Velocity Autocorrelation Function Research Articles

Enhancing efficient computation of long-wavelength relaxation dynamics in a 2D liquid involving millions of particles

Recently, a two-dimensional liquid cooled toward the glass transition was found to exhibit a t −1 long-time tail in the velocity autocorrelation function (VACF) owing to the presence of long-wavelength fluctuations. To directly observe this power-law behaviour, it is necessary to simulate a large system with millions of particles, which is a challenging task from the computational viewpoint. In this study, to address this difficulty, I first show that this power-law tail can be reproduced by differentiating the finite-time diffusivity with respect to time. In addition, the feasibility of another direction, a direct on-the-fly computation of the VACFs utilizing GPGPUs, wherein VACFs are evaluated as the simulation runs, is also demonstrated. A performance benchmark was executed on Wisteria/BDEC-01 (Aquarius subsystem) supercomputer using a simulation code developed by the author, which enabled the direct computation of the VACF of 4 million particlesx for as long as the 108 simulation steps within 10 days.

Quantum Langevin dynamics of a charged particle in a magnetic field: Response function, position–velocity and velocity autocorrelation functions

We use the quantum Langevin equation as a starting point to study the response function, the position–velocity correlation function and the velocity autocorrelation function of a charged quantum Brownian particle in the presence of a magnetic field and linearly coupled to a heat bath via position coordinate. We study two bath models – the Ohmic bath model and the Drude bath model and make a detailed comparison in various time–temperature regimes. For both bath models, there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low-temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time-scale which comes into play in the Drude model and study the effect of this additional time-scale. We discuss the experimental implications of our analysis in the context of experiments in cold ions.

Inside out Approach to Rotator State in Hydrogen-Bonded System-Experimental and Theoretical Cross-Examination in n-Octanol.

The experimental and theoretical description of premelting behavior is one of the most challenging tasks in contemporary material science. In this paper, n-octanol was studied using a multi-method approach to investigate it at macroscopic and molecular levels. The experimental infrared (IR) spectra were collected in the solid state and liquid phase at temperature range from C to −15 C to detect temperature-related indicators of pretransitional phenomena. Next, the nonlinear dielectric effect (NDE) was measured at various temperatures (from −30 C to −15 C) to provide insight into macroscopic effects of premelting. As a result, a two-step mechanism of premelting in n-octanol was established based on experimental data. It was postulated that it consists of a rotator state formation followed by the surface premelting. In order to shed light onto molecular-level processes, classical molecular dynamics (MD) was performed to investigate the time evolution of the changes in metric parameters as a function of simulation temperature. The applied protocol enabled simulations in the solid state as well as in the liquid (the collapse of the ordered crystal structure). The exact molecular motions contributing to the rotator state formation were obtained, revealing an enabling of the rotational freedom of the terminal parts of the chains. The Car–Parrinello molecular dynamics (CPMD) was applied to support and interpret experimental spectroscopic findings. The vibrational properties of the stretching of OH within the intermolecular hydrogen bond were studied using Fourier transformation of the autocorrelation function of both dipole moments and atomic velocity. Finally, path integral molecular dynamics (PIMD) was carried out to analyze the quantum effect’s influence on the bridged proton position in the hydrogen bridge. On the basis of the combined experimental and theoretical conclusions, a novel mechanism of the bridged protons dynamics has been postulated—the interlamellar hydrogen bonding pattern, resulting in an additional OH stretching band, visible in the solid-state experimental IR spectra.

