Linear Perturbation Theory Research Articles

Quasi-harmonic approximation of lattice dynamics and thermodynamic properties of half Heusler ScXSb (x = Ni, Pd, Pt) from first principles

We report the lattice dynamics and thermodynamic properties of ScXSb (X = Ni, Pd, Pt) half Heusler compounds. Calculations for the structural and electronic properties were performed based on the Perdew–Burke–Ernzerhof–generalized gradient approximation density functional theory. We used the linear response density functional perturbation theory for computations addressing the elastic property, lattice dynamics, and thermodynamic properties. Results for the equilibrium lattice parameter are in reasonable agreement with reports in the existing literature. The electronic band structure behavior and bandgap agree with relevant results in research. The elastic parameters and phonon dispersions establish the mechanical stability of the compounds. Deductions from the tone of the mode-Grüneisen parameter, specific heat capacity at constant pressure and volume, and thermal expansion favor ScNiSb as the most promising material for thermal conductivity at high temperatures in the three compounds studied. The three compounds obey the Dulong–Petit law at high temperatures. Results for the Dulong–Petit limit is consistent with expectations for solid materials at high temperatures.

The Lynden-Bell bar formation mechanism in simple and realistic galactic models

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

Analytical and numerical treatment of perturbed black holes in horizon-penetrating coordinates

The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio. To facilitate a comparison between the two we derive several results of linear perturbation theory in coordinates which may be adopted in numerical work. Specifically, our results are derived in Kerr-Schild coordinates adjusted by a general height function. In the first part of the paper we address the questions: for an initial configuration of a massless scalar field, what is the amplitude of the excited quasinormal mode (QNM) for any observer outside outside the event horizon, and furthermore what is the resulting tail contribution? This is done by constructing the full Green's function for the problem with exact solutions of the confluent Heun equation satisfying appropriate boundary conditions. In the second part of the paper, we detail new developments to our pseudospectral numerical relativity code bamps to handle scalar fields. In the linear regime we employ precisely the Kerr-Schild coordinates treated by our previous analysis. In particular, we evolve pure QNM type initial data along with several other types of initial data and report on the presence of overtone modes in the signal.

Novel configurations of VN4 and VN4H defects in diamond platelets: Structure, energetics and vibrational properties

Atomic structure and lattice dynamics properties of the novel configurations of VN4 and VN4H defects in combination with the {001} platelet structure in diamond are investigated by first-principles density functional techniques. We find that incorporation of B centers (VN4) in the platelet structure substantially reduce the formation energy of B centers by ~0.45 eV for both structure models, suggesting that they may tend to develop preferentially together with platelets. Moreover, our results provide evidence that VN4 centers in the platelet might be effective sinks for atomic hydrogen in diamond. Vibrational properties of the defective structures are computed by using the linear response density functional perturbation theory (DFPT). NH stretching modes for VN4H centers appear around 3221 (model 1) and 3095 (model 2) cm−1, suggesting that the experimental vibrational modes of 3085.4, 3107 and 3237 cm−1 observed in natural IaA/B diamonds could be attributed to the VN4H defects. Moreover, we observed that incorporation of VN4H centers quenches the platelet IR absorption, which is unconventional but important in understanding the platelet degradation phenomenon. Our calculations shed light on possible novel configurations of VN4H centers and platelets, which can be extrapolated to VN4H2 centers as well as to a more hybrid platelet structure, and elucidate the role of nitrogen and hydrogen in the development of platelet defects in diamond.

Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation

Context.Large-scale Rossby waves have recently been discovered based on measurements of horizontal surface and near-surface solar flows.Aims.We are interested in understanding why it is only equatorial modes that are observed and in modelling the radial structure of the observed modes. To this aim, we have characterised the radial eigenfunctions ofrmodes for slowly rotating polytropes in uniform rotation.Methods.We followed Provost et al. (1981, A&A, 94, 126) and considered a linear perturbation theory to describe quasi-toroidal stellar adiabatic oscillations in the inviscid case. We used perturbation theory to write the solutions to the fourth order in the rotational frequency of the star. We numerically solved the eigenvalue problem, concentrating on the type of behaviour exhibited where the stratification is nearly adiabatic.Results.We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density,rmodes can only exist forℓ = mspherical harmonics in the inviscid case and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification, the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales asrm. For allrmodes, except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance.Conclusions.The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the need for both horizontal and radial force balance. In the absence of super- or sub-adiabatic stratification and viscosity, both the horizontal and radial parts of the force balance independently determine the pressure perturbation. The only quasi-toroidal cases in which these constraints on the pressure perturbation are consistent are the special cases whereℓ = mand the horizontal displacement scales withrm.

