Long-wavelength Perturbations Research Articles

Hydrogeologic Property Estimation in Plate Boundary Observatory Boreholes Using Tidal Response Analysis

Because of the influence pore pressures have on effective stress, understanding hydrogeologic properties that control fluid flow and pressure distribution is important in characterizing earthquake and deformation processes. Here, we utilize borehole pressure changes in response to earth tides to determine hydrogeologic properties and their time variations for 17 boreholes within the NSF Earthscope’s Plate Boundary Observatory (PBO) network along the San Andreas fault and Cascadia subduction zone. Our analysis considers solutions for both confined and unconfined aquiares. Resulting permeability and hydraulic diffusivity values range from6.4×10−16–8.4×10−14 m2 and1×10−4–9×10−1 m2s−1, respectively, whereas specific storage values are generally~1×10−6 m−1. The values are fairly consistent through time, reasonable given lithology, and are comparable to other regional studies. For one borehole, values are also comparable to those determined with traditional aquifer test data. In contrast with previous determinations of the high-frequency poroelastic response to seismic waves, no obvious spatial trends in hydrogeologic properties determined from long-wavelength tidal perturbations are observed. Within the recurring time-series estimates, only one borehole exhibits clear permeability enhancement by earthquakes, whereas nearby boreholes with similar lithology and hydrogeologic property values do not. This highlights the variable susceptibility of rocks to permeability enhancement. Together, these results provide quantitative constraints useful for models of large-scale groundwater flow around large fault systems and the potential hydrologic influence on deformation and fault slip behavior.

Density relaxation in conserved Manna sandpiles.

We study relaxation of long-wavelength density perturbations in a one-dimensional conserved Manna sandpile. Far from criticality where correlation length ξ is finite, relaxation of density profiles having wave numbers k→0 is diffusive, with relaxation time τ_{R}∼k^{-2}/D with D being the density-dependent bulk-diffusion coefficient. Near criticality with kξ≳1, the bulk diffusivity diverges and the transport becomes anomalous; accordingly, the relaxation time varies as τ_{R}∼k^{-z}, with the dynamical exponent z=2-(1-β)/ν_{⊥}<2, where β is the critical order-parameter exponent and ν_{⊥} is the critical correlation-length exponent. Relaxation of initially localized density profiles on an infinite critical background exhibits a self-similar structure. In this case, the asymptotic scaling form of the time-dependent density profile is analytically calculated: we find that, at long times t, the width σ of the density perturbation grows anomalously, σ∼t^{w}, with the growth exponent ω=1/(1+β)>1/2. In all cases, theoretical predictions are in reasonably good agreement with simulations.

Large scale anomalies in the CMB and non-Gaussianity in bouncing cosmologies

We propose that several of the anomalies that have been observed at large angular scales in the CMB have a common origin in a cosmic bounce that took place before the inflationary era. The bounce introduces a new physical scale in the problem, which breaks the almost scale invariance of inflation. As a result, the state of scalar perturbations at the onset of inflation is no longer the Bunch–Davies vacuum, but it rather contains excitations and non-Gaussianity, which are larger for infrared modes. We argue that the combined effect of these excitations and the correlations between CMB modes and longer wavelength perturbations, can account for the observed power suppression, for the dipolar asymmetry, and it can also produce a preference for odd-parity correlations. The model can also alleviate the tension in the lensing amplitude A L. We adopt a phenomenological viewpoint by considering a family of bounces characterized by a couple of parameters. We identify the minimum set of ingredients needed for our ideas to hold, and point out examples of theories in the literature where these conditions are met.

