Maximum Wavenumber Research Articles

Development of AMBER-compliant transferable force field parameters for polytetrafluoroethylene

AbstractNew transferable parameters for polytetrafluoroethylene (PTFE) compatible with the Assisted Model Building with Energy Refinement (AMBER) force field were developed by including many conformational states to improve accuracy. The Austin–Frisch–Petersson functional with dispersion hybrid density functional theory, advantageous for treating dispersion, was used to obtain quantum mechanical reference data. The restrained electrostatic potential method was used to compute the partial charges. The bonds, angles, and dihedral parameters were obtained via Paramfit software fitted to quantum mechanical data. The optimization of van der Waals parameters was obtained in the condensed phase through molecular dynamics simulations and the simplex method. These parameters were transferred to various molecular weights of PTFE assembly systems to calculate the density, radial distribution functions, power spectrum, and specific heat capacity. The highest percent error in density was 1.4% for the modeled PTFE ensembles. The calculated vibrational spectrum peaks closely matched experimental peaks with a maximum wavenumber deviation of 19 cm⁻¹. The highest percent error to specific heat capacity was 5%. These results represent a significant improvement over pre-existing potentials in the literature and provide parameters that can be used to model PTFE in many existing simulation codes.

Weakly nonlocal matter-wave droplets and soliton trains engineering in a Bose-Einstein condensate

We propose a comprehensive analysis of the modulational instability (MI) phenomenon in one-dimensional Bose-Einstein condensate (BEC) in the context of mutually symmetric components in the binary mixture. The proposed model considers weak nonlocal cubic mean-field and quadratic beyond mean-field interactions arising from quantum fluctuations. The instability regions are analyzed using linear stability analysis of a continuous wave, considering maximum perturbation wavenumber and growth rate. The regions for quantum droplets (QDs) and solitons are identified by varying the nonlocality parameter. Numerical simulations confirm analytical predictions, revealing that nonlocality influences the formation of various QD profiles and instability time. Furthermore, solitonic patterns exhibit nonlocality-dependent behavior. Our study opens new doors to a better characterization of QDs in binary mixtures in the presence of higher-order beyond mean-field effects.

Euclid preparation

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of a Eulerian galaxy bias expansion using state-of-the-art prescriptions from the effective field theory of large-scale structure (EFTofLSS) with a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the flagship I N-body simulation at z = (0.9, 1.2, 1.5, 1.8), which have been populated with Hα galaxies leading to catalogues of millions of objects within a volume of about 58 h−3 Gpc3. Our analysis suggests that both models can be used to provide a robust inference of the parameters (h, ωc) in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion – which includes local and non-local bias parameters, a matter counter term, and a correction to the shot-noise contribution – can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber of kmax = 0.45 h Mpc−1, and with a measurement precision of well below the percentage level. Fixing either of the tidal bias parameters to physically motivated relations still leads to unbiased cosmological constraints, and helps in reducing the severity of projection effects due to the large dimensionality of the model. We finally show how we repeated our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, such as purity and completeness, showing that we can get constraints on the combination (h, ωc) that are consistent with the fiducial values to better than the 68% confidence interval over this range of scales and redshifts.

A New Closure Assumption and Formulation Based on the Helmholtz Decomposition for Improving Retrievals for Vortex Circulations from Single-Doppler Radar Observations

Abstract Doppler weather radars are powerful tools for investigating the inner-core structure and intensity of tropical cyclones (TCs). The Doppler velocity can provide quantitative information on the vortex structure in the TCs. The generalized velocity track display (GVTD) technique has been used to retrieve the axisymmetric circulations and asymmetric tangential flows in the TCs from ground-based single-Doppler radar observations. GVTD can have limited applicability to asymmetric vortices due to the closure assumption of no asymmetric radial flows. The present study proposes a new closure formulation that includes asymmetric radial flows, based on the Helmholtz decomposition. Here it is assumed that the horizontal flow is predominantly rotational and expressed with a streamfunction, but limited inclusion of wavenumber-1 divergence is available. Unlike the original GVTD, the decomposition introduces consistency along the radius by solving all equations simultaneously. The new approach, named GVTD-X, is applied to analytical vortices and a real TC with asymmetric structures. This approach makes the retrieval of axisymmetric flow relatively insensitive to the contamination from asymmetric flows and to small errors in storm center location. For an analytical vortex with a wavenumber-2 asymmetry, the maximum relative error of the axisymmetric tangential wind retrieved by GVTD-X is less than 2% at the radius of the maximum wind speed. In practical applications, errors can be evaluated by comparing results for different maximum wavenumbers. When applied to a real TC, GVTD-X largely suppressed an artificial periodic fluctuation that occurs in GVTD from the aliasing of the neglected asymmetric radial flows. Significance Statement In tropical cyclone (TC) wind retrievals from single-Doppler weather radar observations, closure assumptions are required for the retrieval equations. The present study proposes a new closure allowing asymmetric radial winds and improving retrievals for TC winds in the previously developed technique. The relative error of the axisymmetric tangential wind in idealized vortices from the new approach is less than 2% at the radius of the maximum wind speed. In applying to a real TC with an elliptical eyewall, we found that the new approach can largely suppress an artificial evolution of the tangential winds in the previous retrieval technique.

