied by means of piezoresponse force microscopy technique. The temporal change in the domain structure as a set of regions with a scalar order parameter of P (r, t) = +1 and −1 for oppositely polarized domains was analysed by the behaviour of the space-time correlation function C(r,t) = ·Р(r,t)Р(0,t)Ò. At different distances from the Curie point Tc, the characteristic length Lc, as a scale measure of the average domain size, increases with time according to the power law Lc(t)~(t−t0)a. A decrease of the exponent a with distance from Tc can be a consequence of the transition of the domain structure of TGS crystals from a non-conservative state to aconservative one.

Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions

We explain the general theories involved in solving an infinite-dimensional stochastic differential equation (ISDE) for interacting Brownian motions in infinite dimensions related to random matrices. Typical examples are the stochastic dynamics of infinite particle systems with logarithmic interaction potentials such as the sine, Airy, Bessel, and also for the Ginibre interacting Brownian motions. The first three are infinite-dimensional stochastic dynamics in one-dimensional space related to random matrices called Gaussian ensembles. They are the stationary distributions of interacting Brownian motions and given by the limit point processes of the distributions of eigenvalues of these random matrices. The sine, Airy, and Bessel point processes and interacting Brownian motions are thought to be geometrically and dynamically universal as the limits of bulk, soft edge, and hard edge scaling. The Ginibre point process is a rotation- and translation-invariant point process on R 2 \mathbb {R}^2 , and an equilibrium state of the Ginibre interacting Brownian motions. It is the bulk limit of the distributions of eigenvalues of non-Hermitian Gaussian random matrices. When the interacting Brownian motions constitute a one-dimensional system interacting with each other through the logarithmic potential with inverse temperature β = 2 \beta = 2 , an algebraic construction is known in which the stochastic dynamics are defined by the space-time correlation function. The approach based on the stochastic analysis (called the analytic approach) can be applied to an extremely wide class. If we apply the analytic approach to this system, we see that these two constructions give the same stochastic dynamics. From the algebraic construction, despite being an infinite interacting particle system, it is possible to represent and calculate various quantities such as moments by the correlation functions. We can thus obtain quantitative information. From the analytic construction, it is possible to represent the dynamics as a solution of an ISDE. We can obtain qualitative information such as semi-martingale properties, continuity, and non-collision properties of each particle, and the strong Markov property of the infinite particle system as a whole. Ginibre interacting Brownian motions constitute a two-dimensional infinite particle system related to non-Hermitian Gaussian random matrices. It has a logarithmic interaction potential with β = 2 \beta = 2 , but no algebraic configurations are known.The present result is the only construction.

Dynamic Speckle Illumination Digital Holographic Microscopy by Doubly Scattered System

The coherent noise always exists in digital holographic microscopy due to the laser source, degrading the image quality. A method of speckle suppression using the dynamic speckle illumination, produced by double-moving diffusers, is presented in digital holographic microscopy. The space–time correlation functions are theoretically analyzed from the statistics distribution in the doubly and singly scattered system, respectively. The configuration of double-moving diffusers is demonstrated to have better performance in speckle suppression compared with the single diffuser and moving-static double diffusers cases. The experiment results verify the feasibility of the approach. The presented approach only requires a single shot interferogram to realize the speckle reduction, accordingly it has the potential application in real-time measurement.

Modeling for geometry-based massive MIMO V2V channels and analysis of space-time correlation

This paper proposed a three-dimensional dual-spheres confocal ellipsoid geometry-based model for massive MIMO vehicle-to-vehicle (V2V) communication. In this proposed model, the received signal is composed of non-line-of-sight propagation components generated via effective scatterers and line-of-sight propagation components. According to the geometric relationships in the model, the information of angle and distance can be derived, and then the space-time correlation function expression is obtained. To calculate parameters, modified method of equal areas is employed, and the influence on space-time correlation of scatters in different environments is analyzed. Channel characteristics in different scenarios such as highway scenario, urban road scenario and tunnel scenario are compared and studied. Simulation results show that the scatterers distribution and angle information of antenna arrays make a joint contribution on spatial cross-correlation, and moreover, the degree of anisotropy of scatterers and multipath components have distinct impacts on temporal auto-correlation. Compared with the results of 2D model, the proposed 3D model in this paper is more appropriate to characterize V2V communication in various scenarios.

Optimal radar cross section estimation in synthetic aperture radar with planar antenna array

The optimization problem of statistical synthesis of the method for radar cross section estimation in synthetic aperture radar with planar antenna array is solved. The desired radar cross section is given as a statistical characteristic of a spatially inhomogeneous complex scattering coefficient of the studying media. In fact it is developed new methods of inverse problems solution not with respect to the restoration of coherent images in the form of spatial distribution of complex scattering coefficient but with respect to the statistical characteristics of inhomogeneous (spatially nonstationary) random processes. The electrophysical parameters of surfaces and their statistical characteristics are considered as functions of spatial coordinates. The maximum likelihood method was chosen as the optimization method. The obtained results make it possible to determine the multichannel structure, the optimal method of surface observation and the potential spatial resolution in aerospace scatterometric radars with antenna array. Optimal operations for processing space-time signals are determined and a modified method for synthesizing antenna aperture is proposed, which in contrast to the classical algorithm for synthesizing antenna aperture that integrates the product of the received signal and the reference signal equal to a single signal additionally implements the decorrelation of signals reflected from the earth's surface, The new operation of the scattered signals decorrelation consists in their integration with the space-time inverse correlation function. To confirm the reliability of the results obtained, simulation modeling of the classical method for the synthesis of coherent images and the proposed optimal one was carried out. From the analysis of the results it flows that propose method has higher quality and smaller size of spackle noise. The results obtained in the article can be used to develop and substantiate the requirements for the tactical and technical characteristics of promising aerospace-based scatterometric radars with planar phased antenna arrays.

Spatiotemporal mapping of mesoscopic liquid dynamics.

The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated: a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.

A Novel Nonstationary 6G UAV-to-Ground Wireless Channel Model With 3-D Arbitrary Trajectory Changes

In order to provide reliable and efficient connections between unmanned aerial vehicles (UAVs) and ground stations (GSs), realistic UAV-to-ground channel models are indispensable. In this article, we propose a novel 3-D nonstationary geometry-based stochastic model (GBSM) for UAV-to-ground multiple-input-multiple-output (MIMO) channels. Distinctive UAV-to-ground channel characteristics, such as time-domain nonstationarity, distinctions between different altitudes, spatial consistency, and 3-D arbitrary UAV movement trajectories, are taken into account. By adjusting parameter settings, the proposed channel model framework is sufficiently general to support multiple frequency bands and multiple scenarios, including millimeter wave (mmWave) and massive MIMO configurations. Statistical properties, including power delay profile (PDP), stationary interval, space-time correlation function (STCF), and root-mean-square (RMS) delay spread are derived and analyzed for different frequencies and scenarios. The accuracy of the proposed model is validated by comparing its statistical properties with corresponding available channel measurements. The proposed channel model will provide a fundamental support for the design, performance evaluation, and optimization of future UAV integrated sixth-generation (6G) wireless networks.