Unperturbed Medium Research Articles

Development of mathematical model and numerical simulation of plasma ignition of flammable mixture with microwave subcritical streamer discharge

The study of ignition of flammable mixtures by a microwave discharge is of interest for the design of propulsion systems with increased reliability and possibility of the use of lean fuel/air mixtures. A mathematical model for estimating plasma heating and conversion caused by a microwave subcritical streamer discharge is developed. Pressure of the medium is 13.3 kPa, temperature is 300 K. Plasma is created by microwave discharge with flat mirror and initiator (thin antenna). The initiator is hollow, fuel mixture (propane/air) is pumped through it to the exterior medium. Power of microwave radiation is 1.5 kW. Air flows around the initiator with velocity varying from 11 to 500 m/s. The plasma region and its conductivity are set based on experimental statistics, this is a key feature that reduces the consumption of computing resources. The mathematical model consists of three main stages. At the first stage, the Boltzmann equation for the electron gas in unperturbed medium is solved. At the second stage, the Helmholtz equations and plasma domain are considered for microwave system under study. At the third stage, the Navier–Stokes and transport equations with external heat power and additional plasma reactions for a compressible medium are solved. The results of numerical calculations are compared with the data of a physical experiment. The proposed model gives approximate estimations of discharge parameters and flow quantities, while the requirements for computational resources and time are significantly reduced in comparison to traditional models.

Interaction of a singular surface with a strong shock in the interstellar gas clouds

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions. doi:10.1017/S1446181121000328

Mirror-symmetry breaking mitigates finite-size related performance degradation in guided mode resonance filters

Guided mode resonances in subwavelength patterned thin-films endow them with narrow-linewidth near-unity reflectance peaks. Their ultrathin profile is particularly attractive when mated with image sensor arrays that enables compact field-deployable spectral filtering and sensing systems. While this approach enjoys several advantages over other approaches, a well known limitation is the trade-off between the lateral footprint and spectral linewidth. Mirroring strategies involving metallic or distributed Bragg reflectors have been explored in the past to improve lateral confinement at the expense of increased fabrication complexity, footprint, and insertion loss. Here, we numerically study mirrorless grating modification strategies and predict the mitigation of finite-size related performance degradation. Specifically, we consider mirror symmetry broken miniaturized medium refractive index contrast (silicon nitride) gratings, which exhibit quasi bound states in the continuum (QBIC) resonances. For the same lateral footprint, a nearly 2 fold improvement in quality factor is predicted for the proposed design in comparison to a simple grating surrounded by aluminium mirrors. Numerical study of the design and operational performance of visible-wavelength arrayed filters and multiplexed refractive index sensors is presented. For a typical lateral device footprint of 8 µm, the gratings span wavelengths ranging from 560 nm–800 nm with a coupling efficiency of 43–60%, and a full width half maximum (FWHM) of 4 nm–12 nm. Besides this, the proposed geometry gives a four times better figure of merit (FOM) than the unperturbed medium contrast grating in surface refractometric sensing.

INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS

AbstractWe investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.

Parameterizing the Outflow from a Central Black Hole in Dwarf Spheroidal Galaxies: A 3D Hydrodynamic Simulation

Abstract Large galaxies harbor massive central black holes and their feedback exerts a substantial impact on their evolution. Recently, observations have suggested that dwarf galaxies might host black holes in their centers, but with lower masses (intermediate-mass black holes—IMBHs). The impact of IMBHs on the evolution of dwarf spheroidal galaxies (dSphs), however, has so far not been properly analyzed. In this work, we investigate the effects of an outflow from an IMBH on gas dynamics in dSphs by means of noncosmological, three-dimensional hydrodynamic simulations, letting the galactic gas distribution evolve over 3 Gyr under the influence of the IMBH’s outflow and supernova feedback. All simulations have a numerical resolution of 20.0 pc cell−1. Two scenarios are considered to infer differences in the propagation of the outflow, one with a homogeneous interstellar medium (ISM) and another one with inhomogeneities caused by supernova feedback. A minimal initial speed and a minimal initial density are required for the outflow to propagate, with the values depending on the conditions of the medium. In an unperturbed medium, the outflow propagates freely in both directions with the same velocity (lower than the initial one), removing a small fraction of gas from the galaxy (the exact fraction depends on the initial physical conditions of the outflow). However, in an inhomogeneous ISM, the impact of the outflow is substantially reduced, and its contribution to the removal of gas from the galaxy is almost negligible.