The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller

This paper focuses on two fundamental issues in traffic flow modelling: string stability of car following (CF), and oscillation of traffic flow. Its aim is to explore the complementary use of CF instability analysis and oscillation analysis to compress and ease traffic congestion in a connected environment. Each of these topics has been extensively investigated in the literature. However, each topic has been investigated separately and, despite the inherent conceptual and empirical closeness of the two concepts, little effort has been devoted to untangling their relationship.To address this failing, we first define four types of oscillation – amplitude-decay oscillation, amplitude-ceiling oscillation, speed-deviation ceiling oscillation, and speed-deviation growth oscillation – and reveal their similarities and dissimilarities to CF instability. Based on the stability criterion, we then develop oscillation criteria to identify different types of oscillation by relaxing two unrealistic assumptions used in CF stability analysis (i.e., infinitely-long platoon and long-wavelength perturbation). Finally, to demonstrate how CF instability analysis and oscillation analysis can be combined to influence individual vehicle stability and improve traffic oscillations in a connected environment, a platoon of vehicles that experience an oscillation in the NGSIM data is used in a case study. In this case study, different control factors are used for different vehicle types: connected (but human-driven) vehicles, and automated vehicles.Our analysis shows that a higher stability of some individual vehicles can alleviate the oscillation severity for the platoon. It also shows that desired time gap and maximum acceleration are two promising parameters that can be used to both improve individual vehicle stability and significantly smooth the oscillation of the platoon in a connected and/or automated environment. Of particular note, when considering all of the factors explored in our analysis, adjustment of the desired time gap is the most effective factor in smoothing traffic oscillations.

Non-linear edge dynamics of an integer quantum Hall fluid(a)(a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We report a theoretical study of the linear and nonlinear dynamics of edge excitations of an integer quantum Hall state of non-interacting fermions. New features beyond the chiral Luttinger liquid picture are anticipated to arise from the interplay of the curvature of the Landau level dispersion and of the Pauli exclusion principle. For long-wavelength perturbations, the microscopic numerical results are captured by a chiral nonlinear hydrodynamic equation including a density-dependent velocity term. In the wave-breaking regime, shock waves are found to be regularized into a complex ripple pattern by higher-order dispersive effects. Our results are of specific relevance for experiments with synthetic quantum matter, in particular ultracold atomic gases.

Dynamics of Perturbations under Diffusion in a Porous Medium

We consider the dynamics of finite perturbations of a plane phase transition surface in the problem of evaporation of a fluid inside a low-permeability layer of a porous medium. In the case of a nonwettable porous medium, the problem has two stationary solutions, each containing a discontinuity. These discontinuities correspond to plane stationary phase transition surfaces located inside the low-permeability porous layer. One of these surfaces is unstable with respect to long-wavelength perturbations, while the other is stable. We study the evolution of perturbations of the stable plane phase transition surface. It is known that when two phase transition surfaces are located close enough to each other, the dynamics of a weakly nonlinear and weakly unstable wave packet is described by the Kolmogorov–Petrovskii–Piskunov (KPP) diffusion equation. As traveling wave solutions, this equation has heteroclinic solutions with either oscillating or monotonic structure of the front. The boundary value problem in the full statement, which should be considered if the distance between the stable and unstable plane phase transition surfaces is not small, also has similar solutions. We formulate a sufficient condition for the decrease of finite perturbations of the stable plane phase transition surface. This condition depends on their position with respect to the standing wave type and traveling front type solutions of the model equations in the model description when the KPP equation holds.

Primordial gravitational waves from galaxy intrinsic alignments

Galaxy shapes have been observed to align with external tidal fields generated by the large-scale structures of the Universe. While the main source for these tidal fields is provided by long-wavelength density perturbations, tensor perturbations also contribute with a non-vanishing amplitude at linear order. We show that parity-breaking gravitational waves produced during inflation leave a distinctive imprint in the galaxy shape power spectrum which is not hampered by any scalar-induced tidal field. We also show that a certain class of tensor non-Gaussianities produced during inflation can leave a signature in the density-weighted galaxy shape power spectrum. We estimate the possibility of observing such imprints in future galaxy surveys.

