Quasi-linear Regime Research Articles

Axion string source modeling

In this paper, we investigate the effect of the string radius of curvature RGaussian on the massive and massless scalar radiation emitted from collisions of traveling waves propagating along an axion (global cosmic) string. We construct initial conditions for two colliding Gaussians and perform parameter scans over their amplitude A and standard deviation σd. We show that these collisions emit isotropic bursts of massless radiation and that the energy emitted via this channel obeys a power law ∼∝Aγ, where the coefficient γ depends on the regime of A/δ and δ is the string width. Massive radiation is exponentially suppressed ∼∝e−ζRGaussian in the quasilinear regime σd≫δ and exhibits power-law decay ∼∝RGaussian−γ′ in the nonlinear regime σd≲2δ, with different ζ and γ′ in different regimes of RGaussian. In this nonlinear regime, massive particle radiation can comprise up to 50% of the total energy emitted. Drawing on a known parallel between axion radiation from global strings and gravitational radiation from Abelian-Higgs strings, this suggests that massive particle radiation may become significant with respect to the massless (gravitational) channel for such nonlinear burst signals. For all configurations studied, we obtain a spectral index q≳1 for the axion radiation, where q→1 as A increases; i.e., a higher proportion of radiation is emitted in high-frequency modes. Published by the American Physical Society 2024

Enhanced Efficiency of Solar Wind Electron Interaction with Whistlers Caused by Switchback-related Magnetic Dips

Through test particle simulations based on solar wind observations by the Parker Solar Probe (PSP) mission, we demonstrate that a magnetic gradient can significantly enhance the efficiency of scattering and energization of the strahl electrons by quasi-parallel whistlers, through the phase trapping effect due to the gyrosurfing mechanism. We identify quasi-linear and nonlinear regimes of these interactions for different combinations of wave amplitude (B w /B 0) and the strength of the magnetic field gradient with magnetic field depletion level (B h /B 0) as a proxy. Nonlinear effects are observed for B w /B 0 ≳ 10−3 and B h /B 0 ≳ 0.1. We estimated the extending of the resonant energy range due to the wave and the magnetic field gradient interplay and demonstrated that these mechanisms result in the broadening of the strahl electron pitch-angle distribution typically observed in situ. The combination of parallel whistlers collocated with a magnetic gradient is frequently observed by PSP in magnetic dips at the edges of magnetic switchbacks. Our results indicate that these mechanisms may be highly relevant for pitch-angle scattering of the strahl electrons and regulating the heat flux near the Sun at heliocentric distances of 30–45 R S . Specifically, core and halo electrons may experience a 10% increase in their initial energy, and the majority of strahl electrons may be scattered (by an average of 30°) into the hot and trapped plasma inside magnetic dips.

Temporal Talbot effect: from a quasi-linear Talbot carpet to soliton crystals and Talbot solitons.

The temporal Talbot effect refers to the periodic self-imaging of pulse trains in optical fibers. The connection between the linear and nonlinear temporal Talbot effect is still not fully understood. To address this challenge, we use the soliton radiation beat analysis (SRBA) and numerically investigate the evolution of a phase-modulated continuous-wave laser input in a passive single-mode fiber. We identify three input-power-dependent regimes and their Talbot carpets: the quasi-linear regime for low input powers, the intermediate one, and separated Talbot solitons for higher powers. We show that the intermediate regime hosts soliton crystals rather than rogue waves, as reported in the literature. The Talbot soliton beating can be used for pulse repetition-rate multiplication in the nonlinear regime. We also show two types of solitons involved: some encoded in the whole frequency comb, and the individual solitons carried only by particular comb lines.

