Entropic Mode Research Articles

Plasma-Fluid Energy Transfers in Plasma Assisted Ignition

ABSTRACT A three-dimensional model of plasma-fluid coupling is developed, including the Navier-Stokes, the drift-diffusion, and the radiative transfer equations, to investigate the energy transfers between plasma and fluid in repetitive-pulsed discharge ignition. A modal decomposition of the energy transfer is performed to determine the contributions of plasma to the mechanical coupling and pressure losses during ignition. The detailed model is validated against experiments and compared against a well-known empirical approximation. The main findings are that the modal coupling is dependent on the geometry of the electrodes and flat electrodes provide the strongest mechanical transfer into the acoustic modes. Uniform flow conditions decrease the extent of the mechanical coupling due to the decreased pressure velocity correlations in shear flows. Water vapor production reduces the entropic mode of the energy coupling.

Dispersion analysis of numerical schemes using 2D compressible linearized Navier–Stokes equation for direct numerical simulation

The dispersion analysis of numerical schemes for finite difference computations based on 2D compressible linearized Navier–Stokes equation (LNSE) is presented here. The analysis presents a more holistic view of the applicability of the schemes while solving compressible NSE, rather than analyzing model 1D or 2D convection or convection–diffusion equations. A theoretical dispersion analysis of model 2D−LNSE is performed first which categorizes it into vortical, entropic and two acoustic modes. The variation of the theoretical dispersion relation for each of the modes with wavenumber, Mach number and Reynolds number is analyzed. It is noted that the entropic mode is the most diffusive among all the modes. Two acoustic modes are less diffusive than the vortical mode up to a certain absolute wavenumber Kb depending upon the Mach number and Reynolds number. It is also shown that while vortical and entropic modes are non-dispersive in nature, the two acoustic modes are dispersive only up to K=Kb. Next, numerical dispersion and diffusion corresponding to each of the modes are analyzed for second order central difference (CD2) and sixth order central compact difference scheme proposed in Lele (J. Comput. Phys., Vol-103(1), 1992) for discretization of convective and diffusive derivatives using fourth-order Runge–Kutta (RK4) time integration method. Results show the existence of numerical unstable zone and regions where spurious upstream propagating waves are noted for each of the modes in the spectral plane. From these and the relative size of the dispersion relation preserving zones for the modes, applicability of the numerical schemes can be assessed. Analysis of the variation of the numerical unstable zone with Mach number, orientation of the mean flow and the unit CFL number Nc=Δt/Δx for each of the modes are presented. It is noted that entropic mode displays the lowest critical CFL number of all the four modes. Lastly, linearized and nonlinear numerical simulations for the convection of acoustic and vortical pulse with varying spectral content are presented. The linearized simulations are also compared with corresponding exact solutions. Obtained results indicate a direct correspondence of the stability analysis performed based on 2D−LNSE even for nonlinear simulations which result in additional intra modal energy transfer and interactions.

Velocity and temperature fluctuations in a high-speed shock–turbulence interaction

Abstract

Revisiting non-Gaussianity in multifield inflation with curved field space

Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.

Cascades of temperature and entropy fluctuations in compressible turbulence

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

Diagnostics of Atmospheric Disturbances Using the Method of Projection Operators

Theoretical foundations of the diagnostics of wave disturbances of the atmosphere, including slowly varying ones, are considered. Special attention is given to the latter type of variations, such as the entropic mode. The mathematical apparatus of the theory is based on the projection operators for the problem of boundary regime propagation. This procedure makes it possible to perform diagnostics using measurements in the neighborhood of a single point. A one-dimensional problem of acoustic waves in an exponential atmosphere is analyzed in detail.

Entropic binding mode preference in cooperative homo-dimeric drug–DNA recognition

The present work reveals the entropic preference in the two-step binding process of small molecule DNA minor groove binders (MGBs), involving the formation of a dimer in free solution followed by the binding of that dimer to DNA, which contrasts with the sequential or simultaneous cooperative binding of two unbound MGB molecules with DNA that is implicitly assumed in the majority of reported DNA–MGB binding studies. The results are generalized for the n-mer binding case and the methodological outcomes are discussed.

Exploring the glass transition region: crowding effect, nonergodicity and thermorheological complexity

Monte Carlo simulations performed on multiple polymer chains have produced accurate relaxation modulus Gs(t) curves which match the experimental G(t) curves of polystyrene reasonably well, over a wide temperature range around the glass transition region. The inter-segmental interactions, defined in terms of ε* (well depth) and σ (monomer size), exert a strong influence on the modulus, the length scale and the relaxation time scale of the system. Judicious selection of these interaction parameters has enabled us to create the whole range of temperature dependence of the thermorheological complexity, from ΔT = 40 °C to ΔT = 0 °C. Near the glass transition temperature, the development of nonergodicity vis-à-vis a crowding effect in the system emerges naturally from the analysis of the G(t) line shapes. The entropic slow mode is well described by the Rouse theory and the energetic fast mode shifts to longer time scales, revealing the generic behavior of the thermorheological complexity. Typical Gs(t) curves, when partitioned into glassy and rubbery components, are shown to obey Inoue-Okamoto-Osaki's modified stress-optical rule, with different stress-optical coefficients for each component. Closer to the glass transition temperature, the distance of the closest monomer shows a considerable increase, suggesting a penetrable resistance to the approach of another monomer. The parameter σ represents the characteristic length scale of the system in the glassy region. The thermorheological complexity incorporates the dynamic length scale of structural relaxation, increasing with the decrease of temperature towards the glass transition point.