Water film falling down an ice sheet

A gravity-driven water film falling down an ice sheet is considered within the framework of a long-wave approximation. The integral-boundary-layer method, modified with the account of the phase transition, is adopted to describe the evolution of both the free surface of a water film and the interface between the ice and water. A set of governing equations consisting of five coupled nonlinear partial differential equations is established. The linear instability analysis of the uniform base flow is performed, and the result is in good agreement with the Orr–Sommerfeld analysis of the linearized Navier–Stokes equations. The phase transition at the interface between the ice and water plays a role in stabilizing the system linearly with long-wavelength perturbations. The nonlinear solutions of the steady travelling waves are constructed numerically. The phase transition tends to suppress the dispersion of the interfacial wave. Comparisons to direct numerical simulation of the Navier–Stokes equations, which are performed with an extended marker and cell method, show a remarkable agreement. The integral-boundary-layer method captures the water film thickness and the topography of the ice sheet satisfactorily. The phase transition is observed to enhance the backflow phenomenon in the capillary region of the solitary-like interfacial wave.

Normal modes of vibrations around Hubble flow in jellium

A macroscopic Coulomb system of identical charged particles with or without a compensating background charge can evolve maintaining spatial homogeneity and isotropy that mimic the cosmological evolution of a universe with repulsive gravity. Here we study dynamics of small perturbations on the background of the corresponding Hubble flow by analyzing its normal modes of vibrations. Arbitrary disturbance of the flow can be resolved into two electroacoustic, two vortical, and one entropic modes whose dynamics is investigated. Specifically, in the zero pressure or long-wavelength limits perturbations of density and velocity evolve in a manner that is independent of the form of the initial disturbance. The same conclusion applies to vortical perturbations of the velocity for arbitrary pressure while entropic perturbations are advected by the Hubble flow. Without the background charge the underlying Hubble flow describes a Coulomb explosion whose stability with respect to small disturbances is also demonstrated.

Baryon-CDM isocurvature galaxy bias with IllustrisTNG

We study the impact that baryon-CDM relative density perturbations δbc have on galaxy formation using cosmological simulations with the IllustrisTNG model. These isocurvature (non-adiabatic) perturbations can be induced primordially, if multiple fields are present during inflation, and are generated before baryon-photon decoupling when baryons did not comove with CDM. The presence of long-wavelength δbc perturbations in our simulations is mimicked by modifying the ratios of the cosmic densities of baryons Ωb and CDM Ωc, at fixed total matter density Ωm. We measure the corresponding galaxy bias parameter bδbc as the response of galaxy abundances to δbc. When selecting by total host halo mass, bδbc is negative and it decreases with mass and redshift. Stellar-mass selected simulated galaxies show a weaker or even the opposite trend because of the competing effects of δbc on the halo mass function and stellar-to-halo-mass relations. We show that simple modeling of the latter two effects describes bδbc for stellar-mass-selected objects well. We find bδbc =0.6 for M* = 1011 M⊙/h and z=0.5, which is representative of BOSS DR12 galaxies. For δbc modes generated by baryon-photon interactions, we estimate the impact on the DR12 power spectrum to be below 1%, and shifts on inferred distance and growth rate parameters should not exceed 0.1%.

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: I. General theory and application to fluid interfaces

An arbitrary Lagrangian–Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity need not depend on the in-plane material velocity, and can be specified arbitrarily. A finite element implementation of the theory is formulated and applied to curved and deforming surfaces with in-plane incompressible flows. Numerical inf–sup instabilities associated with in-plane incompressibility are removed by locally projecting the surface tension onto a discontinuous space of piecewise linear functions. The general isoparametric finite element method, based on an arbitrary surface parametrization with curvilinear coordinates, is tested and validated against several numerical benchmarks. A new physical insight is obtained by applying the ALE developments to cylindrical fluid films, which are computationally and analytically found to be stable to non-axisymmetric perturbations, and unstable with respect to long-wavelength axisymmetric perturbations when their length exceeds their circumference. A Lagrangian scheme is attained as a special case of the ALE formulation. Though unable to model fluid films with sustained shear flows, the Lagrangian scheme is validated by reproducing the cylindrical instability. However, relative to the ALE results, the Lagrangian simulations are found to have spatially unresolved regions with few nodes, and thus larger errors.