Effects of bulk viscosity, heat capacity ratio, and Prandtl number on the dispersion relationship of compressible flows

Here, we present the variation of the dispersion characteristics of the three-dimensional (3D) linearized compressible Navier–Stokes equation (NSE) to bulk viscosity ratio, specific heat ratio (γ), and Prandtl number (Pr). The 3D compressible NSE supports five types of waves, two vortical, one entropic, and two acoustic modes. While the vortical and entropic modes are non-dispersive, the acoustic modes are dispersive only up to a specific bifurcation wavenumber. We illustrate the characteristics and variation of relative (with respect to the vortical mode) diffusion coefficient for entropic and acoustic modes and a specially designed dispersion function for acoustic modes with depressed wavenumber η=KM/Re, the bulk viscosity ratio, γ, and Prandtl number Pr of the flow. Here, K, M, and Re denote the absolute wavenumber of disturbances, Mach number, and Reynolds number of the flow, respectively. At lower wavenumber components, the deviation of the dispersion function from the inviscid and adiabatic case is proportional to η2 at the leading order, and the relative diffusion coefficients increase linearly with bulk viscosity ratio and γ while varying inversely with Pr. With the increase in the bulk viscosity ratio, the shape and extent of the dispersion function alter significantly, and the change is more substantial for higher wavenumber components. The relative diffusion coefficient for entropic and acoustic modes shows contrasting variation with wavenumber depending upon bulk viscosity ratio, γ, and Pr. We also show by solving linearized compressible NSE that relatively significant evolution and radiation of acoustic and entropic disturbances occur when the bulk viscosity ratio is close to the corresponding critical value of maximum bifurcation wavenumber. Based on this criterion, we have presented an empirical relation for estimating bulk viscosity ratio depending upon γ and Pr, giving the corresponding range for obtaining relatively significant disturbance evolution.

Efficient source wavefield reconstruction for full-waveform inversion

Full-waveform inversion (FWI) is a useful tool for estimating the properties of subsurface media, but it has the disadvantage of incurring considerable computing costs. Therefore, we develop a method for reducing the computing memory requirement in the time domain of FWI that uses a new approach with the discrete cosine transform (DCT) and the Nyquist sampling theorem. Our method enables accurate reconstruction of a wavefield with several optimal DCT coefficients derived by considering the maximum wavenumber component of the virtual source wavefield and the maximum frequency of the source wavelet. Consequently, virtual source wavefields can be stored in a computer’s memory rather than on a disk. Our FWI algorithm is compared with existing compression methods that use DCT and wavelet transform in a numerical example. The results of this comparison demonstrate that our algorithm provides significantly improved computational efficiency.

A stable staggered-grid finite-difference scheme for acoustic modeling beyond conventional stability limit

Staggered-grid finite-difference (SGFD) schemes have been widely used in acoustic wave modeling for geophysical problems. Many improved methods are proposed to enhance the accuracy of numerical modeling. However, these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy (CFL) numbers, making them unstable when modeling with large time sampling intervals or small grid spacings. To solve this problem, we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers. First, to improve modeling stability, we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region, and make the FD dispersion approach a given function outside the given wave-number area, thus breaking the conventional limits of the maximum CFL number. Second, to obtain high modeling accuracy, we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients. In addition, the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme. Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber, indicating that the proposed scheme improves stability during the modeling.

