Maximum Wavenumber Research Articles

Information content in the redshift-space galaxy power spectrum and bispectrum

We present a Fisher information study of the statistical impact of galaxy bias and selection effects on the estimation of key cosmological parameters from galaxy redshift surveys; in particular, the angular diameter distance, Hubble parameter, and linear growth rate at a given redshift, the cold dark matter density, and the tilt and running of the primordial power spectrum. The line-of-sight-dependent selection contributions we include here are known to exist in real galaxy samples. We determine the maximum wavenumber included in the analysis by requiring that the next-order corrections to the galaxy power spectrum or bispectrum, treated here at next-to-leading and leading order, respectively, produce shifts of ≲ 0.25σ on each of the six cosmological parameters. With the galaxy power spectrum alone, selection effects can deteriorate the constraints severely, especially on the linear growth rate. Adding the galaxy bispectrum helps break parameter degeneracies significantly. We find that a joint power spectrum-bispectrum analysis of a Euclid-like survey can still measure the linear growth rate to 10% precision after complete marginalization over selection bias. We also discuss systematic parameter shifts arising from ignoring selection effects and/or other bias parameters, and emphasize that it is necessary to either control selection effects at the percent level or marginalize over them. We obtain similar results for the Roman Space Telescope and HETDEX.

Prospects for detection and application of the alignment of galaxies with the large-scale velocity field

Studies of intrinsic alignment effects mostly focus on the correlations between the shapes of galaxies with each other or with the underlying density field of the large scale structure of the Universe. Lately, the correlation between the shapes of galaxies and the large-scale velocity field has been proposed as an additional probe of the large scale structure. We use a Fisher forecast to make a prediction for the detectability of this velocity-shape correlation with a combination of redshifts and shapes from the $4\mathrm{MOST}+\mathrm{LSST}$ surveys, and radial velocity reconstruction from the Simons Observatory. The signal-to-noise ratio for the velocity-shape (dipole) correlation is 23, relative to 44 for the galaxy density-shape (monopole) correlation and for a maximum wave number of $0.2\text{ }\text{ }\text{Mp}{\mathrm{c}}^{\ensuremath{-}1}$. Increasing the signal-to-noise ratio for higher values of the maximum wave numbers (respectively, 56 and 69, for a maximum wave number of $1\text{ }\text{ }\text{Mp}{\mathrm{c}}^{\ensuremath{-}1}$) indicate potential gains in the nonlinear regime. Encouraged by these predictions, we discuss two possible applications for the velocity-shape correlation. Measuring the velocity-shape correlation could improve the mitigation of selection effects induced by intrinsic alignments on galaxy clustering. We also find that velocity-shape measurements could potentially aid in determining the scale dependence of intrinsic alignments when multiple shape measurements of the same galaxies are provided.

Dissipation range of the energy spectrum in high Reynolds number turbulence

We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to $R_\lambda=650$, with excellent small-scale resolution of $k_{max}\eta \approx 6$ for all cases (and additionally at $R_\lambda=1300$ with $k_{max}\eta\approx3$), where $k_{max}$ is the maximum resolved wavenumber and $\eta$ is the Kolmogorov length scale. We find that, for a limited range of wavenumbers $k$ past the bottleneck in the range $0.1 \lesssim k\eta \lesssim0.5$, the spectra for all $R_\lambda$ display a universal stretched exponential behavior of the form $\exp(-k^{2/3})$, in rough accordance with recent theoretical predictions. The stretched exponential fit in the near dissipation range $1 \lesssim k\eta \lesssim 4$ does not possess a unique exponent, which decreases with increasing $R_\lambda$. This region can be regarded as a crossover between the stretched exponential behavior and the far dissipation range $k\eta > 6$, in which analytical arguments as well as DNS data with superfine resolution (S. Khurshid et al., Phys.~Rev.~Fluids 3, 082601, 2018) suggest a $\exp(-k)$ dependence. We remark on the connection to the multifractal model which hypothesizes a pseudo-algebraic law.

Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

Influence of solvents on the enhancement of thermophysical properties and stability of multi-walled carbon nanotubes nanofluid

