Matter dipole and Hubble tension due to large wavelength perturbations

Analytic modeling and magnetohydrodynamic simulations have been conducted to investigate two‐dimensional effects in imploding plasma shells. These effects include short wavelength disturbances caused by instabilities at the plasma‐magnetic field interface, long wavelength disturbances associated with plasma annulus formation, and disturbances resulting from the power flow to the plasma annulus. The numerical calculations were carried out using the two‐dimensional single‐fluid MHD code MACH2 for different plasma density profiles and electrode geometries. Results for short wavelength perturbations show that these phenomena behave in a manner consistent with analytic linear theory and heuristic nonlinear models. At stagnation they have a negligible effect on the uniformity during the initial coupling to the target, even for large initial perturbations. The disturbances manifest themselves primarily in a rippling of the back of the plasma shell with significant effects, even in this region, not occurring until late in the stagnation process. Long wavelength perturbations produced by a straight axial gas injection for gas puff implosions can lead to pronounced axial nonuniformity, ‘‘zippering,’’ at stagnation. Variations of the injection conditions and electrode geometry can produce more uniform stagnation. Changes in mass profile, gas injection angle, and electrode shape can all be used to achieve significantly greater stagnation uniformity. Consistent calculations for an entire implosion process from gas injection to stagnation, including vacuum power flow, incidate the degree of coupling of short wavelength, long wavelength, and power flow perturbations. Comparison with experimental data show good agreement among analytic, numerical, and experimental results.

We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche–Riemann ellipsoids moving on circular Kepler orbits. However, previous stability studies have to be reassessed. Indeed, they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open-source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

In a recent paper Abeyaratne et al. (J. Mech. Phys. Solids 167:104958, 2022) concerning the stability of surface growth of a pre-stressed elastic half-space with surface tension, it was shown that steady growth is never stable, at least not for all wave numbers of the perturbations, when the growing surface is traction-free. On the other hand, steady growth was found to be always stable when growth occurred on a flat frictionless rigid support and the stretch parallel to the growing surface was compressive. The present study is motivated by these somewhat unexpected and contrasting results.In this paper the stability of a pre-compressed neo-Hookean elastic half-space undergoing surface growth under plane strain conditions is studied. The medium outside the growing body resists growth by applying a pressure on the growing surface. At each increment of growth, the incremental change in pressure is assumed to be proportional to the incremental change in normal displacement of the growing surface. It is shown that surface tension stabilizes a homogeneous growth process against small wavelength perturbations while the compliance of the surrounding medium stabilizes it against large wavelength perturbations. Specifically, there is a critical value of stretch,$\lambda _{\mathrm{cr}} \in (0,1)$λcr∈(0,1), such that growth is linearly stable against infinitesimal perturbations ofarbitrarywavelength provided the stretch parallel to the growing surface exceeds$\lambda _{\mathrm{cr}}$λcr. Thisstability threshold,$\lambda _{\mathrm{cr}}$λcr, is a function of the non-dimensional parameter$\sigma \kappa /G^{2}$σκ/G2, which is the ratio between two length-scales$\sigma /G$σ/Gand$G/\kappa $G/κ, where$G$Gis the shear modulus of the elastic body,$\sigma $σis the surface tension, and$\kappa $κis the stiffness of the surrounding compliant medium.It is shown that$(a)$(a)$\lambda _{\mathrm{cr}} \to 1$λcr→1as$\kappa \to 0$κ→0and$(b)$(b)$\lambda _{\mathrm{cr}} \to 0^{+}$λcr→0+as$\kappa \to \infty $κ→∞, thus recovering the results in Abeyaratne et al. (J. Mech. Phys. Solids 167:104958, 2022) pertaining to the respective limiting cases where growth occurs$(a)$(a)on a traction-free surface and$(b)$(b)on a frictionless rigid support. The results are also generalized to include extensional stretches.

We have analysed the stability of a solitary shear kinetic wave in a hot relativistic plasma for oblique long wavelength perturbation following the method of Zakharov and Rubenchik. The Zakharov{Kuznetsov equation describing the wave propagation is deduced and the growth rate of instabilities due to large amplitude magnetic fleld perturbations is obtained as a function of the angle µ between the direction of propagation of the solitary wave and magnetic fleld, the streaming parameter v0=c and the electron temperature ae.

Morphological evolution of pre-perturbed pore channels in sapphire

Stability of a frictional material layer resting on a viscous half-space

The microscopic-scale Richtmyer-Meshkov (RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude, wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio ($\eta$). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to $\eta$, while the second one depends heavily on it.

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black holes (PBHs) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBHs are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order 1020 g can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.