Theoretical analysis on electrohydrodynamic instability of a low viscous electrified jet

In present work, a dispersion equation describing electrohydrodynamic (EHD) instability of a low viscous electrified jet was derived, where the Naiver-Stokes equations combined with the electrodynamic and hydrodynamic boundary conditions are utilized. The effect of operating parameters containing electric potential, initial jet velocity and electrode spacing on stability of the electrified jet was systematically examined and extensively analyzed, as well as liquid properties including liquid viscosity and surface tension. The analysis indicate that the axisymmetric surface waves dominate the breakup instability of the electrified jet at low electric potential or low flowrate. As flowrate or electric potential increases, the influence of the non-axisymmetric surface waves is gradually enhanced. The electrode spacing and initial diameter of the jet also have extremely slight effect on the surface wave growth rate. The viscosity could stabilize the electrified jet and almost has no influence on the maximum wave number. With the surface tension increasing, the stability of the jet is usually enhanced. The analytical results agree well with the experimental observation in the varicose instability. Meanwhile, the discrepancy between the predicted and experimental data in the whipping instability indicates the influence of non-linear perturbations is indispensable.

The halo bispectrum multipoles in redshift space

We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate f of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction finding discrepancies of 10% or less for all configurations with the sole exception of the squeezed triangles in the monopole case. We find the range of validity of the tree-level model, for the total simulation volume of about 1000 h -3Gpc3, reaches a maximum wavenumber of 0.08 h Mpc-1 for the monopole, while it is limited to 0.06 and 0.045 h Mpc-1 respectively for quadrupole and hexadecapole. Despite this, the addition of the quadrupole to the analysis allows for significant improvements on the determination of the model parameters and specifically on f, similarly to the power spectrum case. Finally, we compare our numerical estimate for the full covariance with its theoretical prediction in the Gaussian approximation and find the latter to work remarkably well in the context of simulation boxes with periodic boundary condition.

The Mira–Titan Universe – IV. High-precision power spectrum emulation

ABSTRACT Modern cosmological surveys are delivering data sets characterized by unprecedented quality and statistical completeness; this trend is expected to continue in the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the non-linear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira–Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. This gravity-only set of simulations covers the standard six cosmological parameters {ωm, ωb, σ8, h, ns, w0} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state {ων, wa}. In this paper, we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1 Gpc)3 volume and evolving 32003 particles. An additional set of 1776 lower resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly non-linear regimes (maximum wavenumber k = 5 Mpc−1). The emulator provides predictions at the 2–3 per cent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper.

Instability of liquid film flow inside of a vertical tube in presence of an interfacial surfactant.

Liquid film coating inside a tube becomes unstable to surface-tension-driven Rayleigh-Plateau (RP) instability. The presence of interfacial surfactant reduces the growth rate of RP instability but is unable to completely eliminate it. Further, it is known that the surfactant mode, an eigenmode emerging because of the presence of surfactant, remains stable for such liquid films. However, the above two observations hold true only when the liquid film remains stationary (i.e., in the absence of base flow). Here, we investigate the linear stability of surfactant-laden liquid film inside of the tube with base flow included in the analysis. We observed a complete suppression of Rayleigh-Plateau instability because of the presence of surfactant when the basic flow is included in the analysis. However, the surfactant mode, which otherwise remains stable in the absence of base flow, is found to be unstable when the basic flow is taken into account in the stability analysis. More importantly, depending on the base flow strength, the wave number corresponding to maximum growth rate and cutoff wave number for surfactant mode are greater than unity for a wide variety of parameters. This is unlike the (RP) instability observed for surfactant-covered stationary films where the cutoff wave number is always less than unity. Further, we show that the growth rate observed for this surfactant-mode instability in the presence of sufficiently strong basic flow is significantly higher than the growth rate of RP instability observed for a stationary liquid film. These observations imply that depending on the strength of basic flow, the effect of presence of surfactant is destabilizing for such film flows as opposed to a stabilizing effect observed for stationary liquid films in earlier studies.

Forward and inverse cascades by exact resonances in surface gravity waves.

