Mass-weighted Velocity Research Articles

Investigating thermal conductivity and mechanical properties of a hybrid material based on cellulose nanofibers and boron nitride nanotubes using molecular dynamics simulations

Cellulose nanofibers (NFCs) have emerged as a preferred choice for fabricating nanomaterials with exceptional mechanical properties. At the same time, boron nitride nanotubes (BNNTs) have long been favored in thermal management devices due to their superior thermal conductivity (k). This study uses reverse non-equilibrium molecular dynamics (MD) simulations to investigate k for a hybrid material based on NFCs and BNNTs. The result is then compared with pure NFC and BNNT-based structures with equivalent total weight content to elucidate how incorporating BNNT fillers enhances k for the hybrid system. Furthermore, the fundamental phonon vibration modes responsible for driving thermal transport in NFC-based materials upon incorporating BNNTS are identified by computing the vibrational density of states from the Fourier transform analysis of the averaged mass-weighted velocity autocorrelation function. Additionally, MD simulations demonstrate how both NFCs and BNNTs synergistically improve the constituting hybrid structure’s mechanical properties (e.g. tensile strength and stiffness). The overarching aim is to contribute towards the engineered design of novel functional materials based on nanocellulose that simultaneously improve crucial physical properties pertaining to thermal transport and mechanics.

Testing the Momentum-driven Supernova Feedback Paradigm in M31

Abstract Momentum feedback from isolated supernova remnants (SNRs) have been increasingly recognized by modern cosmological simulations as a resolution-independent means to implement the effects of feedback in galaxies, such as turbulence and winds. However, the integrated momentum yield from SNRs is uncertain due to the effects of SN clustering and interstellar medium (ISM) inhomogeneities. In this paper, we use spatially resolved observations of the prominent 10 kpc star-forming ring of M31 to test models of mass-weighted ISM turbulence driven by momentum feedback from isolated, nonoverlapping SNRs. We use a detailed stellar age distribution (SAD) map from the Panchromatic Hubble Andromeda Treasury survey, observationally constrained SN delay-time distributions, and maps of the atomic and molecular hydrogen to estimate the mass-weighted velocity dispersion using the Martizzi et al. ISM turbulence model. Our estimates are within a factor of two of the observed mass-weighted velocity dispersion in most of the ring, but exceed observations at densities ≲0.2 cm−3 and SN rates >2.1 × 10−4 SN yr−1 kpc−2, even after accounting for plausible variations in SAD models and ISM scale height assumptions. We conclude that at high SN rates the momentum deposited is most likely suppressed by the nonlinear effects of SN clustering, while at low densities, SNRs reach pressure equilibrium before the cooling phase. These corrections should be introduced in models of momentum-driven feedback and ISM turbulence.

Comparing simulated specific heat of liquid polymers and oligomers to experiments

The specific heat is a central property of condensed matter systems including polymers and oligomers in their condensed phases. Yet, predictions of this quantity from molecular simulations and successful comparisons to experimental data are scarce if existing at all. One reason for this may be that the internal energy and thus the specific heat cannot be coarse-grained so that they defy their rigorous computation with united-atom models. Moreover, many modes in a polymer barely contribute to the specific heat because of their quantum mechanical nature. Here, we demonstrate that an analysis of the mass-weighted velocity autocorrelation function allows specific heat predictions to be corrected for quantum effects so that agreement with experimental data is on par with predictions of other routinely computed quantities. We outline how to construct corrections for both all-atom and united-atom descriptions of chain molecules. Corrections computed for eleven hydrocarbon oligomers and commodity polymers deviate by less than $k_\textrm{B}/10$ within a subset of nine molecules. Our results may benefit the prediction of heat conductivity.

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid.

The accurate molecular simulation prediction of vibrational spectra, and other structural, energetic and spectral characteristics, of photo-active metal-oxide surfaces in contact with light-absorbing dyes is an ongoing thorny and elusive challenge in physical chemistry. With this in mind, a molecular-dynamics (MD) simulation were performed by using optimized empirical potentials for a well-representative and prototypical dye-sensitized solar cell (DSC) solvated by a widely-studied room temperature ionic liquid (RTIL), in the guise of a [bmim]+[NTf2]- RTIL solvating an N719-sensitizing dye adsorbed onto 101 anatase-titania. In doing so, important insights were gleaned into how using a RTIL as the electrolytic hole acceptor modulates the dynamical and vibrational properties of a N719 dye, estimating the spectra for the DSC photo-active interface via Fourier transformation of mass-weighted velocity autocorrelation functions from MD. The acquired vibrational spectra were compared with the experiment spectra and those sampled from ab initio molecular dynamics (AIMD); in particular, various empirical-potential spectra generated from MD provide insight into how partial-charge charge parameterization of the ionic liquid affects vibrational spectra prediction. In any event, careful fitting of empirical force-field models has been shown to be an effective tool in handling DSC vibrational properties, when validated by AIMD and an experiment.