Effect of Manufacturing Inaccuracies on the Wake Past Asymmetric Airfoil by PIV

The effect of manufacturing geometry deviations on the flow past a NACA 64(3)-618 asymmetric airfoil is studied. This airfoil is 3D printed according to the coordinates from a public database. An optical high-precision 3D scanner, GOM Atos, measures the difference from the idealized model. Based on this difference, another model is prepared with a physical output closer to the ideal model. The velocity in the near wake (0–0.4 chord) is measured by using the Particle Image Velocimetry (PIV) technique. This work compares the wakes past three airfoil realizations, which differ in their similarity to the original design (none of the realizations is identical to the original design). The chord-based Reynolds number ranges from 1.6×104 to 1.6×105. The ensemble average velocity is used for the determination of the wake width and for the rough estimation of the drag coefficient. The lift coefficient is measured directly by using force balance. We discuss the origin of turbulent kinetic energy in terms of anisotropy (at least in 2D) and the length-scales of fluctuations across the wake. The spatial power spectral density is shown. The autocorrelation function of the cross-stream velocity detects the regime of the von Karmán vortex street at lower velocities.

Anharmonic lattice dynamics in large thermodynamic ensembles with machine-learning force fields: CsPbBr3 , a phonon liquid with Cs rattlers

The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principles accuracy. Through large-scale molecular dynamics simulations the projected velocity autocorrelation function (PVACF) is obtained. We apply this approach to the inorganic perovskite CsPbBr$_{3}$. Imaginary modes in the harmonic picture of this perovskite are absent in the PVACF, indicating a dynamic stabilization of the crystal. The anharmonic nature of the potential makes a decoupling of the system into a weakly interacting phonon gas impossible. The phonon spectra of CsPbBr$_{3}$ show the characteristics of a phonon liquid. Rattling motions of the Cs$^{+}$ cations are studied by self-correlation functions and are shown to be nearly dispersionless motions of the cations with a frequency of $\sim$0.8THz within the lead-bromide framework.

Dynamics of active particles with space-dependent swim velocity.

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

A perfect probe: Resonance of underdamped scaled Brownian motion

We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function and mean squared displacement of a single particle, we find that for the steady state, diffusions are free ballistic motion in short time, become the transitions between superdiffusion and subdiffusion in intermediate time, and converge to zero at long times. Via the power spectrum density corresponding to the transitions between superdiffusion and subdiffusion, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles.

Dispersion of heavy particles under sea waves

We report the results of a series of numerical simulations performed with the aim to describe the dispersion of heavy particles transported by sea waves. Recent studies investigated the interplay between the wave Stokes drift and the inertial character of negatively buoyant particles that, ultimately, yields an augmented settling velocity. Our interest is to investigate the possible occurrence of a Brownian regime that would allow for the definition of a diffusion coefficient. The velocity and acceleration auto-correlation functions and the corresponding integral time scales show that already at a very low Stokes number the particles behave very differently from the fluid. The main consequence is that an asymptotic diffusive regime is rarely observed, except as a transient regime or when the background random noise is comparable with the wave field velocities.

Study of SO2 into nanoporous silica Y Zeolite: Molecular dynamics simulation

The dynamic, structure, and thermodynamic properties of sulfur dioxide guest gas inside nanoporous fixed silica Y zeolite were studied by molecular dynamics simulation at different loadings of SO2 per unit cell and within a range of temperature. At loading 20, greater deviation from Fickian behavior is observed. Generally, self-diffusion coefficient increases with temperature. The activation energy for diffusion follows a decreasing trend by loading increase, except at loading 20, which shows an increase in activation energy. The velocity autocorrelation function demonstrates oscillating behavior and cage effect decrease with temperature. From the radial distribution function (RDF) between gas and zeolite framework, it is found that the first layer around the central atom at a low temperature is established more easily and the first peak of the RDF appears at a short distance with more intensity. The interaction between S and Si atoms was examined by the potential of mean force that is independent of loading. The results indicate that SO2 is able to disperse homogeneously into the zeolite at all concentrations and temperatures without much perturbation.