Thermorheological complexity revisited: A simple Monte Carlo simulation scheme to create the near Tg behavior in linear homopolymer melts

Using a coarse-grained multiple chain description for a homopolymer system which includes the inter-segmental interactions (ISI) of the chains, Monte Carlo simulations were performed in order to generate fairly accurate relaxation modulus Gs(t) curves which could be matched with the experimental G(t) curves, over a wide temperature range around the glass transition point (Tg). The ISI, defined in terms of ε* (well-depth) and σ (bead diameter), exert strong influence on the modulus, length scale and relaxation time scale of the system. Judicious combinations of the ISI parameters lead to the creation of the whole range of the temperature dependence (from ΔT = 40 °C to ΔT = 0 °C) of the thermorheological complexity in the system. Near the Tg, the development of nonergodicity in the system emerges from the analysis of the G(t) line shapes. The entropic slow mode is well described by the Rouse theory and the energetic fast mode shifts to longer time scales, revealing the generic behavior of the thermorheological complexity. Typical Gs(t) curves, when partitioned into glassy and rubbery components, could be shown to obey Inoue et al.'s modified stress-optical rule, with different stress-optical coefficients for each. Closer to the Tg, the distance of the closest bead shows a considerable increase, suggesting a penetrable resistance to the approach of another bead. The bead size σ represents the characteristic length scale of the system in the glassy region. The thermorheological complexity thus incorporates the dynamic length scale of the structural relaxation, increasing with the decrease of temperature towards the Tg.

Avoided crossings of modes of a finite target with adiabat shaping in inertial fusion implosions

In Inertial Confinement Fusion (ICF), a cold target material is accelerated by a hot low density plasma. In this work, the small amplitude disturbances in ablative Rayleigh-Taylor instability in the presence of entropy gradients is studied using a sharp boundary approximation, being the inverse entropy-gradient scale length the quantity Ko = ∝LnSo/∝y. For simplicity, the target considered here is a finite incompressible slab. Due to ablation, the phenomenon of the interactions of two types of modes (Rayleigh mode and entropic mode) is shown. This manifest itself in the occurrence of rapid shifts of rate growth (bumping, avoided crossings). The entire situation is strongly reminiscent of the well-know "avoided crossings" of modes of two coupled oscillators. The growth rate of one mode (Rayleigh mode) approaches that of another one (entropic mode) which is "bumped" to a quite different rate growth, while the "bumping" mode settles at roughly at the original rate growth of the bumped mode.

Using Boundary Conditions to Account for Mean Flow Effects in a Zero Mach Number Acoustic Solver

The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modeling of a compressor or a turbine must be prescribed under an energetical form instead of the classical acoustic variables. Then we demonstrate the feasibility to take into account the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new delayed entropy coupled boundary condition (DECBC) and proves able to capture a family of low frequency entropic mode even though no mean flow term is included in the fluctuating pressure equation.

Continuous Mode Transition in High-speed Boundary-layers

Mode interaction is studied via direct numerical simulations of a Mach 4.5 boundary layer with discrete and continuous modes imposed at the inflow. An approximate decoupling procedure is developed to create separate vortical, acoustic and entropic continuous mode components. Oblique horizontal vorticity modes induce boundary layer disturbances that grow with downstream distance, similarly to their incompressible counterpart. One salient difference is that a low frequency vorticity mode, alone, is found to induce transition by spawning two-dimensional, unstable discrete modes. The discrete modes are non-linearly excited at high harmonics of the inlet perturbation. Adding a Mack second mode, in addition to the vorticity mode, causes even earlier transition, suggesting that, in supersonic flow, unstable discrete modes play a crucial role in breakdown of boundary-layer streaks.

Note on non-Gaussianities in two-field inflation

Two-field slow-roll inflation is the most conservative modification of a single-field model. The main motivations to study it are its entropic mode and non-Gaussianity. Several years ago, for a two-field model with additive separable potentials, Vernizzi and Wands invented an analytic method to estimate its non-Gaussianities. Later on, Choi et al. applied this method to the model with multiplicative separable potentials. In this note, we design a larger class of models whose non-Gaussianity can be estimated by the same method. Under some simplistic assumptions, roughly these models are unlikely able to generate a large non-Gaussianity. We look over some specific models of this class by scanning the full parameter space, but still no large non-Gaussianity appears in the slow-roll region. These models and scanning techniques would be useful for future model hunt if observational evidence shows up for two-field inflation.

Implementation of nonreflecting boundary conditions for the nonlinear Euler equations

Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier–Bessel modes. This leads to an ‘exact’ nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier–Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.

A Virus in Info-Space

A Virus in Info-Space