Entropy Perturbations Research Articles

Towards a momentum potential theory for reacting flows

Mutual coupling of (thermofluiddynamic) modes of perturbations can affect the thermo-acoustic stability of combustors and contribute to combustion noise. For example, vortical or entropic perturbations can be transferred to acoustic perturbations if accelerated by the mean flow. The decomposition of perturbation fields into the respective modes and a linear description of their interactions in terms of fluctuating primitive variables is challenging. In contrast, Doak’s momentum potential theory promises an unambiguous decomposition in terms of momentum fluctuations, which is not limited to the linear regime. Whereas classical momentum potential theory takes into account hydrodynamic, acoustic and entropic modes in unconfined flows, the investigation of noise generation in combustion chambers requires the extension of the momentum potential theory to capture modes linked to the fluctuation of species mass fractions (“species mode”) arising from the change in chemical composition due to the reaction. Furthermore, a rigorous treatment of boundary conditions due to the confinement of the flow inside the combustor is required. The herein presented extension to reactive flows consists of two steps, (i) the formulation of a potential for momentum fluctuations related to species modes and (ii) identification of the total fluctuating enthalpy related to species modes. The extended theory is applied to post-process computational fluid dynamic simulation data of the propagation of entropy and species perturbations through one-dimensional ducts, nozzles and premixed flames. We find that although momentum potential theory offers a complete decomposition of momentum perturbations for reactive flows, the meaningful interpretation of this decomposition is rather challenging, even for non-reactive flows.

Testing scale-invariant inflation against cosmological data

There is solid theoretical and observational motivation behind the idea of scale-invariance as a fundamental symmetry of Nature. We consider a recently proposed classically scale-invariant inflationary model, quadratic in curvature and featuring a scalar field non-minimally coupled to gravity. We go beyond earlier analytical studies, which showed that the model predicts inflationary observables in qualitative agreement with data, by solving the full two-field dynamics of the system — this allows us to corroborate previous analytical findings and set robust constraints on the model's parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We demonstrate that scale-invariance constrains the two-field trajectory such that the effective dynamics are that of a single field, resulting in vanishing entropy perturbations and protecting the model from destabilization effects. We derive tight upper limits on the non-minimal coupling strength, excluding conformal coupling at high significance. By explicitly sampling over them, we demonstrate an overall insensitivity to initial conditions. We argue that the model predicts a minimal level of primordial tensor modes set by r ≳ 0.003, well within the reach of next-generation CMB experiments. These will therefore provide a litmus test of scale-invariant inflation, and we comment on the possibility of distinguishing the model from Starobinsky and α-attractor inflation. Overall, we argue that scale-invariant inflation is in excellent health, and possesses features which make it an interesting benchmark for tests of inflation from future CMB data.

Freestream Temperature Effects on the Receptivity of Hypersonic Boundary Layer Induced by Finite-Amplitude Pulse Entropy Waves

The unsteady hypersonic flow under finite amplitude pulse entropy perturbation at different freestream temperatures was calculated by direct numerical simulation. The flow response characteristics under the perturbation of entropy waves in freestreaming are analyzed. The temperature effect of freestreaming is studied based on the sensitivity of the boundary layer caused by pulse entropy perturbation. The results show that the higher freestream temperature promotes the first growth of the above third-order modes after leaving the head region, and strongly inhibits the first attenuation. The influence of the freestream temperature on the evolution of the induced disturbance wave is more significant than that on the development of the main flow disturbance waves. Low freestream temperature can suppress the attenuation of the modes below the second order. As the disturbance wave evolves downstream, the frequency band of the finite frequency disturbance wave gradually narrows, and the frequency band narrows faster when the temperature of freestreaming is low than when the temperature of freestreaming is high.

Adiabatic and isocurvature perturbations in extended theories with kinetic couplings

The scalar field sector in low-energy effective field theories motivated by string theory often contains several scalar fields, some of which possess non-standard kinetic terms. In this paper we study theories with two scalar fields, in which one of the fields has a non-canonical kinetic term. The kinetic coupling is allowed to depend on both fields, going beyond the work in the literature, which usually considers the case of the coupling to depend on the other field only. Our aim is to study adiabatic and isocurvature perturbations in these extended theories. Our results show that the evolution equation for the curvature perturbation does not change when allowing the coupling to depend on both fields, while the effective mass of the entropy perturbation changes. We find expressions for the spectral index and its running at horizon crossing and at the end of inflation. We apply the formalism and study three phenomenological models, with different kinetic couplings.

Impact of Boundary Conditions on Acoustic Excitation of Entropy Perturbations in a Bounded Volume of Newtonian Gas

Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsive sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.