On longitudinal and transversal diffusion of carbon nanotubes

In this work, the anisotropy of diffusion of carbon nanotubes in water was studied by the molecular dynamics method. Two models of nanotubes were used, their lengths varied from 4 to 31 nanometers. The first model is a nanotube with armchair chirality, the second is connected solid nanoscale rods. The behavior of various components of the velocity autocorrelation function of the nanotubes center of mass has been studied. It was established that the transverse component of this function has a negative region and a minimum point, in contrast to the average autocorrelation function, which decays monotonically. It is shown that the diffusion coefficients in the longitudinal and transverse directions can differ several times; the method proposed in this work was used to determine them. The effect of anisotropy increases with an increase in the ratio of the characteristic sizes of the nanotube. Using the Stokes - Einstein formula, the effective hydrodynamic radii of nanotubes have been determined. In all cases, the effective radius is significantly less than the tube length.

Bootstrapping time correlation functions of molecular dynamics.

Molecular dynamics is often considered as a numerical experiment. The error bars on the results are therefore mandatory, but sometimes difficult to determine and computationally demanding. As a low-cost approach, we describe the application of the bootstrap (BS) method to the quantification of uncertainties pertaining to the time correlation functions. We chose the autocorrelation functions of velocity and interdiffusion current for a binary ionic mixture as a test bed, and we assessed the merit of the Darken approximation relating both of them. The intrinsic errors related to phase space sampling is investigated comparing the BS method with the reference method of replica. We also study how the BS method can assist in addressing the finite-size effects.

Fundamentals of turbulent flow spectrum imaging.

PurposeTo introduce a mathematical framework and in‐silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase‐contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.Theory and MethodsThe spectral response of velocity‐encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase‐contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity‐compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.ResultsPractical velocity‐encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity‐compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel‐by‐voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity‐encoding gradients.ConclusionTo address systematic underestimation of turbulence parameters using bipolar velocity‐encoding gradients in phase‐contrast MRI of stenotic flows with short correlation times, tailored velocity‐compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.

Generalized Acoustic Analogy Modeling of Hot Jet Noise

A generalized acoustic analogy model is implemented for the hot and cold static high-speed jet cases corresponding to conditions of the Strategic Investment in Low-carbon Engine Technology (SILOET) experiment performed by QinetiQ. The model is statistical and based on the covariance of fluctuating Reynolds stresses and enthalpy source terms in accordance with Goldstein’s theory. These quantities are obtained from a solution of the validated large-eddy simulation accelerated on graphics processing units. The covariance of fluctuating enthalpy terms is represented by the Khavaran and Bridges model, which involves the velocity autocorrelation function and temperature gradient in the jet. The velocity autocorrelation function and the covariance of fluctuating Reynolds stresses are approximated by an analytical Gaussian-exponential function. The input parameters of the acoustic model include single-point quantities such as the time-averaged local streamwise velocity, sound speed, temperature, vorticity magnitude, turbulent kinetic energy, and dissipation rate. Modeling choices for the acoustic length and time scales based on either the turbulent kinetic energy dissipation rate or mean flow vorticity are discussed. In each case, the model involves two dimensionless parameters associated with the acoustic correlation length and time scale. These two parameters are calibrated based on the far-field noise data at 90° observer angle. The sensitivity of the calibration coefficients to the jet type, cold versus hot, is investigated. Furthermore, the same acoustic model without recalibration is applied for far-field noise predictions of two NASA Small Hot Jet Acoustic Rig jets for acoustic Mach numbers 0.5 and 0.9. To probe the sensitivity of the acoustic model to the input flow data, Reynolds-averaged Navier–Stokes solutions of the same jet cases are considered along with the large-eddy-simulation solutions. The comparison of the predicted far-field noise spectra with the experiment is discussed in each case.

Active Ornstein–Uhlenbeck model for self-propelled particles with inertia

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein–Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle’s mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical inertial time, determined by the particle’s mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle’s motion is completely governed by inertial effects as it remains superdiffusive for all times.