A theoretical view of the T-web statistical description of the cosmic web

Context. The objective classification of the cosmic web into different environments is an important aspect of large-scale structure studies, as it can be used as a tool to study the formation of structures (halos and galaxies) in mode detail, and it forms a link between their properties and the large-scale environment; these different environments also offer another class of objects whose statistics contain cosmological information. Aims. In this paper, we present an analytical framework to compute the probability of the different environments in the cosmic web based on the so-called T-web formalism, which classifies structures into four different classes (voids, walls, filaments, and knots) based on the eigenvalues of the Hessian of the gravitational potential, often called the tidal tensor. Methods. Our classification method relies on studying whether the eigenvalues of this Hessian matrix are above or below a given threshold and thus requires knowledge of the joint probability distribution of those eigenvalues. We performed a change of variables in terms of rotational invariants, which are polynomials of the field variables and minimally correlated. We studied the distribution of those variables in the linear and quasi-linear regimes with the help of a so-called Gram-Charlier expansion, using tree-order Eulerian perturbation theory to compute the Gram-Charlier coefficients. This expansion then allowed us to predict the probability of the four different environments as a function of the chosen threshold and at a given smoothing scale and redshift for the density field. We checked the validity regime of our predictions by comparing those predictions to measurements made in the N-body Quijote simulations. Results. Working with fields normalised by their linear variance, we find that scaling the threshold value with the non-linear amplitude of fluctuations allows us to capture almost the entire redshift evolution of the probabilities of the four environments, even if we assume that the density field is Gaussian (corresponding to the linear regime of structure formation). We also show that adding mild non-Gaussian corrections with the help of a Gram-Charlier expansion – hence introducing corrections that depend on third-order cumulants of the field – provides even greater accuracy, allowing us to obtain very precise predictions for cosmic web abundances up to scales of as small as ∼5 Mpc h−1 and redshifts down to z ∼ 0.

Breakdown of Quasilinear Theory in the Tokamak Edge.

In the edge of an L-mode tokamak plasma, particle transport and ion energy transport are shown to follow a strong microturbulence (SMT) scaling, whereas in the plasma core the transport is shown to follow quasilinear turbulence scaling. The dependence of diffusivity on potential fluctuation amplitude is linear in the SMT regime, and quadratic in the quasilinear regime. The transition to strong microturbulence results from larger E×B drift velocities in the edge compared to the plasma core. At these larger velocities, ions traverse the spatially correlated range faster than the stochastic evolution of the electric potential. Hence, these particles do not experience a time-stochastic field as required by the quasilinear approximation. Instead, scattering of particles in the SMT regime is caused by spatial stochasticity. In contrast, electron energy transport remains quasilinear due to decorrelations caused by collisions and fast parallel motion. Improved understanding of transport beyond quasilinear theory opens the path to more accurate modeling of transport in the tokamak plasma edge.

Crossing the Frontier of Validity of the Material Time Approach in the Aging of a Molecular Glass.

We studied the physical aging of glycerol in response to upward temperature steps of amplitude ranging from 0.3 to 18 K. This was done using a specially designed experimental setup allowing quick heating of a liquid film while measuring the evolution of its dielectric properties. Despite the nonlinear evolution of these observables for large steps, a fictive temperature could be obtained. In the case of moderate step amplitudes, we checked that the material time approach in its simplest form, the single parameter aging (SPA), applies well. The memory kernel extracted from the quasi-linear regime was used to test its frontiers of validity for significant step amplitudes. We showed that the observations deviate from the prediction of the material time framework and of SPA simultaneously. As these approaches link aging to equilibrium dynamics, our results help set the bounds beyond which new theoretical arguments are needed.

Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation

We obtain probabilistic local well-posedness in quasilinear regimes for the Schrödinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which is due to the high-low-low nonlinear interactions. The proof is an adaptation of the method of Bringmann on the derivative nonlinear wave equation [6] to Schrödinger-type equations. In addition, we discuss ill-posedness results for this equation.

Post-blowup dynamics for the nonlinear Schrödinger equation

In this work, we present a systematic numerical study of the post-blowup dynamics of singular solutions of the 1D focusing critical NLS equation in the framework of a nonlinear damped perturbation. This study shows that initially, the post-blowup is described by the adiabatic approximation, in which the collapsing core approaches a universal profile and the solution width is governed by a system of ODEs (a reduced system). After that, a non-adiabatic regime is observed soon after the maximum of the solution, in which our direct numerical simulations show a clear deviation from the dynamics based on the reduced system. Our study suggests that such a non-adiabatic regime is caused by the increasing influx of mass into the collapsing core of the solution, which is not considered in the derivation of the reduced system. Also, adiabatic theoretical predictions related to the wave maximum and wave dissipation are compared with our numerical simulations. At the end of the post-collapse, the numerical simulations reveal a dominant quasi-linear regime caused by the rapid defocusing process. The collapsing core approaches the universal profile, after removing some oscillations resulting from interference with the tail. Finally, our numerical study suggests that in the limit of vanishing dissipation and, a free-space domain, the critical mass is radiated to infinity instantly at collapse time.