Magnetosonic Excitation of the Entropy Perturbations in a Plasma with Thermal Conduction Depending on Temperature

Nonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle θ (0≤θ≤π) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear excitation of the entropy mode. A dynamic equation is derived which describes excitation of perturbation in the entropy mode in the field of dominant magnetosonic mode. Effects associatiated with temperature dependent and anisotropic thermal conduction are considered and discussed.

Use of Composite Multivariate Multiscale Permutation Fuzzy Entropy to Diagnose the Faults of Rolling Bearing.

The study focuses on the fault signals of rolling bearings, which are characterized by nonlinearity, periodic impact, and low signal-to-noise ratio. The advantages of entropy calculation in analyzing time series data were combined with the high calculation accuracy of Multiscale Fuzzy Entropy (MFE) and the strong noise resistance of Multiscale Permutation Entropy (MPE), a multivariate coarse-grained form was introduced, and the coarse-grained process was improved. The Composite Multivariate Multiscale Permutation Fuzzy Entropy (CMvMPFE) method was proposed to solve the problems of low accuracy, large entropy perturbation, and information loss in the calculation process of fault feature parameters. This method extracts the fault characteristics of rolling bearings more comprehensively and accurately. The CMvMPFE method was used to calculate the entropy value of the rolling bearing experimental fault data, and Support Vector Machine (SVM) was used for fault diagnosis analysis. By comparing with MPFE, the Composite Multiscale Permutation Fuzzy Entropy (CMPFE) and the Multivariate Multiscale Permutation Fuzzy Entropy (MvMPFE) methods, the results of the calculations show that the CMvMPFE method can extract rolling bearing fault characteristics more comprehensively and accurately, and it also has good robustness.

Indirect noise from weakly reacting inhomogeneities

Indirect noise is a significant contributor to aircraft engine noise, which needs to be minimized in the design of aircraft engines. Indirect noise is caused by the acceleration of flow inhomogeneities through a nozzle. High-fidelity simulations showed that some flow inhomogeneities can be chemically reacting when they leave the combustor and enter the nozzle (Giusti et al., Trans. ASME J. Engng Gas Turbines Power, vol. 141, issue 1, 2019). The state-of-the-art models, however, are limited to chemically non-reacting (frozen) flows. In this work, first, we propose a low-order model to predict indirect noise in nozzle flows with reacting inhomogeneities. Second, we identify the physical sources of sound, which generate indirect noise via two physical mechanisms: (i) chemical reaction generates compositional perturbations, thereby adding to compositional noise; and (ii) exothermic reaction generates entropy perturbations. Third, we numerically compute the nozzle transfer functions for different frequency ranges (Helmholtz numbers) and reaction rates (Damköhler numbers) in subsonic flows with hydrogen and methane inhomogeneities. Fourth, we extend the model to supersonic flows. We find that hydrogen inhomogeneities have a larger impact on indirect noise than methane inhomogeneities. Both the Damköhler number and the Helmholtz number markedly influence the phase and magnitude of the transmitted and reflected waves, which affect sound generation and thermoacoustic stability. This work provides a physics-based low-order model which can open new opportunities for predicting noise emissions and instabilities in aeronautical gas turbines with multi-physics flows.

Acoustics of thermoviscous fluids: The Kirchhoff-Helmholtz representation in generalized form.

The Kirchhoff-Helmholtz representation of linear acoustics is generalized to thermoviscous fluids, by deriving separate bounded-region equations for the acoustic, entropy, and vorticity modes in a uniform fluid at rest. For the acoustic and entropy modes we introduce modal variables in terms of pressure and entropy perturbations, and develop asymptotic approximations to the mode equations that are valid to specified orders in two thermoviscous parameters. The introduction of spatial windowing for the mode variables leads to surface source and dipole distributions as a way of representing boundary conditions for each mode. For the acoustic mode the boundary source distribution is expressible in terms of the fluid normal velocity, the normal heat flux, and the vector ω×n̂, where ω is the vorticity on the boundary and n̂ is the unit normal; only the first of these is present in the usual lossless-fluid version of the Kirchhoff-Helmholtz representation. Use of the generalized thermoviscous representation to project exterior sound fields from surface data, where the data may contain contributions from all three linear modes, is shown to be robust to cross-modal contamination. The asymptotic limitations of the thermoviscous modal equations are discussed in an appendix.

Entropy bounds for multi-word perturbations of subshifts

AbstractGiven a subshift $\Sigma $ of finite type and a finite set S of finite words, let $\Sigma \langle S\rangle $ denote the subshift of $\Sigma $ that avoids S. We establish a general criterion under which we can bound the entropy perturbation $h(\Sigma ) - h(\Sigma \langle S\rangle )$ from above. As an application, we prove that this entropy difference tends to zero with a sequence of such sets $S_1, S_2,\ldots $ under various assumptions on the $S_i$ .