Multi-walled carbon nanotubes (MWCNTs) are a contemporary class of nanoparticles that have a prominent thermal, electrical and mechanical properties. There have been numerous studies on the enhancement of thermophysical properties of nanofluids. However, there is only limited research on thermal and stability analysis of MWCNT nanofluids with various kinds of solvents or base fluids, namely propylene glycol, ethanol, ethylene glycol, polyethylene glycol, methanol and water. This paper reports the enhancement of thermophysical properties and stability of MWCNTs with six different base fluids in the presence of sodium dodecyl benzene sulfonate surfactant with a mass concentration of 0.5 wt%. Thermal and dispersion stabilities were determined using a thermogravimetric analyzer (TGA) and Zeta potential, along with a visual inspection method to evaluate the agglomeration or sedimentation of MWCNT nanoparticles over a period of one month. Ultraviolet–visible spectroscopy and Fourier transform infrared spectroscopy were utilized to identify the molecular components and light absorption of the formulated nanofluids at their maximum wavenumber (4500 cm−1) and wavelength (800 nm). In addition, thermophysical properties such as thermal conductivity, specific heat capacity, viscosity and density with a peak temperature of 200 °C were also experimentally evaluated. The TGA results illustrated that MWCNT/ethylene glycol nanofluid achieved maximum thermal stability at 140 °C and it revealed a maximum zeta potential value of −61.8 mV. Thus, ethylene glycol solution was found to be the best base liquid to homogenize with MWCNTs for acquiring an enhanced thermophysical property and a long-term stability.

Experimental and Theoretical Studies of Preferential Solvation of 4-Nitroaniline and 4-Nitroanisole in an Amino Acid Ionic Liquid with Molecular Solvents

Amino acid ionic liquids (AAILs) are a new green class of ILs. Maximum wave numbers of 4-nitroaniline and 4-nitroanisole based on the solvatochromic method were calculated in binary mixtures of tet...

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: Criterion for direct numerical simulation

In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime. To validate the performance of HGKS, the compressible isotropic turbulence with initial turbulent Mach number Mat0=0.5 and Taylor microscale Reynold number Reλ0=72 is simulated as a benchmark. With the consideration of robustness and accuracy, the WENO-Z scheme is adopted for spatial reconstruction in the current higher-order scheme. Statistical quantities are compared with the high-order compact finite difference scheme to determine the spatial and temporal criterion for DNS. According to the grid and time convergence study, it can be concluded that the minimum spatial resolution parameter κmaxη0 ≥ 2.71 and the maximum temporal resolution parameter Δtini/τ0 ≤ 27.08/1000 are adequate for HGKS to resolve the compressible isotropic turbulence, where κmax is the maximum resolved wave number, Δtini is the initial time step, η0 and τ0 are the initial Kolmogorov length scale and time scale, respectively. Guided by such criterion, the compressible isotropic turbulence from subsonic regime Mat0=0.8 to supersonic one Mat0=1.2, and the Taylor microscale Reynolds number Reλ0 ranging from 10 to 72 are simulated. With the high initial turbulent Mach number, the strong random shocklets and high expansion regions are identified, as well as the wide range of probability density function over local turbulent Mach number. All those impose great challenge for high-order schemes. In order to construct compressible large eddy simulation models at high turbulent Mach number, the ensemble budget of turbulent kinetic energy is fully analyzed. The solenoidal dissipation rate decreases with the increasing of Mat0 and Reλ0. Meanwhile, the dilational dissipation rate increases with the increasing of Mat0, which cannot be neglected for constructing supersonic turbulence model. The current work shows that HGKS provides a valid tool for the numerical and physical studies of isotropic compressible turbulence in supersonic regime, which is much less reported in the current turbulent flow study.

Wall Temperature and Suction Control of Linear Modes in Compressible Corner Flow

Linear stability behavior of self-similar streamwise corner flows is investigated under the influence of constant wall temperatures and suction rates perpendicular to each wall. For three Mach numbers, 0.1, 0.95, and 1.5, representing subsonic, transonic, and supersonic flow regimes, modes that propagate in the streamwise direction, i.e., with a wave number at the lateral boundaries, are studied first. Then, the influence of and on the stability of oblique modes with is investigated for the transonic flow. It is shown that the effect on the leading viscous mode with is the same for cooling and suction in the case of small variations in temperature and suction relative to the reference flow without control. However, the increase in stability of the inviscid corner modes depends on both the control method and the Mach number. The stability of oblique viscous modes increases as well and it is shown that at the critical point is independent of the wall temperature and the suction rate. In addition, a maximum spanwise wave number is observed for which the most critical viscous mode is still amplified.

Cosmological information in the redshift-space bispectrum

We use the Fisher-matrix formalism to investigate whether the galaxy bispectrum in redshift space, B, contains additional cosmological information with respect to the power spectrum, P. We focus on a Euclid-like survey and consider cosmological models dominated by dark energy and cold dark matter with Gaussian primordial perturbations. After discussing the phenomenology of redshift-space distortions for the bispectrum, we derive an expression for the cross-covariance between B and P at leading order in perturbation theory. Our equation generalizes previous results that did not consider binning in the orientation of wavevector triangles with respect to the line of sight. By considering Fourier modes with wavenumber |$k\lt 0.15 \, h$| Mpc−1, we find that B and P set similar constraints on the cosmological parameters. Generally, error bars moderately improve when the two probes are combined together. For instance, the joint 68.3 per cent credible region for the parameters that describe a dynamical dark-energy equation of state shrinks by a factor of 2.6 with respect to only using the power spectrum. Regrettably, this improvement is cancelled out when the clustering analysis is combined with priors based on current studies of the cosmic microwave background. In this case, combining B and P does not give any appreciable benefit other than allowing a precise determination of galaxy bias. Finally, we discuss how results depend on the binning strategy for the clustering statistics as well as on the maximum wavenumber. We also show that only considering the bispectrum monopole leads to a significant loss of information.

