Growth Rate Of Perturbations Research Articles

The effect of odd-viscosity on Rayleigh–Taylor instability of a liquid film under a heated inclined substrate

We discuss the effect of odd viscosity on Rayleigh–Taylor instability of a thin Newtonian liquid film with broken time-reversal symmetry as it flows down a uniformly heated, inclined substrate. Although considerable experimental and theoretical studies have been performed regarding Rayleigh–Taylor instability, there is still a need to understand the instability mechanism in the presence of odd viscosity, which creates nondissipative effects. Odd viscosity represents broken time reversal and parity symmetries in the two-dimensional active chiral fluid and characterizes deviation of the system from one that contains a passive fluid. Adopting the long-wave approach allows a nonlinear free surface evolution equation of the thin film that considers the influence of odd viscosity to be derived. New, interesting linear stability analysis results illustrate that larger odd viscosity leads to a lower perturbation growth rate ωr and cutoff wave number kc. In other words, odd viscosity has a stabilizing effect on the Rayleigh–Taylor instability. Numerical simulations are conducted using the method of lines to solve the nonlinear evolution equation. The numerical results show that enhancing the odd viscosity effect suppresses the disturbance amplitude and wave frequency. In addition, the numerical results show that the inclination angle and the Weber number have stabilizing effects on the Rayleigh–Taylor instability. However, the Biot number has the opposite effect when the thin liquid film conductivity is poor. Also, the oscillation tends to accumulate downstream of the inclined substrate if the evolution time is sufficiently long.

Coupled dark energy model inspired from general conformal transformation

We study the coupled dark energy model constructed from the general conformal transformation in which the coefficient of the conformal transformation depends on both the scalar field and its kinetic term. Under this conformal transformation, the action for subclass of Degenerate Higher-Order Scalar-Tensor (DHOST) theories is related to the Einstein-Hilbert action. The evolution of the background universe has the scaling fixed point which corresponds to acceleration of the universe at late time. For the choices of parameters which make the late-time scaling point stable, the fixed point corresponding to $\phi$-matter-dominated-era ($\phi$MDE) is a saddle point, and the universe can evolve from radiation dominated epoch through $\phi$MDE before reaching the scaling point at late time with the cosmological parameters which satisfy the observational bound. During the $\phi$MDE, the effective equation of state parameter is slightly positive, so that one of possible mechanisms for alleviating the $H_0$ tension can be achieved. In this coupled dark energy model, the effective gravitational coupling for dark matter perturbations on small scales can be smaller than that in the $\Lambda$CDM model. Therefore a growth rate of the dark matter perturbations is suppressed compare with the $\Lambda$CDM model, which implies that the $\sigma_8$ tension could be alleviated.

Investigation on hydrogen/ethanol intrinsic flame instability

The instability of laminar premixed hydrogen–ethanol flame was studied under different initial pressure, hydrogen ratio, and equivalence ratio conditions by using a constant volume combustion bomb. The unstable laminar premixed flame was measured using its thermal expansion ratio, flame thickness, effective Lewis number, and logarithmic growth rate of perturbation. The results demonstrated that the thermal expansion ratio and effective Lewis number were insensitive to initial pressure variation, but hydrogen ratio variation was significantly affected. The linear stability analysis indicated that when the hydrogen ratio increased, the premixed flame became hydrodynamically unstable; thermal diffusion effects later stabilized the flame as the hydrogen ratio increased. The critical radius and Peclet number decreased with the increased equivalence ratio of a 20% hydrogen mixture, but both parameters increased with an increased equivalence ratio under an 80% hydrogen ratio. Finally, the growth rate of perturbation decreased when the equivalence ratio increased.

New parameterizations of generalized Chaplygin gas model constrained at background and perturbation levels

We study the main cosmological properties of the generalized Chaplygin gas (GCG) dark energy model at the background and perturbation levels. By using the latest cosmological data in both the background and perturbation levels, we implement a joint likelihood analysis to constrain the cosmological parameters of the model. Using the available expansion and growth rate data, we place constraints on the free parameters of the GCG model based on the statistical Markov chain Monte Carlo method. Then, the best-fit values of cosmological parameters and those of confidence regions are found. We obtain the best-fit value of the current expansion rate of the Universe in the GCG model and show that it is in good agreement with the $$\Lambda$$ CDM model. Moreover, the growth rate of matter perturbations is investigated in the context of a unified GCG model. It is shown that in this model, the dark energy component, like the $$\Lambda$$ sector in the $$\Lambda$$ CDM model, can suppress the amplitude of matter perturbations. We show that the growth rate of perturbations in GCG parametrization is consistent with cluster-scale observations similar to the case of the concordance $$\Lambda$$ CDM model. Our results show that the tension on $$\sigma _{8}$$ appeared in the concordance model can be alleviated in GCG cosmology.

