Initial Perturbation Research Articles

Thermal-mechanical buckling analysis and optimization of the stringer stiffened cylinder using smeared stiffener based reduced-order models

In this work, the thermal-mechanical buckling analysis and optimization of stringer stiffened cylindrical shells are achieved using the smeared stiffener based reduced-order models. A novel reduced-order modeling method is proposed for nonlinear buckling analysis of the stringer stiffened cylinder subjected to an axially compressive load and initial temperature field. The reduced-order model is constructed based on the improved Koiter perturbation theory and the smeared stiffener method. The axially compressive load, initial temperature field and perturbation loads are converted to be the degrees of freedom in the smeared stiffener based reduced-order model. The thermoelastic geometrically nonlinear response of the stringer stiffened cylinder can be obtained using the proposed method accurately and efficiently. Optimization problems are designed to achieve the optimal stiffening configuration for minimum weight and maximum buckling load, where the solutions of reduced-order models are selected as inputs. Stringer stiffened cylinders with various ratios of radius to thickness and length to radius are considered to illustrate the good performance of the proposed method. Compared to the fully nonlinear analysis based on the classical finite element method, the proposed method can achieve the nonlinear buckling load of the stringer stiffened cylinder much more efficiently and realize the optimization of the stiffening configuration at an affordable computational cost.

Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations

Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations

Convergence rates to the planar stationary solution to a 2D model of the radiating gas on half space

This paper is concerned with the asymptotic stability of a planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic–elliptic coupled system of the radiating gas on half space. We show that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity under small initial perturbation. This result is proved by the standard L2-energy method and the div–curl decomposition. Moreover, we prove that the solution (u, q) converges to the corresponding planar stationary solution at the rate t−α/2−1/4 for the non-degenerate case and t−1/4 for the degenerate case. The proof is based on the time and space weighted energy method.

Intrinsic instabilities of hydrogen and hydrogen/ammonia premixed flames: Influence of equivalence ratio, fuel composition and pressure

Premixed lean hydrogen-air flames exhibit instabilities due to hydrodynamic instabilities but also thermo-diffusive instabilities. However, in the case of ammonia/hydrogen blends, the effect of ammonia addition on instabilities is still unclear. To investigate intrinsic instabilities in premixed ammonia/hydrogen-air flames, a parametric study of laminar premixed flames is performed for different fuel contents, from pure hydrogen (H2) to a blend of 40% of H2 and 60% of ammonia (NH3) in volume, equivalence ratios (0.4 to 1.0) and pressures (1 and 10 bar) to investigate thermo-diffusive instabilities. Numerical simulations using detailed chemistry are performed where an initial perturbation is set to disturb the planar flame front and to compute its growth rate. During the initial linear phase, the perturbation’s amplitude grows or decreases depending on the flame’s mixture propensity to be unstable or stable, respectively. At small times, the linear growth rate of the perturbation can be estimated and compared to theory. As expected, the maximum growth rate obtained in the linear phase depends on the mixture’s equivalence ratio, fuel ratio, and pressure. Ammonia addition leads to a reduced peak growth rate, likely due to lower reactivity leading to a higher Zel’dovich number. Very lean mixtures (equivalence ratios of 0.4 and 0.5) are thermo-diffusively unstable, regardless of the ammonia content, due to hydrogen’s preferential diffusion.

Modulation depth of the gyrosynchrotron emission as an identifier of fundamental sausage modes

Aims. We aim to study the intensity, the modulation depth, and the mean modulation depth of the gyrosynchrotron (GS) radiation as a function of the frequency and the line of sight (LOS) in fast sausage modes. Methods. By solving the 2.5D magnetohydrodynamics (MHD) ideal equations of a straight coronal loop considering the chromosphere and with typical flaring plasma parameters we analyse the wavelet transform of the density and the GS emission for different radio frequencies and different spatial resolutions, given impulsive and general perturbations with energies in the microflare range. Results. A wavelet analysis performed over the GS radiation emission showed that a fast fundamental sausage mode of ∼7 s with a first harmonic mode of 3 s developed, for all the initial energy perturbations used. For both the high spatial resolution (central pixel integration) and the low spatial resolution (entire loop integration), the larger the radio frequency, the larger the modulation depth. However, high- and low-resolution integrations differ in that the larger the LOS angle with respect to the loop axis, the larger and smaller the modulation depth, respectively. Conclusions. Fast MHD modes triggered by instantaneous energy depositions of the order of a microflare energy are able to reproduce deep intensity modulation depths in radio emission as observed in solar events. As the trends of the GS emission previously obtained for a linear and forced oscillation remain present when analysing a more general context, considering the chromosphere and where the sausage mode is triggered by an impulsive, non-linear perturbation, it seems that the behaviour found can be used as observational identifiers of the presence of sausage modes with respect to other quasi-periodic pulsation features. It can be inferred from this that finite-amplitude sausage modes have the potential to generate the observed deep modulation depths.