We study the energy transfer by exact resonances for deep-water surface gravity waves in a finite periodic spatial domain. Based on a kinematic model simulating the generation of active wave modes in a finite discrete wave number space S_{R}, we examine the possibility of direct and inverse cascades. More specifically, we set an initially excited region which iteratively spreads energy to wave modes in S_{R} through exact resonances. At each iteration, we first activate new modes from scale resonances (which generate modes with new lengths), then consider two bounding situations for angle resonances (which transfer energy at the same length scale): the lower bound where no angle resonance is included and the upper bound where all modes with the same length as any active mode are excited. Such a strategy is essential to enable the computation for a large domain S_{R} with the maximum wave number R∼10^{3}. We show that for both direct and inverse cascades, the modal propagation to the boundaries of S_{R} can be established when the initially excited region is sufficiently large; otherwise a frozen turbulence state occurs, with a sharp transition between the two regimes especially for the direct cascade. Through a study on the structure of resonant quartets, the mechanism associated with the sharp transition and the role of angular energy transfer in the cascades are elucidated.

On the Resolution of Triangular Meshes

AbstractIt is generally agreed that the resolution of a regular quadrilateral mesh is the side length of quadrilateral cells. There is less agreement on the resolution of triangular meshes, exacerbated by the fact that the numbers of edges or cells on triangular meshes are approximately three or two times larger than that of vertices. However, the geometrical resolution of triangular meshes, that is, maximum wavenumbers or smallest wavelengths that can be represented on such meshes, is a well defined quantity, known from solid state physics. These wavenumbers are related to a smallest common mesh cell (primitive unit cell), and the set of mesh translations that map it into itself. They do not depend on whether discrete degrees of freedom are placed on vertices, cells or edges. For equilateral triangles the smallest wavelength equals twice the triangle height. Resolutions of quadrilateral and triangular meshes approximately agree if they have the same numbers of vertices.

Experimental investigation on the wave performance with the interference of floating aquaculture cages in single and tandem arrangements

Floating aquaculture cages deployed in the nearshore affect the wave field and contribute to the coastal defense by damping incoming waves. Most pioneering works concerning aquaculture cages have concentrated on the hydrodynamics of the structures instead of their influence on the wave field. In order to bridge the gap, this paper examines the wave performance with the interference of floating aquaculture cages via physical model tests. The results show that the existence of cages increases wave height on the weather side. The wave-dissipation performance of the net cage is closely related to the ratio of the wavelength to the structural span, and the minimum transmission coefficients appear in the conditions with the maximum wave number. Moreover, the crests of the free surface elevation inside the floating frames are almost flat, which is particularly obvious in the long-period wave conditions. The surface elevations show nonlinearity in small-wavelength conditions, which is dominantly caused by the pitch motion of the cages. Nevertheless, the presence of the cage does not affect the phase differences in the wave elevation at different positions. The nets have an opposite effect on wave response inside the cage under the conditions of long-period and short-period waves.

Temporal instability of curved viscous fibers with a radial electric field

Abstract One-dimensional equations are derived for a rotating viscous slender liquid jet in a radial electric field using asymptotic methods. The trajectory of the curved Newtonian liquid jets is found by solving the nonlinear one-dimensional equations. The temporal instability of the steady solutions is analysed. It was found that the electric force enhances the growth rate and increases its corresponding maximum wavenumber.

A framework for automatically choosing the optimal parameters of finite-difference scheme in the acoustic wave modeling

An effective finite-difference (FD) scheme requires suitable FD parameters to ensure stability while having sufficient accuracy in the seismic modeling. The FD parameters such as time step, grid spacing and FD operator also affect the computational costs and storage requirements significantly. Thus, choosing the FD parameters should be the optimal trade-off between the stability, numerical accuracy and computational efficiency. However, the FD parameters usually be chosen through repeated manual tests, which is prone to unnecessary consumption. In this paper, we propose a framework for automatically choosing the FD parameters to achieve the optimal FD scheme in the acoustic wave modeling. Considering the computational efficiency, the proposed framework provides the maximum admissible time step under the stability condition. On the premise of the maximum time step, the proposed framework can find suitable parameters to ensure that the FD scheme has sufficient wavenumber bandwidth to deal with the maximum wavenumber or frequency of the wavefield. Dispersion and stability analyses prove that the FD parameters determined by our framework can effectively avoid dispersion errors while ensuring stability under the given conditions. Numerical experiments also prove the effectiveness of the framework in choosing FD parameters for the inhomogeneous velocity model. The framework can easily obtain the optimal FD parameters and can be recommended as a routine step for the FD methods.