Explaining multiple patches of aquatic vegetation through linear stability analysis

Aquatic vegetation is ubiquitous in lowland rivers, and it is typically present in the shape of spatial self-organized patches of biomass. In this work, we mathematically define the threshold conditions for the incipient formation of self-organized vegetated patterns in the shape of central or multiple row patches. The analysis is carried out through a linear stability analysis whereby the 2D eco-hydrodynamic model is linearized and the growth rate of small-scale perturbations is evaluated considering a basic state represented by an initially uniformly vegetated and straight channel having a certain aspect ratio and Froude number. Results illustrate that, for given vegetation properties, instability arises when both the Froude number and the aspect ratio are higher than a given threshold; in this case, self-organization occurs, and spatial patterns of patches will develop according to the wavelength associated to the maximum growth rate. Moreover, instability and self-organization take place when the undisturbed vegetation density is lower than upper bound; this suggests that densely vegetated channels, as in the case of rivers populated by invasive species, will not experience the formation of any spatial patterns.

An extended analysis for a generalized Chaplygin gas model

In this work, we have extended the analysis on the generalized Chaplygin gas (GCG) model as the unification of dark energy and dark matter. Specifically, we have shown that the model of our consideration known as the new generalized Chaplygin gas (NGCG) model, admits a scalar field description, which means that there exist a minimally coupled scalar field for a given scalar field potential where the equation of state is that of the NGCG. With the use of the later property we can construct the slow-roll parameters and derive the corresponding values for the spectral indices for the tensor to scalar perturbation and for the density perturbations. We have also studied the growth rate of matter perturbations in the NGCG scenario. Finally, we have studied the viability of the generalized second law of thermodynamics by assuming that the dynamical apparent horizon in a NGCG universe is endowed with Hawking temperature and Bekenstein entropy.

Morphological evolution of grain boundaries under lateral strains

A theory for the lateral strain-induced grain boundary instability is proposed by considering two crucial factors, namely, the dependence of the boundary energy on coincidence sites and the differences in elastic responses of the grain and the boundary regions. In contrast to the Asaro-Tiller-Grinfeld instability, where strains, however small, lead to breakup of the interfaces and the amplitudes of the perturbations are only a function of wavelength and time, we find that there exists a critical strain for the grain boundary instability to occur which is due to the periodicity of coincidence site lattices, and the growth rate of perturbations is dependent on the amplitude. These theoretical predictions are validated by the phase field crystal simulations in two dimensions. In addition, the amplitude-dependent growth rate gives rise to two distinct outcomes for the late stage evolution predicted by the proposed theory, namely, the grain boundary structural transformation and the dislocation emission, as seen in the phase field crystal simulations. Not only is the predicted oscillatory behavior of the growth rate observed in simulations, but also the phase diagram predicted by the theory is in quantitative agreement with the phase field crystal simulations.

Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes.

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl-von Kármán number Γ and the recently introduced Scriven-Love number SL, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions-reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher-Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

Growth factor parametrization

The growth rate of matter perturbations can be used to distinguish between different general relativity dark energy models and also between general relativity dark energy and modified gravity models in explaining cosmic acceleration. We propose as an approximation to the growth factor [Formula: see text] the analytical expression [Formula: see text] (with [Formula: see text]) when the radiation [Formula: see text] is included. The growth factor is analyzed for the dark energy models within general relativity. The growth index [Formula: see text] takes distinct values for each model. We find that the new analytical form [Formula: see text] approximates [Formula: see text] better than [Formula: see text].