Propagation of electric field generated by periodic pumping in a stable medium of two-level atoms of the Maxwell–Bloch model

We consider the problem of the propagation of an electric field generated by periodic pumping in a stable medium of two-level atoms as the mixed problem for the Maxwell–Bloch equations without spectrum broadening. An approach to the study of such a problem is proposed. We use the inverse scattering transform method in the form of the matrix Riemann–Hilbert (RH) problem, using simultaneous spectral analysis of both the Lax equations. The proposed matrix RH problem solves the problem of the propagation of a sinusoidal signal in an unperturbed stable medium (attenuator). It is proved that this RH problem provides the causality principle for the region t < x, and for the region of the light cone, 0 < x < t allows us to find the asymptotics of the transmitted signal. First, we study the asymptotics of the RH problem for large times, and then, we obtain asymptotic formulas for the mixed problem solution of the Maxwell–Bloch equations when the attenuator is long enough. Three sectors are obtained in the light cone where the asymptotics have essentially different behaviors.

Density of Neutral Hydrogen in the Sun's Interstellar Neighborhood

Abstract Interstellar neutral atoms, unlike charged particles, freely penetrate the heliosphere, allowing us to sample the physical state of the interstellar matter directly. Most interstellar hydrogen atoms are ionized before reaching the inner heliosphere and become energetic protons picked up by the solar wind and transported away from the Sun. Consequently, observations of interstellar hydrogen atoms by missions operating within a few astronomical units from the Sun are subject to significant systematic uncertainties. We analyze observations from the Solar Wind Around Pluto instrument on New Horizons, the first experiment to provide extensive measurements of the picked-up protons far from the Sun. Analyzing the density of these protons, we find an interstellar neutral hydrogen density at the termination shock of 0.127 ± 0.015 cm−3, i.e., ∼40% higher than previously thought. We show that the Voyager observations of the slowdown of the solar wind further support this value. This result resolves a problem of why energetic neutral atom fluxes, created from pickup ions by charge exchange with hydrogen atoms, are roughly twice that expected from numerical models. Our result also implies higher charge exchange rates at the heliospheric boundaries and, consequently, a less asymmetric shape of the heliosphere. Based on a previous study of the atom filtration in the heliospheric boundaries, we estimate the neutral hydrogen density in the unperturbed local interstellar medium of 0.195 ± 0.033 cm−3. This value agrees with astrophysical observations of the interstellar clouds in the Sun proximity.

Shock within a shock: revisiting the radio flares of NS merger ejecta and gamma-ray burst-supernovae

ABSTRACT Fast ejecta expelled in binary neutron star (NS) mergers or energetic supernovae (SNe) should produce late-time synchrotron radio emission as the ejecta shocks into the surrounding ambient medium. Models for such radio flares typically assume the ejecta expands into an unperturbed interstellar medium (ISM). However, it is also well known that binary NS mergers and broad-lined Ic SNe Ic can harbour relativistic jetted outflows. In this work, we show that such jets shock the ambient ISM ahead of the ejecta, thus evacuating the medium into which the ejecta subsequently collides. Using an idealized spherically symmetric model, we illustrate that this inhibits the ejecta radio flare at early times $t \lt t_{\rm col} \approx 12 \, {\rm yr} \, (E_{\rm j}/10^{49} \, {\rm erg})^{1/3} (n/1 \, {\rm cm}^{-3})^{-1/3} (\upsilon _{\rm ej}/0.1c)^{-5/3}$, where Ej is the jet energy, n the ISM density, and $\upsilon$ej the ejecta velocity. We also show that this can produce a sharply peaked enhancement in the light curve at t = tcol. This has implications for radio observations of GW170817 and future binary NS mergers, gamma-ray burst (GRB) SNe, decade-long radio transients such as FIRST J1419, and possibly other events where a relativistic outflow precedes a slower moving ejecta. Future numerical work will extend these analytic estimates and treat the multidimensional nature of the problem.