On the choice of entropy variables in multifield inflation

We discuss the usefulness and theoretical consistency of different entropy variables used in the literature to describe isocurvature perturbations in multifield inflationary models with a generic curved field space. We clarify which is the proper entropy variable to be used to match the evolution of isocurvature modes during inflation to the one after the reheating epoch in order to compare with observational constraints. In particular, we find that commonly used variables, as the relative entropy perturbation or the one associated to the decomposition in tangent and normal perturbations with respect to the inflationary trajectory, even if more useful to perform numerical studies, can lead to results which are wrong by several orders of magnitude, or even to apparent destabilisation effects which are unphysical for cases with light kinetically coupled spectator fields.

Universe before Big Bang

The ghost condensation of the early universe in a pre-big bang phase has been presented in this paper through duration of a non-singular bounce. The undergoing universe contracts and passes smoothly in an expanding universe via a post-big bang phase. Initially developing and then taming any ghost like instabilities, the Null Energy Condition (NEC) is explicitly violated through the curvature mechanism of an adiabatic perturbed metric. The vacuum state of the ongoing phase is stabilized via a Lagrangian that in essence stabilizes the vacuum state under the higher order derivatives. The violation of the NEC regards a catastrophic vacuum instability, which re-emerges with a correction valid at small energies and momenta, below the UV-cut-off scale that, could potentially be problematic if one tries to construct a UV-completed theory of this Ekpyrotic model. The scale-invariant curvature perturbation, that arises and is sourced out of the scale-invariant entropy perturbations sourced by 2-Ekpyrotic scalar fields, that, in contrast, becomes constant on the super-horizon limits, due to the non-singular nature of the background geometry. Apart, from the ghost condensates, this theory addresses the new Ekpyrotic theory which in order becomes a distinguishable alternative to inflation theory for the birth of the universe. As per the recent WMAP data, the Ekpyrotic model has a spectral red tilt that shows the bounced scalar potential falling through a negative phase shift during the matter-fluid fluctuations in the hot big bang phase.

Multifluid cosmology in f(G) gravity

The treatment of (1+3)-covariant perturbation in a multifluid cosmology with the consideration of [Formula: see text] gravity, [Formula: see text] being the Gauss–Bonnet term, is done in this paper. We define a set of covariant and gauge-invariant variables to describe density, velocity and entropy perturbations for both the total matter and component fluids. We then use different techniques such as scalar decomposition, harmonic decomposition, quasi-static approximation together with the redshift transformation to get simplified perturbation equations for analysis. We then discuss a number of interesting applications like the case where the universe is filled with a mixture of radiation and Gauss–Bonnet fluids as well as dust with Gauss–Bonnet fluids for both short- and long-wavelength limits. Considering polynomial [Formula: see text] model, we get numerical solutions of energy density perturbations and show that they decay with increase in redshift. This feature shows that under [Formula: see text] gravity, specifically under the considered [Formula: see text] model, one expects that the formation of the structure in the late Universe is enhanced.

Initial conditions for the scalaron dark matter

The scalaron of the metric f(R) gravity can constitute dark matter if its mass is in the range 4 meV ≲ m ≲ 1 MeV. We give an overview of such f(R) gravity theory minimally coupled to the Standard Model. Similarly to other dark-matter models based on scalar fields, this model has the issue of initial conditions. Firstly, the initial conditions for the scalaron are to be tuned in order to produce the observed amount of dark matter. Secondly, the primordial spatial inhomogeneities in the field are to be sufficiently small because they generate entropy (or isocurvature) perturbations, which are constrained by observations. We consider these issues in the present paper. The initial conditions for the scalaron presumably emerge at the inflationary stage. We point out that the homogeneous part of the scalaron initial value is largely unpredictable because of quantum diffusion during inflation. Thus, to account for the observed amount of dark matter, one has to resort to anthropic considerations. Observational constraints on the primordial spatial inhomogeneity of the scalaron are translated into upper bounds on the energy scale of inflation, which happen to be low but not too restrictive.

A fake instability in string inflation

In type IIB fibre inflation models the inflation is a Kähler modulus which is kinetically coupled to the corresponding axion. In this setup the curvature of the field space induces tachyonic isocurvature perturbations normal to the background inflationary trajectory. However we argue that the associated instability is unphysical since it is due to the use of ill-defined entropy variables. In fact, upon using the correct relative entropy perturbation, we show that in fibre inflation axionic isocurvature perturbations decay during inflation and the dynamics is essentially single-field.