Density weighted angular redshift fluctuations: a new cosmological observable

ABSTRACT We propose the use of angular fluctuations in the galaxy redshift field as a new way to extract cosmological information in the Universe. This new probe $\delta z (\hat{\mathbf {n}})$ consists of the statistics of sky maps built by projecting redshifts under a Gaussian window of width σz centred upon a redshift zobs, and weighted by the galaxy density field. We compute the angular power spectrum of the $\delta z (\hat{\mathbf {n}})$ field in both numerical simulations and in linear perturbation theory. From these, we find that the $\delta z (\hat{\mathbf {n}})$ field (i) is sensitive to the underlying density and peculiar velocity fields; (ii) is highly correlated, at the $\gtrsim 60\, {{\ \rm per\ cent}}$ level, to the line-of-sight projected peculiar velocity field; (iii) for narrow windows (σz < 0.03), it is almost completely uncorrelated to the projected galaxy angular density field under the same redshift window; and (iv) it is largely unaffected by multiplicative and additive systematic errors on the observed number of galaxies that are redshift-independent over ∼σz. We conclude that $\delta z (\hat{\mathbf {n}})$ is a simple and robust tomographic measure of the cosmic density and velocity fields, complementary to angular clustering, that will contribute to more complete exploitations of current and upcoming galaxy redshift surveys.

Planet–Disk Interaction in Disks with Cooling: Basic Theory

Abstract Gravitational coupling between young planets and their parent disks is often explored using numerical simulations, which typically treat the disk thermodynamics in a highly simplified manner. In particular, many studies adopt the locally isothermal approximation, in which the disk temperature is a fixed function of the stellocentric distance. We explore the dynamics of planet-driven density waves in disks with more general thermodynamics, in which the temperature is relaxed toward an equilibrium profile on a finite cooling timescale t c. We use both linear perturbation theory and direct numerical simulations to examine the global structure of density waves launched by planets in such disks. A key diagnostic used in this study is the behavior of the wave angular momentum flux (AMF), which directly determines the evolution of the underlying disk. The AMF of free waves is constant for slowly cooling (adiabatic) disks but scales with the disk temperature for rapidly cooling (and locally isothermal) disks. However, cooling must be extremely fast, with β = Ωt c ≲ 10−3 for the locally isothermal approximation to provide a good description of density wave dynamics in the linear regime (relaxing to β ≲ 10−2 when nonlinear effects are important). For intermediate cooling timescales, density waves are subject to a strong linear damping. This modifies the appearance of planet-driven spiral arms and the characteristics of axisymmetric structures produced by massive planets: in disks with β ≈ 0.1–1, a near-thermal mass planet opens only a single wide gap around its orbit, in contrast to the several narrow gaps produced when cooling is either faster or slower.

Origin of giant stellar clumps in high-redshift galaxies

ABSTRACT We examine the nature of kpc-scale clumps seen in high-redshift galaxies using a suite of cosmological simulations of galaxy formation. We identify rest-frame UV clumps in mock HST images smoothed to 500 pc resolution, and compare them with the intrinsic 3D clumps of young stars identified in the simulations with 100 pc resolution. According to this comparison for the progenitors of Milky Way-sized galaxies probed by our simulations, we expect that the stellar masses of the observed clumps are overestimated by as much as an order of magnitude, and that the sizes of these clumps are also overestimated by factor of several, due to a combination of spatial resolution and projection. The masses of young stars contributing most of the UV emission can also be overestimated by factor of a few. We find that most clumps of young stars present in a simulation at one time dissolve on a timescale shorter than ∼150 Myr. Some clumps with dense cores can last longer but eventually disperse. Most of the clumps are not bound structures, with virial parameter αvir > 1. We find similar results for clumps identified in mock maps of H α emission measure. We examine the predictions for effective clump sizes from the linear theory of gravitational perturbations and conclude that they are inconsistent with being formed by global disc instabilities. Instead, the observed clumps represent random projections of multiple compact star-forming regions.

Instability of magneto hydro dynamics Couette flow for electrically conducting fluid through porous media

In this article, the hydrodynamic stability of the Couette flow of an electrically conducting fluid flowing in a parallel-plate channel with a normal magnetic field is investigated through a porous medium. The transport phenomena in the porous medium have been of enduring interest from the last few decades. The linear perturbation theory of hydrodynamic stability along with the presumption of low magnetic Reynolds number is applied to the governing equations to derive the governing magnetohydrodynamic stability equation. A Chebyshev collocation method is operated to numerically elucidate the magnetohydrodynamic stability equation. A linearized velocity solution for developing flow is used in the stability calculations. The numerically determined neutral stability results for the fully developed Couette flow are in excellent agreement with those of the analytical solution. The results presented here for Hartmann flow are believed to be more accurate owing to the more exact nature of the numerical solution.

Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance

Local structure can have important effects on luminosity distance observations, which could for example affect the local estimation of the Hubble constant based on low red-shift type Ia supernovae. Using a spherically symmetric exact solution of the Eistein's equations and a more accurate expansion of the solution of the geodesic equations, we improve the low red-shift expansion of the monopole of the luminosity distance in terms of the curvature function. Based on this we derive the coordinate independent low red-shift expansion of the monopole of the luminosity distance in terms of the monopole of the density contrast. The advantage of this approach is that it relates the luminosity distance directly to density observations, without any dependency on the radial coordinate choice. We compare our formulae to numerical calculations, and find that the formula in terms of the density contrast is in good agreement with the numerical calculations, in the non linear regime is more accurate than the results obtained using linear perturbation theory, especially in the regime of large Laplacian of the perturbations, and is also more accurate than the formula in terms of the curvature function.

Retrieval of Aerosol Optical Thickness in the Arctic Snow-Covered Regions Using Passive Remote Sensing: Impact of Aerosol Typing and Surface Reflection Model

Currently, no aerosol optical thickness (AOT) data set over the Arctic snow/ice-covered regions derived from space-borne passive remote sensing is available. The challenge is to develop an accurate and robust technique to derive AOT above highly variable and bright snow/ice surfaces. To extend data coverage of the eXtensible Bremen Aerosol/cloud and surfacE Retrieval (XBAER) AOT data product in the future, we propose a new algorithm for the retrieval of AOT and surface properties over snow/ice simultaneously. The algorithm utilizes the linear perturbation theory and does not use any simplified atmospheric correction techniques. Key issues like the selection of a proper aerosol type and optimal surface parameterization method for the retrieval of AOT over the Arctic have been investigated. The aerosol type is investigated using the aerosol climatology microphysical properties derived from four Aerosol Robotic Network (AERONET) sites (Barrow, Hornsund, Kangerlussuaq, and Tiksi). The three-parametric Ross-Li linear kernel model is used to describe the snow bidirectional reflectance distribution function (BRDF). The a priori knowledge of wavelength-dependent features of the coefficients in the Ross-Li linear kernel model is derived from Polarization and Directionality of the Earth's Reflectances (POLDER) measurements over the Arctic and utilized as constraints in the retrieval. The studies show that the combination of Ross-Li surface model and weakly absorbing aerosol parameterization provides an optimal way to derive AOT over the Arctic snow/ice-covered regions from passive remote sensing observations. The retrieved AOTs using POLDER show good agreement with AERONET observations.

XAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.

A comparative study of reactivity feedback effects for a HALEU molybdenum-producing PHWR fuel bundle and a standard PHWR fuel bundle

A new 37-element PHWR fuel bundle, which can produce Molybdenum-99 (99Mo) when irradiated inside a PHWR, has recently been proposed (Nichita and Haroon, 2016). The modified 37-element fuel bundle uses High-Assay Low-Enriched Uranium (HALEU) at the periphery of fuel pellets and has been shown to be neutronically and thermal-hydraulically equivalent to the standard CANDU bundle for steady-state conditions.The first step towards comparing the behavior of the molybdenum-producing bundle (MPB) and the standard CANDU bundle (SCB) under transient conditions is a comparison of their reactivity feedback effects. This study calculates and compares the reactivity effects of the two bundles over a wide range of perturbations in coolant density, moderator density, coolant temperature, moderator temperature, fuel temperature and moderator poison concentration (boron and gadolinium), for burnups ranging from zero to 7500 MWd/t(U) (discharge burnup). An analysis of reactivity coefficients based on linear perturbation theory is also included.The study concludes that the reactivity effects of the MPB are very similar (within 1 mk) to those of the SCB over a wide range of perturbations at all burnups (zero to discharge burnup).

Analyzing Magnetically Induced Currents in Molecular Systems Using Current-Density-Functional Theory

A suite of tools for the analysis of magnetically induced currents is introduced. These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the high-field regime, which is inaccessible to such methods. A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule and the ring, bowl and cage isomers of the C_20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para- to dia-magnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear-response methods.