Transition control of cylinder wake via Lorentz force

The flow around a cylinder is a typical flow acting as the oscillator, and the perturbations can grow with time at a fixed position. This phenomenon can induce the laminar-turbulent transition in the wake, thus increasing the vibrations of the cylinder as well as the noise in the flow system. There exist three control strategies, i.e. the streamwise Lorentz force from the electromagnetic actuator set on the windward surface named windward control, the leeward surface named leeward control, and the whole surface of cylinder named global control, which are adopted to modify the two-dimensional base flow, thereby reducing the growth rates of perturbations in the wake and changing the transition mode. According to the Floquet stability analysis, it is found that the growth rates of the transition modes A and B present small changes in the windward control, while the growth rates of the two modes decrease with the increase of the control number in the other two control cases. Comparing the inviscid growth rates induced by the elliptic instability and the hyperbolic instability with each other, it is observed that the high inviscid growth rate in the windward control can be similar to those without control, while the inviscid growth rates can decrease with the increase of control number in the other two control cases. Three-dimensional direct numerical simulations are performed to validate the control effects. The results shows that the three-dimensional shape of the wake is changed from mode B to mode A when the actuator is set on the leeward surface or the whole surface of the cylinder. This is consistent with the result from the Floquet stability analysis. In addition, the drag of the cylinder reduces 15.2% for the leeward control and 14.4% for the the global control.

Density maximum and finite Darcy–Prandtl number outlooks on Gill's stability problem subject to a lack of thermal equilibrium

The Gill stability problem encompasses the investigation of stability of natural convection flow in a vertical porous layer governed by Darcy's law under a local thermal equilibrium (LTE) perspective and was proved analytically by Gill [Gill, J. Fluid Mech. 35, 545–547 (1969)] that the flow is always stable. The present study deals with the simultaneous influence of the Darcy–Prandtl number and the density maximum property on Gill's stability problem subject to a lack of thermal equilibrium. The density variation with fluid temperature is assumed to be pure quadratic, and it is established that the linear stability of the basic state for a three-dimensional problem can be Squire-transformed. It is observed that Gill's proof of linear stability cannot be extended to the present model and hence we approached numerically by evaluating the growth rate of normal mode perturbations. The neutral stability curves are obtained, and the critical parameters at the onset of instability are determined. Even though the isolation presence of time-dependent velocity term and the density maximum property evidence the basic flow to be stable for all infinitesimal perturbations, their simultaneous occurrence induces instability under certain parametric conditions. The finite range of values of the scaled interphase heat transfer coefficient within which the flow is stable is found to increase with increasing Darcy–Prandtl number but vanishes with increasing porosity-modified conductivity ratio. Moreover, the basic state becomes stable when the Darcy–Prandtl number is larger than 7.08. The results of LTE model are delineated as a particular case from the present study.

Trapped particle instability in : I homogeneous Vlasov plasmas

Kinetic instability due to trapped particles in non-linear evolution of large amplitude electrostatic waves i.e BGK (Bernstein-Greene-Kruskal) mode is investigated in a one dimensional, collisionless, homogeneous Vlasov-Poisson plasma with immobile ions and kinetic electrons. Considering a cosinusoidal density perturbation with non-linear perturbation amplitude α = 0.05 as starting point, we have demonstrated that long time BGK solutions with scale (where corresponds to the longest length scale in the system) are not stable due to Landau growth in the secondary sideband modes. This growth in the sideband modes is primarily related to trapped particles in the potential well of the perturbation which leads to trapped particle instability when the amplitude of the sidebands become comparable to that of the primary nonlinear mode. In the past, to explain trapped particle instability, two physical mechanisms were held responsible, namely, wave particle interaction phenomenon at resonance location v ϕ = ω/k and mode coupling interaction phenomenon between primary and secondary sideband modes. We have demonstrated and emphasized both the phenomena in our study. In addition, effect of primary mode perturbation amplitude on trapped particle instability is investigated and growth rates corresponding to secondary sideband modes are reported alongwith a new scaling law for detrapping time as a function of perturbation amplitude. Also, scaling of growth rates corresponding to lower and upper sideband modes with respect to perturbation amplitude is obtained which demonstrates the existence of a transition point at α = 0.075 between small and large perturbation amplitudes and growth rate scales as γ ∼ α 2 for α < 0.075 whereas γ ∼ α 1/2 for α > 0.075.