Model-independent approach to effective sound speed in multi-field inflation

For any physical system satisfying the Einstein’s equations, the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed, valid for any system with a well defined energy-stress tensor, including multi-fields models of inflation. We derive a general model-independent formula for the effective sound speed of comoving adiabatic perturbations, valid for a generic field-space metric, without assuming any approximation to integrate out entropy perturbations, but expressing the momentum-dependent effective sound speed in terms of the components of the total energy-stress tensor. As an application, we study a number of two-field models with a kinetic coupling between the fields, identifying the single curvature mode of the effective theory and showing that momentum-dependent effective sound speed fully accounts for the predictions for the power spectrum of curvature perturbations. Our results show that the momentum-dependent effective sound speed is a convenient scheme for describing all inflationary models that admit a single-field effective theory, including the effects of entropy pertubations present in multi-fields systems.

Sound generated by axisymmetric non-plane entropy waves passing through flow contractions

For a single-component perfect gas, entropy perturbations are associated with the difference between the overall density fluctuation and that coming from the acoustic perturbation. Entropy perturbations can generate sound when accelerated/decelerated by a non-uniform flow and this is highly relevant to thermoacoustic instabilities for gas turbines and rocket engines, and to noise emission for aero-engines. Widely used theories to model this entropy-generated sound rely on quasi-1D assumptions for which questions of validity were raised recently from both numerical and experimental studies. In the present work, we build upon an acoustic analogy theory for this problem. This theory was initiated by Morfey (J. Sound Vib. 1973) and Ffowcs Williams and Howe (J. Fluid Mech. 1975) about 50 years ago and extended recently by Yang, Guzmán-Iñigo and Morgans (J. Fluid Mech. 2020) to study the effect of non-plane entropy waves at the inlet of a flow contraction on its sound generation. Comparisons against both numerical simulations and previous theory are performed to validate the results.

Effective action, spectrum and first law of wedge holography

In this paper, we study the effective action, the mass spectrum and the first law of entanglement entropy for a novel doubly holographic model called wedge holography. We work out the effective action of quantum gravity on the branes. In the perturbative formulation, it is given by an infinite sum of Pauli-Fierz actions. In the non-perturbative formulation, the effective action is composed of a higher derivative gravity and a matter action. Usually, a higher derivative gravity can be renormalizable but suffers the ghost problem. For our case, since the effective theory on the brane is equivalent to Einstein gravity in the bulk, it must be ghost-free. We notice that the matter action plays an important role in eliminating the ghost. We also provide evidences that the higher derivative gravity on the brane is equivalent to a ghost-free multi-gravity. Besides, we prove that the effective action yields the correct Weyl anomaly. Interestingly, although the effective action on the brane is an infinite tower of higher derivative gravity, the holographic Weyl anomaly is exactly the same as that of Einstein gravity. We also analyze the mass spectrum of wedge holography. Remarkably, there is always a massless mode of gravitons on the end-of-the-world branes in wedge holography. This happens because one imposes Neumann boundary condition on both branes. On the other hand, the massless mode disappears if one imposes Dirichlet boundary condition on one of the branes as in brane world theory and AdS/BCFT. Finally, we verify the first law of entanglement entropy for wedge holography. Interestingly, the massive fluctuations are irrelevant to the first order perturbation of the holographic entanglement entropy. Thus, in many aspects, the effective theory on the brane behaves like massless Einstein gravity.

Dark matter from entropy perturbations in curved field space

The accumulated energy density of the excited entropy modes in multiple field inflationary scenarios can play the role of dark matter. In the usual case of a flat field space without any turning trajectory, only light superhorizon entropy modes can be excited through the gravitational instability. In the case of a negatively curved field space, we show that subhorizon entropy modes can be excited as well through the tachyonic instability induced by the negative curvature of the field space. The latter allows for production of entropy modes with masses larger than or at the order of the Hubble expansion rate during inflation, leading to a new dark matter scenario. Due to the contribution of subhorizon modes, the corresponding spectral density has a peak at a scale smaller than its counterpart in the models based on a flat field space. This difference makes our model observationally distinguishable.

Multifield mimetic gravity

In this paper, we extend the mimetic gravity to the multifield setup with a curved field space manifold. The multifield mimetic scenario is realized via the singular limit of the conformal transformation between the auxiliary and the physical metrics. We look for the cosmological implications of the setup where it is shown that at the background level the mimetic energy density mimics the roles of dark matter. At the perturbation level, the scalar field perturbations are decomposed into the tangential and normal components with respect to the background field space trajectory. The adiabatic perturbation tangential to the background trajectory is frozen while the entropy mode perpendicular to the background trajectory propagates with the speed of unity. Whether or not the entropy perturbation is healthy directly depends on the signature of the field-space metric. We perform the full nonlinear Hamiltonian analysis of the system with the curved field space manifold and calculate the physical degrees of freedom verifying that the system is free from the Ostrogradsky-type ghost.