Gaia DR3 features of the phase spiral and its possible relation to internal perturbations

ABSTRACT Disc stars from the Gaia DR3 RVS catalogue are selected to explore the phase spiral in the Galaxy. The data reveal a two-armed phase spiral pattern in the local z–vz plane inside the solar radius, which appears clearly when colour-coded by 〈vR〉(z, vz): this is characteristic of a breathing mode that can in principle be produced by in-plane non-axisymmetric perturbations. The phase spiral pattern becomes single armed outside the solar radius. When a realistic analytic model with a steadily rotating bar and 2-armed spiral arms as perturbation is used to perform particle test integrations, the pseudo-stars get a prominent spiral pattern in the 〈vR〉 map in the x–y plane. Additionally, clear breathing mode evidence at a few $\, \mathrm{km\, s}^{-1}$ level can be seen in the 〈vz〉 map on the x–z plane, confirming that such breathing modes are non-negligible in the joint presence of a bar and spiral arms. However, no phase spiral is perceptible in the (z, vz) plane. When an initial vertical perturbation is added to carry out the simulation, the one-armed phase spirals can clearly be seen 500 Myr after the perturbation and gradually disappear inside out. Finally, we show as a proof of concept how a toy model of a time-varying non-axisymmetric in-plane perturbation with varying pattern speed can produce a strong two-armed phase spiral. We conclude a time-varying strong internal perturbation together with an external vertical perturbation could perhaps explain the transition between the two-armed and one-armed phase spirals around the solar radius.

Solitary wave solutions for the fourth-order nonlinear Schrödinger equation with variables coefficients

We study the existence and propagation properties of solitary waves within the framework of a fourth-order nonlinear Schrödinger equation with variables coefficients. The model applies to the description of the transport of biological energy inside alpha helical proteins. Both gray, dipole and tripole types are found by adopting the complex multipole ansatz solution. Parametric conditions for the existence of the solitary wave solutions are presented and their dynamic behavior is analyzed for different choice of system parameters. In addition, the stability of the tripole-managed solitons under some initial perturbations is studied by employing the numerical simulation methods. Finally, the collision dynamics of two similar tripole solitons in an inhomogeneous periodic medium is explored.

Asymptotic stability of viscous contact wave to a radiation hydrodynamic limit model

This paper is concerned with the large time behavior of the solutions for 1D radiation hydrodynamic limit model without viscosity and its asymptotic stability of the viscous contact discontinuity wave under the smallness assumption of the strength of the contact wave and initial perturbations. The present pressure includes a fourth-order term about the absolute temperature from radiation effect which brings the main difficulty. Furthermore, the dissipative of the system is weaker for the lack of viscosity. All these make the problem more challenging. The prove is mainly based on the energy method, including normal and radial directions energy estimates.

Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations

AbstractWe investigate the long‐time properties of the two‐dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical Miles‐Howard stability condition on the Richardson number, we prove that the system experiences a shear‐buoyancy instability: the density variation and velocity undergo an inviscid damping while the vorticity and density gradient grow as . The result holds at least until the natural, nonlinear timescale . Notice that the density behaves very differently from a passive scalar, as can be seen from the inviscid damping and slower gradient growth. The proof relies on several ingredients: (A) a suitable symmetrization that makes the linear terms amenable to energy methods and takes into account the classical Miles‐Howard spectral stability condition; (B) a variation of the Fourier time‐dependent energy method introduced for the inviscid, homogeneous Couette flow problem developed on a toy model adapted to the Boussinesq equations, that is, tracking the potential nonlinear echo chains in the symmetrized variables despite the vorticity growth.