Separate universe void bias

Voids have emerged as a novel probe of cosmology and large-scale structure. These regions of extreme underdensity are sensitive to physics beyond the standard model of cosmology, and can potentially be used as a testing ground to constrain new physics. We present the first determination of the linear void bias measured in separate universe simulations. Our methods are validated by comparing the separate universe response bias with the clustering bias of voids. We find excellent agreement between the two methods for voids identified in the halo field and the down-sampled dark matter field. For voids traced by halos, we identify two different contributions to the bias. The first is due to the bias of the underlying halo field used to identify voids, while the second we attribute to the dynamical impact of long-wavelength density perturbations on void formation and expansion. By measuring these contributions individually, we demonstrate that their sum is consistent with the total void bias. We also measure the void profiles in our simulations, and determine their separate universe response. These can be interpreted as the sensitivity of the profiles to the background density of the Universe.

Direct-drive double-shell implosion: A platform for burning-plasma physics studies.

Double-shell ignition designs have been studied with the indirect-drive inertial confinement fusion (ICF) scheme in both simulations and experiments in which the inner-shell kinetic energy was limited to ∼10-15kJ, even driven by megajoule-class lasers such as the National Ignition Facility. Since direct-drive ICF can couple more energy to the imploding shells, we have performed a detailed study on direct-drive double-shell (D^{3}S) implosions with state-of-the-art physics models implemented in radiation-hydrodynamic codes (lilac and draco), including nonlocal thermal transport, cross-beam energy transfer (CBET), and first-principles-based material properties. To mitigate classical unstable interfaces, we have proposed the use of a tungsten-beryllium-mixed inner shell with gradient-density layers that can be made by magnetron sputtering. In our D^{3}S designs, a 70-μm-thick beryllium outer shell is driven symmetrically by a high-adiabat (α≥10), 1.9-MJ laser pulse to a peak velocity of ∼240 km/s. Upon spherical impact, the outer shell transfers ∼30-40 kJ of kinetic energy to the inner shell filled with deuterium-tritium gas or liquid, giving neutron-yield energies of ∼6 MJ in one-dimensional simulations. Two-dimensional high-mode draco simulations indicated that such high-adiabat D^{3}S implosions are not susceptible to laser imprint, but the long-wavelength perturbations from the laser port configuration along with CBET can be detrimental to the target performance. Nevertheless, neutron yields of ∼0.3-1.0-MJ energies can still be obtained from our high-mode draco simulations. The robust α-particle bootstrap is readily reached, which could provide a viable platform for burning-plasma physics studies. Once CBET mitigation and/or more laser energy becomes available, we anticipate that break-even or moderate energy gain might be feasible with the proposed D^{3}S scheme.

Super-sample tidal modes on the celestial sphere

The super-sample tidal effect carries information on long-wavelength fluctuations that we cannot measure directly. It arises from the mode-coupling between short-wavelength and long-wavelength perturbations beyond a finite region of a galaxy survey and violates statistical isotropy of observed galaxy power spectra. In this paper, we propose the use of bipolar spherical harmonic (BipoSH) decomposition formalism to characterize statistically anisotropic power spectra. Using the BipoSH formalism, we perform a comprehensive study of the effect of the super-sample tides on measurements of other cosmological distortions such as the redshift-space distortion (RSD) and Alcock-Paczy\'{n}ski (AP) effects by means of the Fisher information matrix formalism. We find that the BipoSH formalism can break parameter degeneracies among the super-sample tidal, RSD and AP effects, indicating that the super-sample tides have little impact on the measurements of the RSD and AP effects. We also show that the super-sample tides are detectable with an accuracy better than the $\Lambda$CDM prediction without impairing the accuracy of measurements of other anisotropies assuming a SPHEREx-like galaxy survey.