Ab Initio Molecular Dynamics Studies of the Effect of Solvation by Room-Temperature Ionic Liquids on the Vibrational Properties of a N719-Chromophore/Titania Interface

The accurate ab initio modeling of prototypical and well-representative photoactive interfaces for candidate dye-sensitized solar cells (DSCs) is a perennial problem in physical chemistry. To this end, the use of ab initio density functional theory-based molecular dynamics (AIMD) has been studied here to investigate the effect the choice of functional has on a system mimicking the essential workings of a DSC: the energetic properties of a [bmim]+[NTf2]− room-temperature ionic liquid (RTIL) solvating an N719-sensitizing dye adsorbed onto an anatase–titania (101) surface were scrutinized. In so doing, we glean important insights into how using an RTIL as electrolytic hole acceptor alters and modulates the dynamical properties of the widely used N719 dye. A fully crossed study has been carried out comparing the Becke–Lee–Yang–Parr (BLYP) and Perdew–Burke–Ernzerhof (PBE) functionals, both unsolvated and solvated by the RTIL, both with and without Grimme D3 dispersion corrections. Also, vibrational spectra for the photoactive interface in the DSC configuration were calculated by means of Fourier-transforming atomic mass-weighted velocity autocorrelation functions. The ab initio vibrational spectra were compared to high-quality experimental data and against each other; the effects of various methodological choices on the vibrational spectra were also studied, with PBE generally performing best in producing spectra, which matched the experimental frequency modes typically expected.

Vibrational Study of Iodide-Based Room-Temperature Ionic-Liquid Effects on Candidate N719-Chromophore/Titania Interfaces for Dye-Sensitised Solar-Cell Applications from Ab-Initio Based Molecular-Dynamics Simulation

The accurate ab-initio modelling of prototypical and well-representative photo-active interfaces for candidate dye-sensitised solar cells is a challenging problem. To this end, using ab-initio molecular-dynamics (AIMD) simulation based on Density Functional Theory (DFT), the effects of explicit solvation by iodide-based, I−[bmim]+ room-temperature ionic liquids (RTILs) have been assessed on modelling a N719-chromophore sensitising dye adsorbed onto an anatase-titania (101) surface. In particular, the vibrational spectra for this model photo-active interface were calculated by means of Fourier transformed mass-weighted velocity autocorrelation functions. These were compared with experiment and against each other to gain an understanding of how using iodine-based RTILs as the electrolytic hole acceptor alters the dynamical properties of the widely-used N719 dye. The effect of Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) functionals on the vibrational spectra were assessed. PBE generally performed best in producing spectra which matched the typically expected experimental frequency modes.

Radiation pressure in galactic discs: stability, turbulence, and winds in the single-scattering limit

The radiation force on dust grains may be dynamically important in driving turbulence and outflows in rapidly star-forming galaxies. Recent studies focus on the highly optically-thick limit relevant to the densest ultra-luminous galaxies and super star clusters, where reprocessed infrared photons provide the dominant source of electromagnetic momentum. However, even among starburst galaxies, the great majority instead lie in the so-called "single-scattering" limit, where the system is optically-thick to the incident starlight, but optically-thin to the re-radiated infrared. In this paper we present a stability analysis and multidimensional radiation-hydrodynamic simulations exploring the stability and dynamics of isothermal dusty gas columns in this regime. We describe our algorithm for full angle-dependent radiation transport based on the discontinuous Galerkin finite element method. For a range of near-Eddington fluxes, we show that the medium is unstable, producing convective-like motions in a turbulent atmosphere with a scale height significantly inflated compared to the gas pressure scale height and mass-weighted turbulent energy densities of $\sim 0.01-0.1$ of the midplane radiation energy density, corresponding to mass-weighted velocity dispersions of Mach number $\sim 0.5-2$. Extrapolation of our results to optical depths of $10^3$ implies maximum turbulent Mach numbers of $\sim20$. Comparing our results to galaxy-averaged observations, and subject to the approximations of our calculations, we find that radiation pressure does not contribute significantly to the effective supersonic pressure support in star-forming disks, which in general are substantially sub-Eddington. We further examine the time-averaged vertical density profiles in dynamical equilibrium and comment on implications for radiation-pressure-driven galactic winds.