Local stability analysis of interface region of astrophysical viscous shear flows with a gradual velocity gradient

In this paper, we extend the stability analysis of cold sharp shear flows to warm astrophysical cases with, inevitable, gradual velocity gradient in the interface region in the presence of viscosity effect. Using linear perturbation theory as well as the local approximation method, the instability growth rate of the excited electromagnetic modes has been investigated for the relativistic and non-relativistic cases of solar wind interacting with interstellar plasma medium. Results show that astrophysical shear systems with a small velocity gradient in the transition region are more stable rather than larger ones. Moreover, dependent on the viscosity coefficient value, the viscosity effects could have a positive role on the instability growth rate of the system in some range of initial bulk velocity, while it plays a destructive role in other velocity ranges.

Simulation of the loss-cone instability in spherical systems – I. Dominating harmonic potential

ABSTRACT A new so-called ‘gravitational loss-cone instability’ in stellar systems has recently been investigated theoretically in the framework of linear perturbation theory and proved to be potentially important in understanding the physical processes in centres of galaxies, star clusters, and the Oort Cloud. Using N-body simulations of a toy model, we confirm previous findings for the dominating harmonic potential and go beyond the linear theory. Unlike the well-known instabilities, the new one shows no notable change in the spherical geometry of the cluster, but it significantly accelerates the speed of diffusion of particles in phase space leading to an early instability saturation.

Asteroseismic Signature of a Large Active Region

Axisymmetric magnetic activity on the Sun and Sun-like stars increases the frequencies of the modes of acoustic oscillation. However, it is unclear how a corotating patch of activity affects the oscillations, since such a perturbation is unsteady in the frame of the observer. In this paper we qualitatively describe the asteroseismic signature of a large active region in the power spectrum of the dipole and quadrupole p modes. In the corotating frame of the active region, the perturbations due to (differential) rotation and the active region completely lift the $(2\ell + 1)$-fold azimuthal degeneracy of the frequency spectrum of modes with harmonic degree $\ell$. In the frame of the observer, the unsteady nature of the perturbation leads to the appearance of $(2\ell+1)^2$ peaks in the power spectrum of a multiplet. These peaks blend into each other to form asymmetric line profiles. In the limit of a small active region, we approximate the power spectrum of a multiplet in terms of $2\times(2\ell+1)$ peaks, whose amplitudes and frequencies depend on the latitude of the active region and the inclination angle of the star's rotation axis. In order to check the results and to explore the nonlinear regime, we also perform numerical simulations using the 3D time-domain pseudo-spectral linear pulsation code GLASS.

Two-field mimetic gravity revisited and Hamiltonian analysis

We revisit the two-field mimetic gravity model with shift symmetries recently proposed in the literature, especially the problems of degrees of freedom and stabilities. We first study the model at the linear cosmological perturbation level by quadratic Lagrangian and Hamiltonian formulations. We show that there are actually two (instead of one) scalar degrees of freedom in this model in addition to two tensor modes. We then push on the study to the full non-linear level in terms of the Hamiltonian analysis, and confirm our result from the linear perturbation theory. We also consider the case where the kinetic terms of the two mimetic scalar fields have opposite signs in the constraint equation. We point out that in this case the model always suffers from the ghost instability problem.

On response spectra and Kramers-Kronig relations in superposition rheometry

In a recent paper, we derived expressions for determining the rate-dependent response spectra directly from parallel superposition rheometry data for the case of a certain Lodge-type integral constitutive model. It was shown that, within the confines of linear Yamamoto perturbation theory, the corresponding parallel superposition moduli satisfy the classical Kramers-Kronig relations. Special bases were presented to convert parallel superposition moduli to orthogonal superposition moduli. In the current paper, we obtain similar results for the integral models of Wagner I and, more generally, K-BKZ. These results facilitate the physical interpretation of parallel superposition moduli and direct model-based comparison of parallel and orthogonal superposition moduli in the study of weak nonlinear response.

Towards a viable effective field theory of mimetic gravity

We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the FLRW background for this kind of models. Restricting to homogeneous scalar field configurations in the action, we derive degeneracy conditions to obtain an effective field theory with three degrees of freedom. However, performing the Hamiltonian analysis for a generic scalar field we show that there are in general four or more degrees of freedom. The discrepancy is resolved because, for a homogeneous scalar field profile, ∂iφ≈ 0, the Dirac matrix becomes singular, resulting in further constraints, which reduces the number of degrees of freedom to three. Similarly, in linear perturbation theory the additional scalar degree of freedom can only be seen by considering a non-homogeneous background profile of the scalar field. Therefore, restricting to homogeneous scalar fields these kinds of models provide viable explicitly Lorentz violating effective field theories of mimetic gravity.