Effective field theory of intrinsic alignments at one loop order: a comparison to dark matter simulations

We test the regime of validity of the effective field theory (EFT) of intrinsic alignments (IA) at the one-loop level by comparing with 3D halo shape statistics in N-body simulations. This model is based on the effective field theory of large-scale structure (EFT of LSS) and thus a theoretically well-motivated extension of the familiar non-linear alignment (NLA) model and the tidal-alignment-tidal-torquing (TATT) model. It contains a total of 8 free bias parameters. Specifically, we measure the dark matter halo shape-shape multipoles P EE (0) (k), P EE (2) (k), P BB (0) (k), P BB (2) (k) as well as the matter-shape multipoles P δE (0) (k), P δE (2) (k) from the simulations and perform a joint fit to determine the largest wavenumber k max up to which the theory predictions from the EFT of IA are consistent with the measurements. We find that the EFT of IA is able to describe intrinsic alignments of dark matter halos up to k max = 0.30 h/Mpc at z = 0. This demonstrates a clear improvement over other existing alignment models like NLA and TATT, which are only accurate up to k max = 0.05 h/Mpc. We examine the posterior distributions of the higher-order bias parameters, and show that their inclusion is necessary to describe intrinsic alignments in the quasi-linear regime. Further, the EFT of IA is able to accurately describe the auto-spectrum of intrinsic alignment B-modes, in contrast to the other alignment models considered.

Neoclassical toroidal plasma viscosity in bounce-transit and drift resonance regimes in tokamaks

Neoclassical toroidal plasma viscosity in the bounce-transit and drift resonance regimes is calculated using a version of the drift kinetic equation that encompasses the physics of the nonlinear trapping and quasilinear plateau regimes in tokamaks. It is demonstrated that the mirror-force like term controls the transition between these two regimes. When the effective collision frequency is larger than the mirroring or the nonlinear bounce frequency, the quasilinear regime prevails; otherwise, the nonlinear trapping regime reigns. The demonstration is accomplished by using the Eulerian approach and is beyond the grasp of the method of the integration along the unperturbed orbit in solving the drift kinetic equation. The neoclassical toroidal plasma viscosity in the quasilinear plateau regime is calculated. Approximate analytic expressions for the neoclassical toroidal plasma viscosity that include the asymptotic limits of the nonlinear trapping and quasilinear regimes are presented to facilitate thermal and energetic alpha particle transport modeling in tokamaks.

Cosmic filament spin from dark matter vortices

The recent observational evidence for cosmic filament spin on megaparsec scales Wang et al. (2021) [41] demands an explanation in the physics of dark matter. Conventional collisionless cold particle dark matter is conjectured to generate cosmic filament spin through tidal torquing, but this explanation requires extrapolating from the quasi-linear regime to the non-linear regime. Meanwhile no alternative explanation exists in the context of ultra-light (e.g., axion) dark matter, and indeed these models would naively predict zero spin for cosmic filaments. In this Letter we study cosmic filament spin in theories of ultra-light dark matter, such as ultra-light axions, and bosonic and fermionic condensates, such as superfluids and superconductors. These models are distinguished from conventional particle dark matter models by the possibility of dark matter vortices. We take a model agnostic approach, and demonstrate that a collection of dark vortices can explain the data reported in Wang et al. Modeling a collection of vortices with a simple two-parameter analytic model, corresponding to an averaging of the velocity field, we find an excellent fit to the data. We perform a Markov Chain Monte Carlo analysis and find constraints on the number of vortices, the dark matter mass, and the radius of the inner core region where the vortices are distributed, in order for ultra-light dark matter to explain spinning cosmic filaments.

Grid-based calculations of redshift-space matter fluctuations from perturbation theory: UV sensitivity and convergence at the field level

Perturbation theory (PT) has been used to interpret the observed nonlinear large-scale structure statistics at the quasi-linear regime. To facilitate the PT-based analysis, we have presented the GridSPT algorithm, a grid-based method to compute the nonlinear density and velocity fields in standard perturbation theory (SPT) from a given linear power spectrum. Here, we further put forward the approach by taking the redshift-space distortions into account. With the new implementation, we have, for the first time, generated the redshift-space density field to the fifth order and computed the next-to-next-to-leading order (2 loop) power spectrum and the next-to-leading order (1 loop) bispectrum of matter clustering in redshift space. By comparing the result with corresponding analytical SPT calculation and $N$-body simulations, we find that the SPT calculation (A) suffers much more from the UV sensitivity due to the higher-derivative operators and (B) deviates from the $N$-body results from the Fourier wavenumber smaller than real space $k_{\rm max}$. Finally, we have shown that while Pad\'e approximation removes spurious features in morphology, it does not improve the modeling of power spectrum and bispectrum.