Weakly nonlinear instability of a Newtonian liquid jet

A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into account the liquid viscosity and the cylindrical geometry. The jet model is used to reveal the effect of both the wavenumber and the Ohnesorge number on the formation of satellite drops, which is known as a nonlinear effect. Results are found in good agreement with direct numerical simulations and forced liquid jet experiments for wavenumbers lower than a threshold value. Satellite drop formation is retarded with increasing Ohnesorge number and wavenumber, as expected by the damping and size effects of viscosity. The threshold number corresponds to the maximum wavenumber for which satellite drop formation is predicted before jet breakup, and for which volume conservation is satisfied within a certain amount. The volume conservation criterion is imposed to ensure that the conclusions inferred by our model are safe.

Reflected wave solution of Alfvén wave turbulence

It was found numerically in Galtier et al (2000 J. Plasma Phys. 63 447–88) that the evolution towards the Kolmogorov–Zakharov (KZ) wave action spectrum of weak magneto–hydrodynamic turbulence (here is the wave number component perpendicular to the external magnetic field) consists of two stages. Stage one is characterised by a wave action spectrum with a front propagating to the maximum wave number kmax in a finite time t*, arguably with as , and with a power law which is steeper than KZ, . This stage was recently studied in Bell et al (2017 J. Phys. A: Math. Theor. 50 435501) by identifying it with a self-similar solution of the second kind. In particular, a corrected value of and the structure of the spectral front were found. In the present paper, we study the second (post-t*) stage which is characterised by formation of the KZ spectrum as an inversely propagating wave, from kmax toward lower wave numbers. We identify this stage with a self-similar solution of the third kind, whose similarity coefficients are fixed by the previous (pre-t*) self-similar stage rather than the energy conservation (as in the first-kind self-similarity) or by a nonlinear eigenvalue problem (as in the second-kind self-similarity).

Optical path design of phase contrast imaging on HL-2A tokamak

A phase contrast imaging (PCI) diagnostic has recently been developed on HL-2A tokamak. It can diagnose plasma density fluctuations with maximum wave number of 15 cm−1 and wave number resolution of 2 cm−1. The time resolution reaches 2 μs. A 10.6 μm CO2 laser is expanded to a beam with a diameter of 30 mm and injected into the plasma as an incident beam, injecting into plasma. The emerging scattered and unscattered beams are contrasted by a phase plate. The ideas of optical path design are presented in this paper, together with the parameters of the main optical components. The whole optical path of PCI is not only carefully designed, but also constructed on HL-2A. First calibration results show the ability of this system to catch plasma turbulence in a wide frequency domain.

The instability of a moving interface in a narrow tapering channel of finite length

We analyse the displacement of one fluid by a second immiscible fluid through a narrow channel of finite length which connects two reservoirs. We assume that the channel width slowly decreases in the direction of flow, and that the fluids have different viscosity and density. We examine the stability of the interface and find that there are Saffman–Taylor and Rayleigh–Taylor type modes, which may dominate in the narrow and wide regions of the channel, respectively. The gradient of the pressure jump across the interface associated with the surface tension acts to stabilise the interface, and for intermediate channel widths, this effect may dominate the destabilisation associated with both the Rayleigh–Taylor and Saffman–Taylor instabilities, provided the rate of change of the channel width with distance along the channel is sufficient. We also note that the effect of the converging channel leads to instability of long-wavelength modes owing to the quasi-static acceleration of the flow through the cell: we consider cases in which this effect only occurs at much lower wavenumbers than the most unstable Saffman–Taylor and Rayleigh–Taylor modes. We show that there is a maximum wavenumber for instability, which varies with position in the channel. By integrating the growth rate of each wavenumber in time as the interface moves across the channel, we predict the mode which grows to the greatest amplitude as the interface traverses the channel.