Edge states and the valley Hall effect

We study energy propagation along line-defects (edges) in two dimensional continuous, energy preserving periodic media. The unperturbed medium (bulk) is modeled by a honeycomb Schroedinger operator, which is periodic with respect to the triangular lattice, invariant under parity, P, and complex-conjugation, C. A honeycomb operator has Dirac points in its band structure: two dispersion surfaces touch conically at an energy level, ED[25,27]. Periodic perturbations which break P or C open a gap in the essential spectrum about energy ED. Such operators model an insulator near energy ED.Our edge operator is a small perturbation of the bulk and models a transition (via a domain wall) between distinct periodic, P or C breaking perturbations. The edge operator permits energy transport along the line-defect. The associated energy channels are called edge states. They are time-harmonic solutions of the underlying wave equation, which are localized near and propagating along the line-defect. They are of great scientific interest due to their remarkable stability, and are a key property of topological insulators.We completely characterize the edge state spectrum within the bulk spectral gap about ED. At the center of our analysis is an expansion of the edge operator resolvent for energies near ED. The leading term features the resolvent of an effective Dirac operator. Edge state eigenvalues are poles of the resolvent, which bifurcate from the Dirac point. The corresponding eigenstates have the multiscale structure identified in [23].We extend earlier work on zigzag-type edges [14] to all rational edges. We elucidate the role in edge state formation played by the type of symmetry-breaking and the orientation of the edge. We prove the resolvent expansion by a new direct and transparent strategy. Our results also provide a rigorous explanation of the numerical observations in [22,38]; see also the photonic experimental study in [42]. Finally we discuss implications for the Valley Hall Effect, which concerns quantum Hall-like energy transport in honeycomb structures.

Multiscale Analysis of Spectral Broadening of Acoustic Waves by a Turbulent Shear Layer

We consider the scattering of acoustic waves emitted by an active source above a plane turbulent shear layer. The layer is modeled by a moving random medium with small spatial and temporal fluctuations of its mean velocity, and constant density and speed of sound. We develop a multi-scale perturbative analysis for the acoustic pressure field transmitted by the layer and derive its power spectral density when the correlation function of the velocity fluctuations is known. Our aim is to compare the proposed analytical model with some experimental results obtained for jet flows in open wind tunnels. We start with the Euler equations for an ideal fluid flow and linearize them about an ambient, unsteady inhomogeneous flow. We study the transmitted pressure field without fluctuations of the ambient flow velocity to obtain the Green's function of the unperturbed medium with constant characteristics. Then we use a Lippmann-Schwinger equation to derive an analytical expression of the transmitted pressure field, as a function of the velocity fluctuations within the layer. Its power spectral density is subsequently computed invoking a stationary-phase argument, assuming in addition that the source is time-harmonic and the layer is thin. We finally study the influence of the source tone frequency and ambient flow velocity on the power spectral density of the transmitted pressure field and compare our results with other analytical models and experimental data.

An Empirical Model of Energetic Neutral Atom Imaging of the Heliosphere and Its Implications for Future Heliospheric Missions at Great Heliocentric Distances