Deep learning potential for superionic phase of Ag2S

Artificial neural networks are used for describing potential energy surface of β-Ag2S silver sulfide. It has allowed performing accurate and fast atomistic simulations for describing behavior of investigated system. We develop neural network potential for high temperature ionic conductor β-Ag2S using DeePMD approach. Reference ab initio dataset was generated using active learning technique implemented in DP-GEN package. Classical molecular simulations with developed neural network potential were performed. Partial radial distribution function for S-S pair and bond-angle distribution function for S-S-S triplet demonstrate crystalline behavior, while the same functions for Ag-Ag pair and Ag-Ag-Ag triplet demonstrate liquid-like behavior. Mean squared displacement of S atoms indicates absence of diffusion for sulfur atoms, while the same function for Ag atoms has linear form at large times that indicates presence of diffusion for this sort of atoms. Velocity autocorrelation functions for S atoms have oscillatory behavior, while for Ag atoms no oscillations are observed. Comparison of mean squared displacement for S atoms and diffusivity for Ag atoms is performed to other ab initio and classical simulations as well as experimental data and demonstrates good agreement in all the cases. Obtained by active learning technique dataset could be expanded to other Ag2S phases for describing Ag2S in wider range of temperatures. Thus accurate, productive, almost free of parameters and promising for future use model for β-Ag2S was created.

Specific Heat Capacity of Confined Water in Extremely Narrow Graphene Nanochannels

Specific heat capacity of extremely confined water determines its performance in the heat transfer as the sizes of devices decrease to nanoscales. Here, we report the basic data of the specific heat capacity of water confined in narrow graphene nanochannels below 5 nm in height using molecular dynamics simulations. The results show that the specific heat capacity of confined water is size-dependent, and the commensurability effect of the specific heat capacity presents as the confinement decreases to 1.7 nm. The deviation of specific heat capacity of confined water with that of bulk water is attributed to the variation of configuration features, including density distribution and hydrogen bonds, and vibration features, including velocity auto-correlation function and vibrational density of states. This work unveils the confinement effects and their physical mechanisms of the specific heat capacity of nanoconfined water, and the data provided here have wide prospects for energy applications at nanoscales.

Velocity auto correlation function of a confined Brownian particle

Motivated by the simple models of molecular motor obeying a linear force-velocity relation, we have studied the stochastic dynamics of a Brownian particle in the presence of a linear velocity dependent force, $$f_s(1-\frac{v}{v_0})$$ where $$f_{s}$$ is a constant. The position and velocity auto correlation functions in different situations of the dynamics are calculated exactly. We observed that the velocity auto correlation function shows an exponentially decaying behaviour with time and saturates to a constant value in the time asymptotic limit, for a fixed $$f_s$$ . It attains saturation faster with increase in the $$f_{s}$$ value. When the particle is confined in a harmonic well, the spectral density exhibits a symmetric behaviour and the corresponding velocity auto correlation function shows a damped oscillatory behaviour before decaying to zero in the long time limit. With viscous coefficient, a non-systematic variation of the velocity auto correlation function is observed. Further, in the presence of a sinusoidal driving force, the correlation in velocities increases with increase in the amplitude of driving in the transient regime. For the particle confined in a harmonic well, the correlation corresponding to the shift relative to the average position is basically the thermal contribution to the total position correlation. Moreover, in the athermal regime, the total correlation is entirely due to the velocity dependent force.

Unique stochastic Lagrangian particle dispersion models for inhomogeneous turbulent flows

It is well established that Lagrangian particle dispersion models, for inhomogeneous turbulent flows, must satisfy the ‘well-mixed condition’ of Thomson (J. Fluid Mech., vol. 180, 1987, pp. 529–556) in order to produce physically reasonable results. In more than one dimension, however, the well-mixed condition is not sufficient to define the dispersion model uniquely. The non-uniqueness, which is related to the rotational degrees of freedom of particle trajectories, permits models with trajectory curvatures and velocity autocorrelation functions which are clearly unphysical. A spin condition is therefore introduced to constrain the models. It requires an ensemble of particles with fixed initial position and velocity to have, at short times, expected angular momentum, measured relative to the mean position and velocity of an ensemble of fluid particles with initially random velocity, equal to the relative angular momentum of the mean flow at the ensemble mean location. The resulting unique model is found explicitly for the canonical example of inhomogeneous Gaussian turbulence and is characterised by accelerations which are exponential in the particle velocity. A simpler unique model with a quadratic acceleration is obtained using a weaker version of the spin condition. Unlike previous models, the unique models defined by the spin condition lead to particles having the correct (ensemble mean) angular speed in a turbulent flow in solid-body rotation. The properties of the new models are discussed in the settings of a turbulent channel flow and an idealised turbulent atmospheric boundary-layer flow.