On the Foundation and Different Interpretations of Ensemble Sensitivity

Abstract In sensitivity analysis, ensemble sensitivity is defined as the regression coefficients resulting from a simple linear regression of changes of a response function on initial perturbations. One of the interpretations for ensemble sensitivity considers this a simplified version of regression-based adjoint sensitivity called univariate ensemble sensitivity whose derivation involves the so-called diagonal approximation. This approximation, which replaces the analysis error covariance matrix by a diagonal matrix with the same diagonal, helps to avoid inversion of the analysis error covariance, but, at the same time causes confusion in understanding and practical application of ensemble sensitivity. However, some authors have challenged such a controversial interpretation by showing that univariate ensemble sensitivity is multivariate in nature, which raises the necessity for the foundation of ensemble sensitivity. In this study, we have tried to resolve the confusion by establishing a robust foundation for ensemble sensitivity without relying on the controversial diagonality assumption. As employed in some studies, we adopt an impact-based definition for ensemble sensitivity by taking into account probability distributions of analysis perturbations. The mathematical results show that standardized ensemble sensitivity carries in itself three important quantities at the same time: 1) standardized changes of the forecast response with one standard deviation changes of individual state variables, 2) correlations between the forecast response and individual state variables, and 3) the most sensitive analysis perturbation. The theory guarantees validity of ensemble sensitivity, demonstrates its multivariate nature, and explains why ensemble sensitivity is effective in practice.

An Analysis of the Impact of Vertical Wind Shear on Convection Initiation Using Large-Eddy Simulations: Importance of Wake Entrainment

Abstract The initiation of thunderstorms in environments characterized by strong wind shear presents a forecast challenge because of the complexities of the interactions between growing cumulus clouds and wind shear. Thunderstorms that develop in such environments are often capable of producing high-impact hazards, highlighting the importance of convection initiation in sheared environments. Although recent research has greatly improved understanding of the structure and evolution of rising thermals in unsheared environments, there remains uncertainty in how wind shear influences the convection initiation process. Two large-eddy simulations (75-m horizontal grid spacing) were performed to study this problem. Convection initiation attempts are forced in the simulations through prescribed surface heat fluxes (the initial boundary layers are statistically horizontally homogeneous and quasi–steady state but contain turbulent eddies as a result of random initial temperature perturbations). The only difference between the two simulations is the presence or absence of wind shear above 2 km. Important differences in the entrainment patterns are present between sheared and unsheared growing cumulus clouds. As found in previous research, the overturning circulation associated with rising thermals drives dynamic entrainment in the unsheared clouds. However, in sheared clouds, wake entrainment resulting from the tilting of environmental vorticity is an important dynamic entrainment pathway. This result has implications for both the structure of sheared growing cumulus clouds and for convection initiation in sheared environments. Significance Statement Forecasts of thunderstorm hazards such as tornadoes, hail, and strong winds, require the accurate prediction of when and where thunderstorms form. Unfortunately, predicting thunderstorm formation is not easy, as there are a lot of different factors to consider. One such factor is environmental vertical wind shear, which describes how winds change speed and direction with height. The purpose of this study is to better understand how wind shear impacts developing clouds. Our results demonstrate a specific mechanism, called “wake entrainment,” through which wind shear can weaken developing clouds and potentially prevent them from becoming strong thunderstorms entirely. Understanding this mechanism may be useful for thunderstorm prediction in environments characterized by wind shear.

Longwave Radiative Effects beyond the Initial Intensification Phase of Tropical Cyclones

Abstract The effects of longwave radiation on tropical cyclone intensification, with an emphasis on the mature stage, are explored in an idealized modeling framework. Results show that although the cloud-radiative effect aids in early intensification of the vortex, it does not promote increase in the maximum tangential wind (Vmax) and could even reduce Vmax at the mature stage. At later stages, maximum radiative heating is located outside the eyewall and promotes convection there, and the secondary circulation encourages convergence of absolute angular momentum outside the eyewall instead of near the eyewall region, based on a budget analysis. Clear-sky radiative cooling helps invigorate domainwide convection, also limiting the Vmax increase at later stages. The area-averaged frozen moist static energy (FMSE) variance increases even though Vmax decreases. In this sense, the FMSE variance is similar to the monotonically growing integrated kinetic energy, and is more indicative of the system-scale strength than of Vmax. Sensitivity experiments are performed with random initial perturbations and varied initial soundings. An axisymmetric model with a 10-member ensemble not only confirms the results from three-dimensional simulations, but also demonstrates that the weak radiative heating outside the eyewall is indeed able to slow down Vmax within 1 day.