The ion streaming effect on Weibel instability in the relativistic dense plasma

The Weibel instability plays an important role in stopping hot electrons and energy deposition mechanism in fast ignition of inertial fusion process. In this paper, the ion Weibel instability in counter propagating electron‐ion plasmas is investigate. The obtained results show that the growth rate of Weibel instability will be decreased about 40% with the anisotropy velocity as vxe = 2vze = 20; the ion density ratio, b = n0i1/n0i2, and density gradient, are increasing 50 and 90% respectively. The ion streaming in density gradient of dense plasma leads to increasing the Weibel instability growth rate and its amplification through ion streaming in the large wavenumber. The maximum unstable wavenumber has been decreased with decreasing the ion beam density ratio. For fixed ion density ratio, increasing 90% of the density gradient in the near of fuel plasma corona leads to reducing growth rate and unstable wavenumber about 43 and 42% respectively.

Dispersion characteristics of surface magnetostatic waves with dissipation

It is shown that unlike undamped waves, the dispersion characteristics of spin surface waves with dissipation have a maximum wave number at which there is a downward reversal in the dispersion curve of a wave number. This forms the upper branch of a dispersion curve with inverse dispersion and high attenuation, leading to an unclear frequency dependence of the wave vector. The lower primary dispersion branch corresponds to waves with forward dispersion, and attenuation is proportional to the small parameter of dissipation. However, the coefficient of wave attenuation grows sharply near the maximum wave number. Some angular and frequency limits of surface wave propagation change as well.

On the internal interfaces in finite-difference schemes

Implementing sharp internal interfaces in finite-difference schemes with high spatial accuracy is challenging. The propagation of fields in a locally homogeneous part of a model can be performed with spectral accuracy. The implementations of interfaces are generally considered accurate to, at best, second order. This situation can be improved by a proper band limitation of the simulation grid. Interfaces can be located anywhere on the grid; however, the fine detail information regarding the interface location must be imprinted correctly in the coarse simulation grid. This can be done by starting out with a representation of a sharp material jump in the wavenumber domain and limiting the highest wavenumber to the maximum wavenumber allowed for the simulation grid. The resulting wavenumber representation is then transformed to the space domain. An alternative procedure is to create a fine grid model that is low-pass filtered to remove wavenumbers above the maximum wavenumber allowed for the coarse simulation grid. The fine grid is thereafter sampled at the required coordinates for the coarse simulation grid. An accurate and flexible interface implementation is a requisite for reducing staircase diffractions in higher dimensional finite-difference simulations. Our strategy achieves this. The frequency content of the source must be constrained to a level in which the spatial sampling is at approximately four to five grid points per shortest wavelength. Simulation results indicate that the implementation of the interface is accurate to at least the sixth order for large contrasts. Our method can be used for all systems of partial differential equations that formally can be expressed as a material parameter times a dynamic field on one side of the equal sign and with spatial derivatives on the other side of the equal sign. For geophysical simulations, the most important cases will be the Maxwell equations and the acoustic and elastic wave equations.

Design of phase contrast imaging on the HL-2A tokamak

In this article we present the design of a phase contrast imaging (PCI) system on the HL-2A tokamak. This diagnostic is developed to infer line integrated plasma density fluctuations by measuring the phase shift of an expanded CO2 laser beam passing through magnetically confined high temperature plasmas. This system is designed to diagnose plasma density fluctuations with the maximum wavenumber of 15cm−1. The designed wavenumber resolution is 2cm−1, and the time resolution can reach 2μs. The broad kρs ranging from 0.2 to 3 makes it suitable for turbulence measurement.

Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows.

The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.

Vibrational properties of FeCoCrMoCBY bulk metallic glasses and their correlation with glass-forming ability

Here, the authors focus on the relationships between the vibrational properties and glass-forming ability (GFA) of an Fe-Co-Cr-Mo-C-B-Y alloy system. Among the alloy systems studied, the best glass former Fe41Co7Cr15Mo14C15B6Y2 bulk metallic glass (BMG) (Co7 alloy) showed the maximum vibrational wavenumber of acoustic and optical modes. The origin of the excellent GFA of the Co7 alloy was discussed in terms of the atomic cluster size and bonding energy.

Far-forward collective scattering measurements by FIR polarimeter-interferometer on J-TEXT tokamak.

The multi-channel three-wave polarimeter-interferometer system on J-TEXT tokamak has been exploited to measure far-forward collective scattering from electron density fluctuations. The diagnostic utilizes far infrared lasers operated at 432 μm with 17-channel vertical chords (3 cm chord spacing), covering the entire cross section of plasma. Scattering laser power is measured using a high-sensitivity Schottky planar diode mixer which can also detect polarimetric and interferometric phase simultaneously. The system provides a line-integrated measurement of density fluctuations with maximum measurable wave number: k⊥max ≤ 2 cm-1 and time response up to 350 kHz. Feasibility of the diagnostic has been tested, showing higher sensitivity to detect fluctuation than interferometric measurement. Capability of providing spatial-resolved information of fluctuation has also been demonstrated in preliminary experimental applications.