The mechanism of formation of surface micro- and nanostructures in the AlCoCrFeNi high-entropy alloy during electron-beam treatment

The paper is devoted to a study of the formation of submicron and nanosized cellular crystallization structures on the surface of a high-entropy AlCoCrFeNi alloy irradiated by high current electron beams with the energy density varying from 10 to 30 J / cm2 and a pulse time of 200 μs. The study revealed that the combination of thermal, evaporation-capillary and thermoelectric instabilities induces the formation of submicro- and nanodimensional cellular structures similarly to high-entropy alloys. The proposed dispersion equation was analyzed to detect the conditions for the generation of this instability. The importance of the evaporation process was investigated by finding a solution to the heat problem with phase transformations. The temperature distribution over time calculated at different distances from the surface of the alloy samples demonstrated that the surface temperature is lower than the evaporation temperature for the energy density Es < 30 J / cm2, therefore, the term of evaporation in the dispersion equation was ignored for these values of the energy density. The analysis of the dispersion equation showed that for Es = 30 J / cm2, the wavelength λm with the maximal growth rate of perturbations on the melt surface gains a value in the submicro-and nano-range, provided that the thermoelectric coefficient equals to ~4 –10 V / K, and the pressure of evaporation is ~105 Pa. If we exclude thermoelectric effects, these values λm are observed for the pressure of evaporation ~1011 Pa. The wavelength λm was revealed to decrease according to a power law as the beam energy density increases.

Comparing entropy inspired holographic dark energy models through statefinder hierarchy and growth rate of perturbations

In this paper, we have investigated some recently proposed entropy-based versions of various HDE models, namely, the TADE, THDE, RHDE and SMHDE for different values of model parameter [Formula: see text] with the help of two diagnostic tools, in the context of a flat Friedmann–Lema[Formula: see text]tre–Robertson–Walker Universe. The statefinder hierarchy is the first diagnostic tool, by which we examine these DE models. The evolution of statefinder hierarchy parameters [Formula: see text], [Formula: see text] [Formula: see text], [Formula: see text] has been investigated by plotting against redshift [Formula: see text]. The evolutionary trajectories of all the DE models approach the [Formula: see text]CDM model, except the TADE model for some values of [Formula: see text] at late time, are well discriminated with the [Formula: see text]CDM model at early time. To get more clear discrimination among the DE models at late time, we have used the CND, i.e. [Formula: see text][Formula: see text], where [Formula: see text] indicates the fractional growth parameter. The evolutionary trajectories of [Formula: see text] and [Formula: see text] show different characteristics and the departure from [Formula: see text]CDM could be well evaluated.

A Surrogate-Based Method for Compressible Boundary-Layer Transition Prediction

To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as -envelope or -database method. Nevertheless, building such a model is challenging when it comes to compressible flows, as the transition mechanism is more complex and multiple flow parameters should be taken into consideration. To address this problem, this paper proposes an efficient surrogate-based method for compressible boundary layers that uses pretrained surrogate models to substitute linear stability analysis, concerning stability analysis of both Tollmien–Schlichting and Mack modes, as well as transition prediction of flow over arbitrary-shaped airfoils. The proposed method is demonstrated by stability analysis of compressible flat-plate boundary layers at a wide range of Mach numbers of . It is also validated by transition prediction of flow over a low-speed natural-laminar-flow (NLF) airfoil NLF-0416 and a transonic NLF airfoil NPU-LSC-72613. Besides, a sample partitioning method is presented to accelerate surrogate-model training with large samples. Results show that the predicted growth rates of perturbations, factors, and corresponding transition locations by our method of using surrogate-based stability analysis agree well with those by a standard method of solving full linear stability equations.

Ensemble Transform Kalman Incremental Smoother and Its Application to Data Assimilation and Prediction

The analysis correction made by data assimilation (DA) can introduce model shock or artificial signal, leading to degradation in forecast. In this study, we propose an Ensemble Transform Kalman Incremental Smoother (ETKIS) as an incremental update solution for ETKF-based algorithms. ETKIS not only has the advantages as other incremental update schemes to improve the balance in the analysis but also provides effective incremental correction, even under strong nonlinear dynamics. Results with the shallow-water model show that ETKIS can smooth out the imbalance associated with the use of covariance localization. More importantly, ETKIS preserves the moving signal better than the overly smoothed corrections derived by other incremental update schemes. Results from the Lorenz 3-variable model show that ETKIS and ETKF achieve similar accuracy at the end of the assimilation window, while the time-varying increment of ETKIS allows the ensemble to avoid strong corrections during strong nonlinearity. ETKIS shows benefits over 4DIAU by better capturing the evolving error and constraining the over-dispersive spread under conditions of long assimilation windows or a high perturbation growth rate.