Measurement of the Spectral Efficiency of a Heterogeneous Network Architecture of the NG-PON Type for a Quasilinear Propagation Regime.

The objective of future optical fiber networks is to provide an efficient infrastructure capable of supporting an increasing and variable number of data traffic generated by the diversification of applications with different speed requirements that the current legacy Line Speed networks Single Line Rate (SLR), with predefined modulation formats, cannot supply, because they do not offer enough flexibility to meet the requirements of the demands with such a wide range of granularities. Therefore, next-generation optical networks will be highly heterogeneous in nature, incorporating mixed modulation formats and Mixed Line Rates (MLR). In this work, an analysis of the measurement of the spectral efficiency of a heterogeneous network architecture of the next-generation passive optical network (NG-PON) type is reported for a quasilinear propagation regime through the use of the equation adapted from Shannon’s information theory and developed by the group from the GNTT Research of the University of Cauca, where it was found that it is better to transmit channels of 10 Gbps and 40 Gbps with robust modulations in MLR networks to make an improvement in the spectral efficiency of the network, achieving the same amount of information in a smaller bandwidth or more information in the same bandwidth.

Solar Wind Magnetic Field Correlation Length: Correlation Functions versus Cross-field Displacement Diffusivity Test

Abstract The estimate of the solar wind magnetic fields’ parallel correlation length, λ, be it from the measured fields’ correlation functions or their spectral power at “zero” frequency, have long pointed toward short values on the order of 0.01 au. Evaluation of the mean cross-field displacements (CFDs), however, fails to show the decorrelation and resulting diffusion at the expected scales, pointing instead toward λ values on the order of 0.1 au or more. In an effort to understand this “order-of-magnitude” discrepancy and reconcile the approaches using correlation functions and the CFD diffusivity test, both approaches are applied here, with renewed attention to the “details” as well as the broader sense of the calculations, to a large, 20 yr long set of magnetic field and flow data from the ACE spacecraft. It is found that solar wind intervals too short relative to λ are a likely reason for some underestimate through the correlation-function approach, causing a premature drop of the correlation functions. Once converged to their long-time limit, however, the correlation functions produce magnetic field correlation lengths very much consistent with the magnetic-field-line (MFL) correlation lengths of the diffusivity test, with nearly matching distributions of the correlation lengths corrected by the proper ratio of their theoretical estimates. The fields’ correlation lengths mostly range from 0.03 to 0.08 au, and the MFL correlation lengths from 0.04 to 0.3 au, with peaks at 0.075 and 0.15 au, likely due to nonlinear and quasilinear regimes of MFL wandering. As for the power-at-zero-frequency approach, it is doomed by the solar rotation.

Detectability of the gravitational redshift effect from the asymmetric galaxy clustering

ABSTRACT It has been recently recognized that the observational relativistic effects, mainly arising from the light propagation in an inhomogeneous universe, induce the dipole asymmetry in the cross-correlation function of galaxies. In particular, the dipole asymmetry at small scales is shown to be dominated by the gravitational redshift effects. In this paper, we exploit a simple analytical description for the dipole asymmetry in the cross-correlation function valid at quasi-linear regime. In contrast to the previous model, a new prescription involves only 1D integrals, providing a faster way to reproduce the results obtained by Saga et al. Using the analytical model, we discuss the detectability of the dipole signal induced by the gravitational redshift effect from upcoming galaxy surveys. The gravitational redshift effect at small scales enhances the signal-to-noise ratio (S/N) of the dipole, and in most of the cases considered, the S/N is found to reach a maximum at z ≈ 0.5. We show that current and future surveys such as DESI and SKA provide an idealistic data set, giving a large S/N of 10–20. Two potential systematics arising from off-centred galaxies are also discussed (transverse Doppler effect and diminution of the gravitational redshift effect), and their impacts are found to be mitigated by a partial cancellation between two competitive effects. Thus, the detection of the dipole signal at small scales is directly linked to the gravitational redshift effect, and should provide an alternative route to test gravity.