Numerical simulation of propagation mechanisms of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The motivation is to investigate the effect of artificial perturbations on the evolution or amplification of cellular instability. The results show that, without artificial perturbations, a planar ZND detonation can evolve into a fully-developed cellular detonation after a distance because of the amplification of the cellular instability. With the artificial perturbations evolved in, at the early stage, the artificial perturbations control the transverse wave spacing by suppressing the amplification of the cellular instability. However, after a steady-state, the cellular instability starts to amplify itself again and eventually transits to a fully-developed cellular detonation. It is demonstrated that the presence of the artificial perturbations delays the formation of the cellular detonation, and the increase of instability factor can slow down this delay. It is also found that, if the wavelength of the artificial perturbations is close to the transverse wave spacing of the cellular detonation in the homogeneous medium, synchronization of these two factors occurs, and hence a cellular detonation with extremely regular cell pattern is immediately formed. The temperature discontinuity causes the front to be more turbulent with the presence of weak triple-wave structure locally besides the natural transverse waves. The artificial perturbations can increase the intrinsic instability, and hence changes the propagation mechanism of the detonation front. In contrast, large artificial perturbations could prohibit the propagation but reduce cellular instability. It is concluded that the competition of artificial perturbations with intrinsic detonation instability dominates the evolution of cellular structures of the detonation front.

The first non-modal linear stability analysis of an unsteady ablation waves in the context of inertial confinement fusion is carried out. Optimal initial perturbations are computed using a direct-adjoint method obtained by applying the Lagrange multiplier technique. Particular attention is paid to a proper formulation of a Lagrange functional for compressible flow equations with perturbed dynamical boundaries. Ablation wave perturbations are found to be prone to transient amplification at both short and intermediate final times whether for small or large perturbation wavelengths. Two distinct mechanisms of optimal growth are presently identified. These results contrast with previous results based on normal mode analysis, simulations and dedicated experiments of selected perturbation configurations, for which only large wavelengths are subject to a possible amplification whereas small wavelengths are damped.

The question of stability of a planar solid-liquid interface in undercooled pure and alloy melts has been reconsidered without the restrictive assumption of no heat flow in the solid made in earlier works. The modified analysis indicates that provided the thermal gradient on the solid side of the interface, Gs, is positive, stability can be achieved in an undercooled alloy melt for growth rates R>Ra, whereas a recent analysis by Trivedi and Kurz, which assumes Gs = 0, suggests that stability is possible only if R>Ra + Rat. Here Ra is the familiar absolute stability limit of Mullins and Sekerka and Rat, is the absolute stability limit in an undercooled pure melt, as identified by Trivedi and Kurz. The absolute stability criterion for steady-state planar growth in an undercooled alloy melt is thus the same as derived earlier by Mullins and Sekerka for directional solidification. Relaxing the restrictive assumption of Gs = 0 also reveals that there is a regime of stability for low growth rates and low supercoolings. Stability is possible under these conditions if Gs>0, and the bath undercooling ΔTb < ΔTO + ΔTh/2, where ΔTO is the freezing range of the alloy and ΔTh is the hypercooling limit for the pure melt. For large supercoolings, Gs < 0, and the interface will be unstable with respect to large wavelength perturbations, even if R > Ra + Rat.

A multiple-scale analysis (homogenization) is applied to study the stability of steady cellular solutions of the one-dimensional Kuramoto-Sivashinsky equation with 2π-periodic boundary conditions. It is found that these solutions exhibit visco-elastic behaviour under very large wavelength perturbations. This elasticity property is then extended to Navier-Stokes turbulence. It is suggested that two-dimensional flame fronts and various turbulent flows (e.g. solar granulation and cloud streets) may display elasticity. Inclusion of elasticity into engineering turbulence modelling is also discussed.

We propose a new cosmological paradigm in which our observed expanding phase is originated from an initially large contracting Universe that subsequently experienced a bounce. This category of models, being geodesically complete, is nonsingular and horizon-free and can be made to prevent any relevant scale to ever have been smaller than the Planck length. In this scenario, one can find new ways to solve the standard cosmological puzzles. One can also obtain scale invariant spectra for both scalar and tensor perturbations: this will be the case, for instance, if the contracting Universe is dust-dominated at the time at which large wavelength perturbations get larger than the curvature scale. We present a particular example based on a dust fluid classically contracting model, where a bounce occurs due to quantum effects, in which these features are explicit.

We review recent theoretical work on photon kinetics and wave kinetics in a plasma, where resonant interactions of waves with photons, and with quasi-particles such as plasmons, is considered. A Wigner function, or quasi-distribution function, for photons and quasi-particles, is introduced. The resulting wave kinetic equation is able to describe the evolution of a broad photon spectrum, or more generally, a turbulent plasma state, if conveniently coupled with the wave equations via ponderomotive force terms. Resonant interactions occur when the phase velocity of the large scale wave (for instance a wakefield) is equal to the group velocity of the short wavelength quasi-particles (for instance a short laser pulse). It is shown that quasi-particle Landau damping can take place, as well as quasi-particle beam instabilities. A direct link between short and large wavelength perturbations in the plasma is established. Photon and quasi-particle acceleration and trapping is also discussed.

We consider spatially homogeneous time periodic solutions of general partial differential equations. We prove that, when such a solution is close enough to a homoclinic orbit or a homoclinic bifurcation for the differential equation governing the spatially homogeneous solutions of the PDE, then it is generically unstable with respect to large wavelength perturbations. Moreover, the instability is of one of the two following types: either the well-known Kuramoto phase instability, corresponding to a Floquet multiplier becoming larger than 1, or a fundamentally different kind of instability, occurring with a period doubling at an intrinsic finite wavelength, and corresponding to a Floquet multiplier becoming smaller than −1.