Discrete SQG models with two boundaries and baroclinic instability of jet flows

In this paper, new vertically discrete versions of the surface quasigeostrophic (SQG) model with two boundaries are formulated. For any number of partition levels, the equations of the discrete model are written in the form of conservation laws for two Lagrangian invariants, which have the meaning of buoyancy distributions at the horizontal boundaries of the fluid layer. The values of the invariants are expressed in terms of the values of the stream function at two internal levels and contain higher order elliptic operators. The use of discrete models greatly simplifies the solution of problems of the linear theory of hydrodynamic stability and provides high accuracy even with a small number of vertical discrete levels. Using the two-level version of the SQG model, which is similar to the classical two–layer Phillips model, we investigated the linear stability of jet flows induced by piecewise constant boundary distributions of buoyancy. For these flows, analytical expressions for the growth rate of perturbations have been obtained and it is shown that the most unstable perturbation has a wavelength of the order of the Rossby baroclinic radius of deformation. Flows with vertical shear induced by smooth and slowly varying boundary buoyancy distributions are also considered. The instability of these flows is found to be absolute, that is, independent of the velocity profile horizontal structure.

Statefinder hierarchy model for the Barrow holographic dark energy

In this paper, we have used the state finder hierarchy for Barrow holographic dark energy (BHDE) model in the system of the FLRW Universe. We apply two DE diagnostic tools to determine ΛBHDE model to have various estimations of ▵. The first diagnostic tool is the state finder hierarchy in which we have studied S3(1)S4(1), S3(2)S4(2) and second is the composite null diagnostic (CND) in which the trajectories (S3(1)−ϵ), (S4(1)−ϵ), (S3(2)−ϵ)(S4(2)−ϵ) are discussed, where ϵ is fractional growth parameter. The infrared cut-off here is taken from the Hubble horizon. Finally, together with the growth rate of matter perturbation, we plot the state finder hierarchy that determines a composite null diagnosis that can differentiate emerging dark energy from ΛCDM. In addition, the combination of the hierarchy of the state finder and the fractional growth parameter has been shown to be a useful tool for diagnosing BHDE, particularly for breaking the degeneracy with different parameter values of the model.

Matter perturbations in Einstein dark energy model

We consider the growth rate of matter perturbations in the Einstein dark energy theory. The theory consists of the Einstein–Hilbert Lagrangian plus the trace of the energy momentum tensor, coupled non-minimally to a dynamical vector field. We will show that the theory has three fixed points corresponding to the dust, radiation and de Sitter universes. Due to the present of trace of the energy–momentum tensor in the Lagrangian, the fixed points occurs in different locations compared to Lambda CDM theory. We will analyze the theory with and without cosmological constant. We will fit the model parameters using two independent data sets corresponding to the Hubble parameter H and also fsigma _8. The theory is then shown to be consistent with observational data.

Gravitational wave spectra from oscillon formation after inflation

We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute both the properties of the emitted gravitational waves as well as the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape of the spectrum and the amplitude of emitted gravitational waves have a universal feature with the peak around the physical wavenumber k/a ∼ m at the inflaton oscillation starting period, irrespective of the exact potential shape. This can be used as a smoking-gun for deducing the existence of a violent preheating phase and possible oscillon formation after inflation. Despite this apparent universality, we also find differences in the shape of the spectrum of emitted gravitational waves between the two families of potentials, leading to discriminating features between them. In particular, all potentials show the emergence of a two-peak structure in the gravitational wave spectrum, arising at the time of oscillon formation. However, potentials that exhibit efficient parametric resonance tend to smear out this structure and by the end of the simulation the two-peak structure is replaced by one broad peak in the GW spectrum. We further compute the number density and properties of the produced oscillons for each potential choice, finding differences in the number density and size distribution of stable oscillons and transient overdensities. We also perform a linear fluctuation analysis and use the corresponding Floquet charts to relate the results of our simulations to the structure of parametric resonance for the various potential types. We find that the growth rate of the scalar perturbations and the associated oscillon formation time are sensitive to the small-field shape of a potential while the macroscopic physical properties of oscillons such as the total number depend on the large-field shape of a potential.