Abstract Several concepts for heliospheric missions operating at heliocentric distances far beyond Earth orbit are currently investigated by the scientific community. The mission concept of the Interstellar Probe, e.g., aims at reaching a distance of 1000 au away from the Sun within this century. This would allow the coming generation to obtain a global view of our heliosphere from an outside vantage point by measuring the energetic neutral atoms (ENAs) originating from the various plasma regions. It would also allow for direct sampling of the unperturbed interstellar medium, as well as for many observation opportunities beyond heliospheric science, such as visits to Kuiper Belt objects, a comprehensive view on the interplanetary dust populations, and infrared astronomy free from the foreground emission of the zodiacal cloud. In this study, we present a simple empirical model of ENAs from the heliosphere and derive basic requirements for ENA instrumentation on board a spacecraft at great heliocentric distances. We consider the full energy range of heliospheric ENAs from 10 eV to 100 keV because each part of the energy spectrum has its own merits for heliospheric science. To cover the full ENA energy range, two or three different ENA instruments are needed. Thanks to parallax observations, some insights about the nature of the IBEX ribbon and the dimensions of the heliosphere can already be gained by ENA imaging from a few au heliocentric distance. To directly reveal the global shape of the heliosphere, measurements from outside the heliosphere are, of course, the best option.

The Evolution of Binaries in a Gaseous Medium: Three-dimensional Simulations of Binary Bondi–Hoyle–Lyttleton Accretion

Abstract Binary stars are common. While only those with small separations may exchange gas with one another, even the widest binaries interact with their gaseous surroundings. Drag forces and accretion rates dictate how these systems are transformed by these interactions. We perform three-dimensional hydrodynamic simulations of Bondi–Hoyle–Lyttleton flows, in which a binary moves supersonically relative to a homogeneous medium, using the adaptive mesh refinement code FLASH. We simulate a range of values of the initial semimajor axis of the orbit relative to the gravitational focusing impact parameter of the pair. When the binary separation is less than the gravitational focusing impact parameter, the pair orbits within a shared bow shock. When the pair is wider, each object has an individual bow shock structure. The long-term evolution of the binary is determined by the timescales for accretion, slowing of the center of mass, and orbital inspiraling. We find a clear hierarchy of these timescales; a binary’s center-of-mass motion is slowed over a shorter timescale than the pair inspirals or accretes. In contrast to previous analytic predictions, which assume an unperturbed background medium, we find that the timescale for orbital inspiraling is proportional to the semimajor axis to the 0.19 ± 0.01 power. This positive scaling indicates that gaseous drag forces can drive binaries either to coalescence or to the critical separation at which gravitational radiation dominates their further evolution. We discuss the implications of our results for binaries embedded in the interstellar medium, active galactic nuclei disks, and common envelope phases.

Model-free Maps of Interstellar Neutral Hydrogen Measured with IBEX between 2009 and 2018

Abstract The Interstellar Boundary Explorer (IBEX) is a NASA satellite in Earth orbit, dedicated to observing interstellar neutral (ISN) atoms entering the heliosphere and energetic neutral atoms from the heliosheath from 11 eV to 6 keV. This work presents comprehensive maps of ISN hydrogen observed with IBEX at energies between 11 and 41 eV, covering almost an entire solar cycle from 2009 to 2018. ISN hydrogen measurements can provide information on the interstellar medium and on the heliosphere that modifies the incoming ISN flow. Whereas hydrogen is the dominant species in the unperturbed interstellar medium, most ISN hydrogen atoms crossing into the heliosphere do not reach the inner solar system: some are filtered out around the heliopause, while others are held off by solar radiation pressure or may be ionized as they approach the Sun. This paper presents and evaluates several approaches for generating model-free maps of ISN hydrogen from IBEX measurements. We discuss the basic implications of our results for ISN hydrogen inflow and outline the remaining discrepancies between observations and model predictions. Our maps show, during weak solar activity from 2009 to 2011, a clear signal of ISN hydrogen for ecliptic longitudes between 240° and 310°, roughly one month after the signal of ISN helium has peaked. When the solar activity approached its maximum around 2014, the ISN hydrogen signal weakened and dropped below the detection threshold because of increasing solar radiation pressure and ionization. The ISN hydrogen signal then reappeared in 2017.