Low-mass disc galaxies and the issue of stability: MOND versus dark matter

We analyse the rotation curves and gravitational stability of a sample of six bulgeless galaxies for which detailed images reveal no evidence for strong bars. We explore two scenarios: Newtonian dark matter models and MOdified Newtonian Dynamics (MOND). By adjusting the stellar mass-to-light ratio, dark matter models can match simultaneously both the rotation curve and bar-stability requirements in these galaxies. To be consistent with stability constraints, in two of these galaxies, the stellar mass-to-light ratio is a factor of ~1.5-2 lower than the values suggested from galaxy colours. In contrast, MOND fits to the rotation curves are poor in three galaxies, perhaps because the gas tracer contains noncircular motions. The bar stability analysis provides a new observational test to MOND. We find that most of the galaxies under study require abnormally-high levels of random stellar motions to be bar stable in MOND. In particular, for the only galaxy in the sample for which the line-of-sight stellar velocity dispersion has been measured (NGC 6503), the observed velocity dispersion is not consistent with MOND predictions because it is far below the required value to guarantee bar stability. Precise measurements of mass-weighted velocity dispersions in (unbarred and bulgeless) spiral galaxies are crucial to test the consistency of MOND.

Coarse-grained cosmological perturbation theory: Stirring up the dust model

We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to one-loop order. In particular, the large-scale vorticity power spectrum that arises naturally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from $N$-body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones.

Constructing Periodic Phase Space Orbits from ab Initio Molecular Dynamics Trajectories to Analyze Vibrational Spectra: Case Study of the Zundel (H5O2+) Cation

A method of analysis is introduced to probe the spectral features obtained from ab initio molecular dynamics simulations. Here, the instantaneous mass-weighted velocities are projected onto irreducible representations constructed from discrete time translation groups comprising operations that invoke the time-domain symmetries (or periodic phase space orbits) reflected in the spectra. The projected velocities are decomposed using singular value decomposition (SVD) to construct a set of "modes" pertaining to a given frequency domain. These modes now include all anharmonicities, as sampled during the dynamics simulations. In this approach, the underlying motions are probed in a manner invariant with respect to coordinate transformations, operations being performed along the time axis rather than coordinate axes, making the analysis independent of choice of reference frame. The method is used to probe the underlying motions responsible for the doublet at ∼1000 cm(-1) in the vibrational spectrum of the H5O2(+), Zundel cation. The associated analysis results are confirmed by projecting the Fourier transformed velocities onto the harmonic normal mode coordinates and a set of mass-weighted, symmetrized Jacobi coordinates. It is found that the two peaks of the doublet are described and differentiated by their respective contributions from the proton transfer, water-water stretch, and water wag coordinates, as these are defined. Temperature dependent effects are also briefly noted.

Phase Change Heat Transfer Simulation for Boiling Bubbles Arising from a Vapor Film by the VOSET Method

This article presents a numerical method directed towards the simulation of flows with changes of phase. The volume-of-fluid level set (VOSET) method, which is a new interface capturing method and combines the advantages of both volume-of-fluid (VOF) and level set methods, is used for interface tracking. A difficulty occurs for the problems studied here: the discontinuous velocity field due to the difference between mass-weighted velocity and volume weighted velocity caused by the phase change at the interface. In this article, some special treatment is made to overcome this difficulty. The VOSET method and the developed treatment for the difference between mass-weighted and volume-weighted velocities are adopted to simulate a one-dimensional Stefan problem, two-dimensional horizontal film boiling, and horizontal film boiling of water at near critical pressure. The predicted results in both Nusselt number and flow patterns are agreeable with experimental results available in the literature.