The mass and galaxy distribution around SZ-selected clusters

ABSTRACT We present measurements of the radial profiles of the mass and galaxy number density around Sunyaev–Zel’dovich (SZ)-selected clusters using both weak lensing and galaxy counts. The clusters are selected from the Atacama Cosmology Telescope Data Release 5 and the galaxies from the Dark Energy Survey Year 3 data set. With signal-to-noise ratio of 62 (45) for galaxy (weak lensing) profiles over scales of about 0.2–20 h−1 Mpc, these are the highest precision measurements for SZ-selected clusters to date. Because SZ selection closely approximates mass selection, these measurements enable several tests of theoretical models of the mass and light distribution around clusters. Our main findings are: (1) The splashback feature is detected at a consistent location in both the mass and galaxy profiles and its location is consistent with predictions of cold dark matter N-body simulations. (2) The full mass profile is also consistent with the simulations. (3) The shapes of the galaxy and lensing profiles are remarkably similar for our sample over the entire range of scales, from well inside the cluster halo to the quasilinear regime. We measure the dependence of the profile shapes on the galaxy sample, redshift, and cluster mass. We extend the Diemer & Kravtsov model for the cluster profiles to the linear regime using perturbation theory and show that it provides a good match to the measured profiles. We also compare the measured profiles to predictions of the standard halo model and simulations that include hydrodynamics. Applications of these results to cluster mass estimation, cosmology, and astrophysics are discussed.

Morphology of weak lensing convergence maps

ABSTRACT We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo-Sℓs, we show how these spectra will allow the reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the-art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics ℓ and source redshift zs, which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from cosmic microwave background observations, and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.

Bridging the gap between simulated and experimental ionic conductivities in lithium superionic conductors

Lithium superionic conductors (LSCs) are of major importance as solid electrolytes for next-generation all-solid-state lithium-ion batteries. While ab initio molecular dynamics have been extensively applied to study these materials, there are often large discrepancies between predicted and experimentally measured ionic conductivities and activation energies due to the high temperatures and short time scales of such simulations. Here, we present a strategy to bridge this gap using moment tensor potentials (MTPs). We show that MTPs trained on energies and forces computed using the van der Waals optB88 functional yield much more accurate lattice parameters, which in turn leads to accurate prediction of ionic conductivities and activation energies for the Li0·33La0·56TiO3, Li3YCl6 and Li7P3S11 LSCs. NPT MD simulations using the optB88 MTPs also reveal that all three LSCs undergo a transition between two quasi-linear Arrhenius regimes at relatively low temperatures. This transition can be traced to an increase in the number and diversity of diffusion pathways, in some cases with a change in the dimensionality of diffusion. This work presents not only an approach to develop high accuracy MTPs, but also outlines the diffusion characteristics for LSCs which is otherwise inaccessible through ab initio computation.

Spectral-angular patterns and energy threshold for linear-to-nonlinear femtosecond laser pulse focusing in air

Focused propagation of a high-power ultrashort laser pulse is strongly influenced by optical medium nonlinearity that can significantly affect pulse parameters in the focusing region as compared to the linear focusing regime. We present the results of our experimental study and numerical simulations of frequency-angular patterns and laser plasma distribution of a gigawatt-power femtosecond Ti-sapphire laser pulse propagating in air under various focusing conditions. For the first time to the best of our knowledge, we found experimentally and confirm theoretically the range of pulse numerical aperture (NA), from approximately NA = 2 ⋅ 10−3 to 5 ⋅ 10−3, when both frequency and angular spectra broadening during supercritical laser pulse focusing in air is minimal. We attribute this NA-range to the transition region between quasilinear and nonlinear pulse focusing regimes. Additionally, the energy threshold for different pulse focusing regimes in the wide range of focusing conditions is obtained for the first time through the numerical simulations. This threshold is demonstrated to decrease with pulse NA increase.

A novel estimator for the equation of state of the IGM by Ly α forest tomography

ABSTRACT We present a novel procedure to estimate the equation of state of the intergalactic medium in the quasi-linear regime of structure formation based on Ly α forest tomography and apply it to 21 high-quality quasar spectra from the UVES_SQUAD survey at redshift z = 2.5. Our estimation is based on a full tomographic inversion of the line of sight. We invert the data with two different inversion algorithms, the iterative Gauss–Newton method and the regularized probability conservation approach, which depend on different priors and compare the inversion results in flux space and in density space. In this way our method combines fitting of absorption profiles in flux space with an analysis of the recovered density distributions featuring prior knowledge of the matter distribution. Our estimates are more precise than existing estimates, in particular on small redshift bins. In particular, we model the temperature–density relation with a power law and observe for the temperature at mean density $T_0 = 13\,400^{+1700}_{-1300}\, \mathrm{K}$ and for the slope of the power law (polytropic index) γ = 1.42 ± 0.11 for the power-law parameters describing the temperature–density relation. Moreover, we measure an photoionization rate $\Gamma _{-12} = 1.1^{+0.16}_{-0.17}$. An implementation of the inversion techniques used will be made publicly available.