Vibration and Jumping of Ferrofluid Marbles under an Initial Magnetic Perturbation.

Liquid marbles are being promoted as a replacement for conventional droplets in digital microfluidics. Liquid marbles can be remotely controlled by an external magnetic field if ferrofluid is utilized as their liquid cores. In this study, the vibration and jumping of a ferrofluid marble is experimentally and theoretically investigated. An external magnetic field is utilized to induce deformation in a liquid marble and an increase in its surface energy. As the magnetic field is switched off, the stored surface energy converts to gravitational potential and kinetic energies until it is dissipated. An equivalent linear mass-spring-damper system is used to study the vibration of the liquid marble, and the effect of its volume and initial magnetic stimulus on the vibrational characteristics, such as natural frequency, damping ratio, and deformation of the liquid marble, is experimentally examined. By analyzing these oscillations, the effective surface tension of the liquid marble is evaluated. Also, a novel theoretical model is proposed to obtain the damping ratio of the liquid marble, suggesting a new tool for the measurement of liquid viscosity. Interestingly, it is observed that the liquid marble jumps from the surface in the case of high initial deformation. Based on conservation law of energy, a theoretical model for predicting the liquid marbles jumping height and the boundary between jumping and non-jumping zones in terms of nondimensional numbers, namely, magnetic and gravitational Bond numbers and Ohnesorge number, is proposed with an acceptable error compared to experimental data.

Structure formation and quasispherical collapse from initial curvature perturbations with numerical relativity simulations

Structure formation and quasispherical collapse from initial curvature perturbations with numerical relativity simulations

Investigation of the halo effect in the evolution of a nonstationary disk of spiral galaxies

Abstract In this article, we consider the problem of the evolution of the disk subsystem of galaxies, taking into account their halos. The global structure of the disk of galaxies strongly depends on the mass and shape of the halo. To this end, we have studied the evolution of nonradial oscillations of a nonstationary disk surrounded by a passive ellipsoidal halo with a uniform density. A system of equations for the evolution of a self-gravitating disk is obtained, taking into account the halo, in the form of matrix differential equations, and a method for its numerical analysis is developed to study the effect of the halo on disk formation. Numerical calculations were performed for various values of the system parameters, such as the initial perturbation, the circular speed of disk rotation, the ratio of the mass of the halo to the mass of the disk, and the time dependences of the major and minor semiaxes of the disk. The critical values of the system parameters are determined at which the halo stabilizes nonlinear and nonradial oscillations of the disk subsystem of galaxies at an early stage of their evolution.

Numerical Simulations of the Decaying Transverse Oscillations in the Cool Jet

In the present paper, we describe a 2.5D (two-and-a-half-dimensional) magnetohydrodynamic (MHD) simulation that provides a detailed picture of the evolution of cool jets triggered by initial vertical velocity perturbations in the solar chromosphere. We implement random multiple velocity, Vy, pulses of amplitude 20–50 km s−1 between 1 Mm and 1.5 Mm in the Sun’s atmosphere below its transition region (TR). These pulses also consist of different switch-off periods between 50 s and 300 s. The applied vertical velocity pulses create a series of magnetoacoustic shocks steepening above the TR. These shocks interact with each other in the inner corona, leading to complex localized velocity fields. The upward propagation of such perturbations creates low-pressure regions behind them, which propel a variety of cool jets and plasma flows in the localized corona. The localized complex velocity fields generate transverse oscillations in some of these jets during their evolution. We study the transverse oscillations of a representative cool jet J1, which moves up to the height of 6.2 Mm above the TR from its origin point. During its evolution, the plasma flows make the spine of jet J1 radially inhomogeneous, which is visible in the density and Alfvén speed smoothly varying across the jet. The highly dense J1, which is triggered along the significantly curved magnetic field lines, supports the propagating transverse wave of period of approximately 195 s with a phase speed of about 125 km s−1. In the distance–time map of density, it is manifested as a transverse kink wave. However, the careful investigation of the distance–time maps of the x- and z-components of velocity reveals that these transverse waves are actually of mixed Alfvénic modes. The transverse wave shows evidence of damping in the jet. We conclude that the cross-field structuring of the density and characteristic Alfvén speed within J1 causes the onset of the resonant conversion and leakage of the wave energy outward to dissipate these transverse oscillations via resonant absorption. The wave energy flux is estimated as approximately of 1.0 × 106 ergs cm−2 s−1. This energy, if it dissipates through the resonant absorption into the corona where the jet is propagated, is sufficient energy for the localized coronal heating.