Separate Universe simulations with IllustrisTNG: baryonic effects on power spectrum responses and higher-order statistics

Abstract We measure power spectrum response functions in the presence of baryonic physical processes using separate universe simulations with the IllustrisTNG galaxy formation model. The response functions describe how the small-scale power spectrum reacts to long-wavelength perturbations and they can be efficiently measured with the separate universe technique by absorbing the effects of the long modes into a modified cosmology. Specifically, we focus on the total first-order matter power spectrum response to an isotropic density fluctuation R1(k, z), which is fully determined by the logarithmic derivative of the non-linear matter power spectrum dlnPm(k, z)/dlnk and the growth-only response function G1(k, z). We find that G1(k, z) is not affected by the baryonic physical processes in the simulations at redshifts z &lt; 3 and on all scales probed (k ≲ 15 h Mpc−1; i.e. length scales $\gtrsim 0.4\, {\rm Mpc}\,h^{-1}$). In practice, this implies that the power spectrum fully specifies the baryonic dependence of its response function. Assuming an idealized lensing survey set-up, we evaluate numerically the baryonic impact on the squeezed-lensing bispectrum and the lensing supersample power spectrum covariance, which are given in terms of responses. Our results show that these higher-order lensing statistics can display varying levels of sensitivity to baryonic effects compared to the power spectrum, with the squeezed bispectrum being the least sensitive. We also show that ignoring baryonic effects on lensing covariances slightly overestimates the error budget (and is therefore conservative from the point of view of parameter error bars) and likely has negligible impact on parameter biases in inference analyses.

Stochastic inflation beyond slow roll

We study the stochastic formalism of inflation beyond the usual slow-roll approximation. We verify that the assumptions on which the stochastic formalism relies still hold even far from the slow-roll attractor. This includes demonstrating the validity of the separate universe approach to evolving long-wavelength scalar field perturbations beyond slow roll. We also explain that, in general, there is a gauge correction to the amplitude of the stochastic noise. This is because the amplitude is usually calculated in the spatially-flat gauge, while the number of e-folds is used as the time variable (hence one works in the uniform-N gauge) in the Langevin equations. We show that these corrections vanish in the slow-roll limit, but we also explain how to calculate them in general. We compute them in difference cases, including ultra-slow roll and the Starobinsky model that interpolates between slow roll and ultra-slow roll, and find the corrections to be negligible in practice. This confirms the validity of the stochastic formalism for studying quantum backreaction effects in the very early universe beyond slow roll.

Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities.

Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength (>25-μm) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. These experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected.

Active Fingering Instability in Tissue Spreading.

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

Instability of gravity-driven flow of a heated power-law fluid with temperature dependent consistency

In this paper we report on our investigation of the instability of a liquid layer flowing along a heated inclined plane. We develop and implement a theoretical model with a power-law constitutive relation which captures the temperature variation in the rheology of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infinitesimal perturbations imposed on the equilibrium flow. Numerical solutions were obtained, as well as asymptotic approximations based on the assumption of perturbations of long wavelength and small variation in the consistency of the fluid with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian rheology and the dependence of the fluid properties on temperature. Nonlinear effects were considered by employing a reduced dimensionality model. Calculations of permanent waves arising from unstable uniform flows were made by carrying out numerical simulations of these equations.

Separate universe framework in group field theory condensate cosmology

We use the separate universe framework to study cosmological perturbations within the group field theory formalism for quantum gravity, based on multi-condensate quantum states. Working with a group field theory action for gravity minimally coupled to four scalar fields that can act as a set of relational clock and rods, we argue that these multi-condensate states correspond to cosmological space-times with small long-wavelength scalar perturbations. Equations of motion for the cosmological perturbations are derived, which in the classical limit agree with the standard results of general relativity and also include quantum gravity corrections that become important when the space-time curvature approaches the Planck scale.