Three-dimensional Features of the Outer Heliosphere Due to Coupling between the Interstellar and Heliospheric Magnetic Field. V. The Bow Wave, Heliospheric Boundary Layer, Instabilities, and Magnetic Reconnection

Abstract The heliosphere is formed due to interaction between the solar wind (SW) and local interstellar medium (LISM). The shape and position of the heliospheric boundary, the heliopause, in space depend on the parameters of interacting plasma flows. The interplay between the asymmetrizing effect of the interstellar magnetic field and charge exchange between ions and neutral atoms plays an important role in the SW–LISM interaction. By performing three-dimensional, MHD plasma/kinetic neutral atom simulations, we determine the width of the outer heliosheath—the LISM plasma region affected by the presence of the heliosphere—and analyze quantitatively the distributions in front of the heliopause. It is shown that charge exchange modifies the LISM plasma to such extent that the contribution of a shock transition to the total variation of plasma parameters becomes small even if the LISM velocity exceeds the fast magnetosonic speed in the unperturbed medium. By performing adaptive mesh refinement simulations, we show that a distinct boundary layer of decreased plasma density and enhanced magnetic field should be observed on the interstellar side of the heliopause. We show that this behavior is in agreement with the plasma oscillations of increasing frequency observed by the plasma wave instrument onboard Voyager 1. We also demonstrate that Voyager observations in the inner heliosheath between the heliospheric termination shock and the heliopause are consistent with dissipation of the heliospheric magnetic field. The choice of LISM parameters in this analysis is based on the simulations that fit observations of energetic neutral atoms performed by Interstellar Boundary Explorer.

Correlation of HI shells and CO clumps in the outer Milky Way

HI shells, which may be formed by the activity of young and massive stars, or connected to energy released by interactions of high-velocity clouds with the galactic disk, may be partly responsible both for the destruction of CO clouds and for the creation of others. It is not known which effect prevails. We study the relation between HI shells and CO in the outer parts of the Milky Way, using HI and CO surveys and a catalogue of previously identified HI shells. For each individual location, the distance to the nearest HI shell is calculated and it is specified whether it lies in the interior of an HI shell, in its walls, or outside an HI shell. The method takes into account irregular shapes of HI shells. We find a lack of CO clouds in the interiors of HI shells and their increased occurrence in walls. Properties of clouds differ for different environments: interiors of HI shells, their walls, and unperturbed medium. CO clouds found in the interiors of HI shells are those that survived and were robbed of their more diffuse gas. Walls of HI shells have a high molecular content, indicative of an increased rate of CO formation. Comparing the CO fractions within HI shells and outside in the unperturbed medium, we conclude that HI shells are responsible for approx. 20 % increase in the total amount of CO in the outer Milky Way.

The peculiarities of cross-correlation between two secondary precursors – Radon and magnetic field variations, induced by stress transfer changes

A model of precursor manifestation mechanisms, stimulated by tectonic activity and some peculiarities of observer strategy, whose main task is the effective measurement of precursors in the spatial area of their occurrence on the Earth's daylight, are considered. In particular, the applicability of Dobrovolsky's approximation is analyzed, when an unperturbed medium (characterized by the simple shear state) and the area of tectonic activity (local inhomogeneity caused by the change only of shear modulus) are linearly elastic, and perturbation, in particular, surface displacement is calculated as a difference of the solutions of two independent static problems of the theory of elasticity with the same boundary condition on the surface. Within the framework of this approximation a formula for the spatial distribution (of first component) of magnetic field variations caused by piezomagnetic effect in the case of perturbed regular medium, which is in simple shear state is derived. Cogent arguments in favor of linear dependence between the radon spatial distribution and conditional deformation are obtained.Changes in magnetic field strength and radon concentrations were measured along a tectonomagnetic profile of the total length of 11 km in the surroundings of the ”Academician Vernadsky” Station on the Antarctic Peninsula (W 64°16′, S 65°15′). Results showed a positive correlation between the annual surface radon concentration and annual changes of magnetic field relative to a base point, and also the good coincidence with theoretical calculation.