Naphthazarin Derivatives in the Light of Intra- and Intermolecular Forces.

Our long-term investigations have been devoted the characterization of intramolecular hydrogen bonds in cyclic compounds. Our previous work covers naphthazarin, the parent compound of two systems discussed in the current work: 2,3-dimethylnaphthazarin (1) and 2,3-dimethoxy-6-methylnaphthazarin (2). Intramolecular hydrogen bonds and substituent effects in these compounds were analyzed on the basis of Density Functional Theory (DFT), Møller–Plesset second-order perturbation theory (MP2), Coupled Clusters with Singles and Doubles (CCSD) and Car-Parrinello Molecular Dynamics (CPMD). The simulations were carried out in the gas and crystalline phases. The nuclear quantum effects were incorporated a posteriori using the snapshots taken from ab initio trajectories. Further, they were used to solve a vibrational Schrödinger equation. The proton reaction path was studied using B3LYP, B97XD and PBE functionals with a 6-311++G(2d,2p) basis set. Two energy minima (deep and shallow) were found, indicating that the proton transfer phenomena could occur in the electronic ground state. Next, the electronic structure and topology were examined in the molecular and proton transferred (PT) forms. The Atoms In Molecules (AIM) theory was employed for this purpose. It was found that the hydrogen bond is stronger in the proton transferred (PT) forms. In order to estimate the dimers’ stabilization and forces responsible for it, the Symmetry-Adapted Perturbation Theory (SAPT) was applied. The energy decomposition revealed that dispersion is the primary factor stabilizing the dimeric forms and crystal structure of both compounds. The CPMD results showed that the proton transfer phenomena occurred in both studied compounds, as well as in both phases. In the case of compound 2, the proton transfer events are more frequent in the solid state, indicating an influence of the environmental effects on the bridged proton dynamics. Finally, the vibrational signatures were computed for both compounds using the CPMD trajectories. The Fourier transformation of the autocorrelation function of atomic velocity was applied to obtain the power spectra. The IR spectra show very broad absorption regions between 700 cm–1700 cm and 2300 cm–3400 cm in the gas phase and 600 cm–1800 cm and 2200 cm–3400 cm in the solid state for compound 1. The absorption regions for compound 2 were found as follows: 700 cm–1700 cm and 2300 cm–3300 cm for the gas phase and one broad absorption region in the solid state between 700 cm and 3100 cm. The obtained spectroscopic features confirmed a strong mobility of the bridged protons. The inclusion of nuclear quantum effects showed a stronger delocalization of the bridged protons.

Reverberant shear wave phase gradients for elastography

Reverberant shear wave fields are produced when multiple sources and multiple reflections establish a complex three-dimensional wave field within an organ. The expected values are assumed to be isotropic across all directions and the autocorrelation functions for velocity are expressed in terms of spherical Bessel functions. These results provide the basis for adroit implementations of elastography from imaging systems that can map out the internal velocity or displacement of tissues during reverberant field excitations. By examining the phase distribution of the reverberant field, additional estimators can be derived. In particular, we demonstrate that the reverberant phase gradient is shown to be proportional to the local value of wavenumber. This phase estimator is less sensitive to imperfections in the reverberant field distribution and requires a smaller support window, relative to earlier estimators based on autocorrelation. Applications are shown in simulations, phantoms, and in vivo liver.