DEPENDENCE OF INTERSTELLAR TURBULENT PRESSURE ON SUPERNOVA RATE

Feedback from massive stars is one of the least understood aspects of galaxy formation. We perform a suite of vertically stratified local interstellar medium (ISM) models in which supernova (SN) rates and vertical gas column densities are systematically varied based on the Schmidt-Kennicutt law. Our simulations have a sufficiently high spatial resolution (1.95 pc) to follow the hydrodynamic interactions among multiple SNe that structure the interstellar medium. At a given SN rate, we find that the mean mass-weighted sound speed and velocity dispersion decrease as the inverse square root of gas density. The sum of thermal and turbulent pressures is nearly constant in the midplane, so the effective equation of state is isobaric. In contrast, across our four models having SN rates that range from 1 to 512 times the Galactic SN rate, the mass-weighted velocity dispersion remains in the range 4-6 km s–1. Hence, gas averaged over ~100 pc regions follows P ∝ ρα with α ≈ 1, indicating that the effective equation of state on this scale is close to isothermal. Simulated H I emission lines have widths of 10-18 km s–1, comparable to observed values. In our highest SN rate model, superbubble blow-outs occur, and the turbulent pressure on large scales is 4 times higher than the thermal pressure. We find a tight correlation between the thermal and turbulent pressures averaged over ~100 pc regions in the midplane of each model, as well as across the four ISM models. We construct a subgrid model for turbulent pressure based on analytic arguments and explicitly calibrate it against our stratified ISM simulations. The subgrid model provides a simple yet physically motivated way to include SN feedback in cosmological simulations.

Generation of vorticity and velocity dispersion by orbit crossing

We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass-weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than 1 order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit-crossing corrections to the evolution of large-scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales ($k\ensuremath{\simeq}0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent-level corrections at $z=0$, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities.

Is the Scaling of Supersonic Turbulence Universal?

The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i.e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of supersonic turbulent flow driven by external forcing, we demonstrate that this is not generally true for the two-point velocity statistics of compressible turbulence. However, a reformulation of the refined similarity hypothesis in terms of the mass-weighted velocity rho1/3v yields scaling laws that are almost insensitive to the forcing. The results imply that the most intermittent dissipative structures are shocks closely following the scaling of Burgers turbulence.

Momentum and Velocity Autocorrelation Functions of a Diatomic Molecule Are Not Necessarily Proportional to Each Other

We present a computation of the classical momentum and velocity correlation functions of Br2 considered as an idealized molecular wire connecting dissipated lead atoms at each end of the dimer. It is demonstrated that coupling of the diatomic relative momentum to the leads may result in momenta that are not equal to the mass-weighted velocity. These differences show up in numerical simulations of both the average value and time correlations of the bond momentum and velocity. These observations are supported by analytical predictions for the average temperature of the diatomic. They imply that the "standard recipes" for modeling the system with a generalized Langevin equation are insufficient.

Jet-driven molecular outflows from class 0 sources: younger and stronger than they seem?

Context. The momentum, age and momentum injection rate (thrust) of molecular outflows are key parameters in theories of star formation. Systematic biases in these quantities as inferred from CO line observations are introduced through simplified calculations. These biases were quantified for radially expanding flows. However, recent studies suggest that the youngest outflows may be better described by jet-driven bowshocks, where additional biases are expected. Aims. We investigate quantitatively the biases in momentum, age, and thrust estimates in the case of young jet-driven molecular outflows, and propose more accurate methods of determining these quantities. Methods. We use long-duration (1500 yr) high resolution numerical simulations in concert with the standard observational methods of inferring the relevant quantities to quantify the systematic biases in these calculations introduced, in particular, by dissociation, erroneous inclusion of transverse momentum, and hidden material at cloud velocity. Jet/ambient density contrasts of 0.1–1 are considered, leading to bow speeds of 60–135 km s −1 . Results. When mass-weighted velocities are used, lifetimes are overestimated by typically an order of magnitude. The molecular thrust is then underestimated by similar amounts. Using the maximum velocity in CO profiles gives better results, if empirical corrections for inclination are applied. We propose a new method of calculating the lifetime of an outflow which dramatically improves estimates of age and molecular thrust independent of inclination. Our results are applicable to younger flows which have not broken out of their parent cloud. Conclusions. Published correlations between the molecular flow thrust and the source bolometric luminosity obtained with the maximum CO velocity method should remain valid. However, dissociation at the bow head may cause the observable thrust to underestimate the total flow thrust by a factor of up to 2–4, depending on the bow propagation speed and the magnetic field strength. Detailed evaluation of this effect would greatly help to better constrain the efficiency of the ejection mechanism in protostars.

Influence of Mass Diffusion in Sea Ice Dynamical Models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction ( k5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.