Contrasts of electromagnetically-induced transparency in unperturbed and perturbed cold atoms of 87Rb

We experimentally measured the relative contrast of an electromagnetically-induced transparency (EIT) spectrum with two cw lasers in a Λ-type system of magneto-optically trapped 87Rb atoms, which is a perturbed cold atomic medium. The contrast depends nonlinearly on the power of the coupling beam. Experimental results showed good agreement qualitatively with the simulation results considering the trapping magnetic field gradient, which induced detuning of the coupling laser. We used a free expanding cold atomic cloud that had a temperature of (36 ± 1) µK. To observe the EIT spectrum in the non-perturbed medium, we used two pulsed lasers. We observed that the relative contrast in the unperturbed medium was three times higher than that in the perturbed medium under our experimental conditions.

Application of small-roughness perturbation theory to reverberation in range-dependent waveguides

A rough-interface reverberation model is developed for range-dependent environments. First-order perturbation theory is employed, and the unperturbed background medium can be layered and heterogeneous with arbitrary range dependence. To calculate the reverberation field, two-way forward scatter due to the slowly changing unperturbed environment is handled by fast numerical methods. Backscatter due to small roughness superimposed on any of the slowly varying interfaces is handled efficiently using a Monte Carlo approach. Numerical examples are presented to demonstrate the application of the model. The primary purpose of the model is to incorporate relevant physics while improving computational speed.

Shock wave structure in an inviscid heat-conducting locally equilibrium medium of a perfect gas with radiation

The structure of a shock wave (SW) in an inviscid heat-conducting locally equilibrium medium of a perfect gas with radiation at temperatures up to hundreds of thousands and millions of degrees is analysed in the approximation of non-linear heat conduction. At such temperatures, heat conduction is far more important than viscosity, the medium consists of ions, electrons and radiation, and the electrons and radiation make a decisive contribution to the heat transfer and an appreciable contribution to the thermodynamic functions of the medium. Combinations with the dimensions of all the flow parameters are constructed from the gas density ahead of the SW and the constants appearing in the equations of state of such a medium. If they are taken as the corresponding scales, the equations of state for different media in dimensionless form only differ in the ratio of the specific heat capacities (the adiabatic exponent) of the gas. The SW structure is studied for adiabatic exponents from 1 to 3, dimensionless temperatures ahead of the SW from zero to infinity and any SW velocities exceeding the speed of sound in the unperturbed medium. The following cases are successively considered: 1) when the contribution due to radiation is neglected in the equations of state, 2) when radiation is taken into account and the SW moves through a gas at a zero temperature (through a cold background), and 3) the radiation contribution is allowed for in the case of a warm background. It is ascertained when the SW structure is continuous and when it contains a finite or infinite forerunner and an isothermal shock. The transition from a continuous structure to a structure with an isothermal shock and the intensity of this shock are independent of the form of the formulae for the thermal conductivity in Fourier's law. In the case of adiabatic exponents greater than unity, the structure is continuous for all SW velocities starting from a certain dimensionless background temperature.

Theory of Images in Spherical-Layered Axisymmetric Viscous Hydrodynamics

A spherical drop of viscosity μ(1) and radius a1 is surrounded by a spherical shell of viscosity μ(2), internal radius a1, and external radius a2, beyond which there is an unbounded matrix fluid of viscosity μ(3). An arbitrary axisymmetric singularity acts inside or outside the viscous spherical shell. It is established that the Stokes’ stream function induced in this heterogeneous medium is explicitly expressible solely in terms of the corresponding stream function for the unperturbed homogeneous unbounded medium. As an application of the general solution, it is shown that there exists a homogeneous spherical drop of viscosity μ and radius a2, which is equivalent to the spherical drop of viscosity μ(1) and radius a1, surrounded by the spherical shell of viscosity μ(2) and outer radius a2. A new formula is also established for the effective viscosity of a multiphase medium comprising an incompressible fluid of viscosity μ(3) in which are embedded N small identical spherical drops of viscosity μ(1), surrounded by spherical shells of viscosity μ(2), assuming that the interference effects of these coated spherical drops are negligible, and that their arrangement is axisymmetrical. The corresponding two-dimensional results are also presented, by slightly modifying the three-dimensional results.