Multiplicity for idealized rotational detonation waves

Simulations of three-dimensional rotational detonation waves are conducted to understand the mechanisms of wave bifurcation. A compressible reacting Euler solver is developed within the framework of OpenFOAM, and a fixed mass flux boundary condition is developed to avoid complex injector dynamics. Influences of inflow mass flow rates and initiations of ignition spots are studied. As the inflow mass flow rate increases, one detonation wave is maintained. Constrained by the circumference of the combustor, the maximum fill height is achieved when the maximum post-shock pressure expansion is reached. Further increasing mass flow rates does not lead to wave bifurcation or higher mean fill height. By introducing multiple ignition regions, an identical number of stable waves are ignited and maintained, which signifies that wave numbers are not uniquely determined by the inlet boundary conditions. The minimum fill height (or largest velocity deficit) owing to either the lowest mass flow rate or the maximum wave number is obtained when the pressure expansion distance is comparable to the hydrodynamic thickness. The scaling of fill height is subsequently explained through a theoretical relation based on mass conservation. It is shown that neither increasing mass flow rates nor existence of multiple waves is a sufficient condition for wave bifurcation. The fill height is intrinsically connected with wave numbers, and both cannot be predicted solely based on boundary conditions. Future work will relax some idealizations in this work to further quantify the limit for the fill height.

On the thermal instability of supercavitating liquid jet surrounded by coaxial rotary gas

Abstract Based on the jet stability theory, under the conditions of gas rotation, fluid compressibility and supercavitation, this paper gives the mathematical model describing the thermal instability of supercavitating liquid jet surrounded by a coaxial rotary gas, and the corresponding numerical method for solving the mathematical model is proposed and verified by the data in reference. Then, this paper analyzes the effects of gas–liquid temperature differences and temperature gradients on jet instability, and studies the thermal stability of supercavitating jet. The results show that the maximum disturbance growth rate, the dominant frequency and the maximum disturbance wave numbers increase linearly with the increase of gas–liquid temperature differences. The existence of temperature gradient inside the jet makes the effects of temperature differences on jet instability more obvious. The temperature gradient will inhibit the effect of supercavitation on jet instability, while gas–liquid temperature difference will promote the effect of supercavitation on jet instability.

A 3D complexity-adaptive approach to explore sparsity in elastic wave propagation

We have developed an adaptive approach for seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining the resolution and accuracy. This azimuthal complexity adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We use a generalization of this solver that can handle local-scale Cartesian models and that features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit when the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Furthermore, we evaluate maps of maximum azimuthal wavenumbers that are created to facilitate ACA. We determine how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case, ACA still reduces the overall degrees of freedom by 92% compared with a complexity-blind AxiSEM3D simulation. In comparison to the reference 3D method, we again find a close fit and a speedup of a factor of 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speedup. Thus, ACA represents a convergent, versatile, and efficient method for a variety of complex settings and scales.

On the pseudospectral method and spectral accuracy

There are numerical accuracy problems related to the implementation of sharp internal interfaces in pseudospectral and finite-difference schemes. It is common practice to classify numerical errors due to the implementation of interfaces as being to some order in a Taylor expansion. An alternative approach is to classify these errors as being to some order in a Fourier expansion. The pseudospectral method does not provide spectral accuracy in inhomogeneous media. The numerical errors for the upper half of the frequency/wavenumber spectra of the propagating fields are not related to the implementation of the derivative operators but to aliasing effects coming from the multiplication of static material-parameter fields with the dynamic propagating fields. The pseudospectral method can only provide half-spectral accuracy. The same type of spatial aliasing errors is also present for finite-difference schemes. High-order finite differences can provide the same accuracy as the pseudospectral method if the staggered finite-difference derivative operators have a negligible error at four grid points per shortest wavelength and above. Smoothing of the material-parameter field leads to additional reduction in the error-free bandwidth of the propagating fields. Assuming that there is a maximum wavenumber up to which the spectrum of the smoothed model coincides with the implementation using a properly band-limited Heaviside step function, then there exists a local critical wavenumber for the propagating field equal to one half of the maximum wavenumber for the smoothed model. Harmonic averaging of material-parameter fields also results in wavenumber spectra where there is a maximum wavenumber above which the wavenumber spectrum deviates from an implementation with a band-limited Heaviside step function. The same one-half rule is also applicable in this case.