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

For an aeroelastic system of a two-dimensional elastic panel subjected to an impinging inviscid oblique shockwave, the nonlinear flutter characteristics are affected by many factors such as shock impingement location, cavity pressure and initial perturbation. The effects of the above factors on the variation of system bifurcation type and dynamic behaviors are investigated numerically. A low-fidelity computational method coupled with local piston theory and van Karman plate model, and a high-fidelity computational method coupled with Euler equations and finite element model are used for fluid-structure interaction simulations. Two sets of new findings are unveiled. First, either the variation of shock impingement location or cavity pressure can induce the aeroelastic system to transition between a subcritical bifurcation and a supercritical bifurcation. For some cases, the system bifurcation characteristics exhibit strong sensitivity to these two factors. Second, it is found that in addition to the limit cycle oscillation in the form of a combination of the second and third structural modes, multiple stable limit cycle oscillations due to the coupling of higher-order modes can be triggered by suitable initial perturbations. These limit cycle oscillations have high frequencies and amplitudes, which suggest a higher risk of structural fatigue failure.

Asymptotic stability of a nonlinear wave for an outflow problem of the bipolar Navier–Stokes–Poisson system under large initial perturbation

Asymptotic stability of a nonlinear wave for an outflow problem of the bipolar Navier–Stokes–Poisson system under large initial perturbation

Improved training of physics-informed neural networks for parabolic differential equations with sharply perturbed initial conditions

We propose a multi-component approach for improving the training of the physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection–dispersion equation (ADE) with a point (Gaussian) source initial condition. In the d-dimensional ADE, perturbations in the initial condition decay with time t as t−d/2. We demonstrate that for d≥2, this decay rate can cause a large approximation error in the PINN solution. Furthermore, localized large gradients in the ADE solution make the (common in PINN) Latin hypercube sampling of the equation’s residual highly inefficient. Finally, the PINN solution of parabolic equations is sensitive to the choice of weights in the loss function. We propose a normalized form of ADE where the initial perturbation of the solution does not decrease in amplitude and demonstrate that this normalization significantly reduces the PINN approximation error. Next, we present an adaptive sampling scheme based on the analytical estimate of the solution decay rate that significantly reduces the PINN estimation error for the same number of sampling (residual) points. Finally, we develop criteria for selecting weights based on the order of magnitude of different terms in the loss function. We demonstrate the accuracy of the proposed PINN model for forward, inverse, and backward ADEs.

The Warm Inflation Story

Warm inflation has normalized two ideas in cosmology, that in the early universe the initial primordial density perturbations generally could be of classical rather than quantum origin and that during inflation, particle production from interactions amongst quantum field, and its backreaction effects, can occur concurrent with inflationary expansion. When we first introduced these ideas, both were met with resistance, but today they are widely accepted as possibilities with many models and applications based on them, which is an indication of the widespread influence of warm inflation. Open quantum field theory, which has been utilized in studies of warm inflation, is by now a relevant subject in cosmology, in part due to this early work. In this review I first discuss the basic warm inflation dynamics. I then outline how to compute warm inflation dynamics from first-principles quantum field theory (QFT) and in particular how a dissipative term arises. Warm inflation models can have an inflaton mass bigger than the Hubble scale and the inflaton field excursion can remain sub-Planckian, thus overcoming the most prohibitive problems of inflation model building. I discuss the early period of my work in developing warm inflation that helped me arrive at these important features of its dynamics. Inflationary cosmology today is immersed in hypothetical models, which by now are acting as a diversion from reaching any endgame in this field. I discuss better ways to approach model selection and give necessary requirements for a well constrained and predictive inflation model. A few warm inflation models are pointed out that could be developed to this extent. I discuss how, at this stage, more progress would be made in this subject by taking a broader view on the possible early universe solutions that include not just inflation but the diverse range of options.