Comoving Frame Research Articles

Langevin dynamics for a heavy particle immersed within a flow of light particles

A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow. Considering a range of stationary background flows and distributions for the solvent particle velocities, the macroscopic Langevin-type description of the behaviour of the heavy particle is derived in the form of a generalized Ornstein–Uhlenbeck process. At leading order, the drift term in this process depends upon both the geometric structure of the background flow and the size of the heavy particle, while both drift and diffusion terms scale with moments of the light particle velocity distribution. Computational methods for simulating the micro-hydrodynamics model are then designed to confirm the theoretical results. To enable long-time calculations, simulations are performed in a frame co-moving with the heavy particle. Efficient methods for sampling the position and velocity distributions of incoming solvent particles at the boundaries of the co-moving frame are derived for a range of distributions of solvent particles. The simulations show good agreement with the theoretical results.

Description of electromagnetic fields in uniformly accelerated frame. Revision of the radiation problem

It is shown that Maxwell equations for electromagnetic fields generated by a uniformly accelerated charge could be reduced to the Laplace equation in a co-moving frame (represented by the Łobaczewski geometry of the one-sheeted hyperboloid) for a single scalar potential. A full solution of this equation is derived. Then, the famous problem of radiation of a uniformly accelerated particle is revised. Finally, a description of the electromagnetic field on the scri is presented. Both of those approaches produce the same result, which, surprisingly, is slightly different to the well-established Larmor formula for radiation.

2D unified atmosphere and wind simulations of O-type stars

Context. Massive and luminous O-type star (O star) atmospheres with winds have been studied primarily using one-dimensional (1D), spherically symmetric, and stationary models. However, observations and theory have suggested that O star atmospheres are highly structured, turbulent, and time-dependent. As such, when making comparisons to observations, present-day 1D modeling tools require the introduction of ad hoc quantities such as photospheric macro- and microturbulence, wind clumping, and other relevant properties. Aims. We present a series of multi-dimensional, time-dependent, radiation-hydrodynamical (RHD) simulations for O stars that encapsulate the deeper sub-surface envelope (down to T ~ 450 kK), as well as the supersonic line-driven wind outflow in one unified approach. Our overarching aim is to develop a framework that is free from the ad-hoc prescriptions that plague present-day 1D models. Here, we start with an analysis of a small set of such multi-dimensional simulations and then compare them to atmospheric structures predicted by their 1D counterparts. Methods. We performed time-dependent, two-dimensional (2D) simulations of O star atmospheres with winds using a flux-limiting RHD finite volume modelling technique. Opacities are computed using a hybrid approach combining tabulated Rosseland means with calculations (based on the Sobolev approximation) of the enhanced line opacities expected for supersonic flows. The initial conditions and comparison models were derived using similar procedures as those applied in standard 1D stationary model atmosphere with wind codes. Results. Structure starts appearing in our simulations just below the iron-opacity peak at ~200 kK. Local pockets of gas with radiative accelerations that exceed gravity then shoot up from these deep layers into the upper atmosphere, where they interact with the line-driven wind outflow initiated around or beyond the variable photosphere. This complex interplay creates large turbulent velocities in the photospheric layers of our simulations, on the order of ~30–100km s−1, with higher values for models with higher luminosity-to-mass ratios. This offers a generally good agreement with observations of large photospheric ‘macroturbulence’ in O stars. When compared to 1D models, the average structures in the 2D simulations display less envelope expansion and no sharp density-inversions, along with density and temperature profiles that are significantly less steep around the photosphere, and a strong anti-correlation between velocity and density in the supersonic wind. Although the wind initiation region is complex and highly variable in our simulations, our average mass-loss rates agree well with stationary wind models computed by means of full co-moving frame radiative transfer solutions. Conclusions. The different atmospheric structures found in 2D and 1D simulations are likely to affect the spectroscopic determination of fundamental stellar and wind parameters for O stars as well as the empirical derivation of their chemical abundance patterns. To qualitatively match the different density and temperature profiles seen in our multi-dimensional and 1D models, we need to add a modest amount of convective energy transport in the deep sub-surface layers and a large turbulent pressure around the photosphere to the 1D models.

Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

The fully nonlinear notion of resonance−geometrical resonance−in the general context of dissipative systems subjected to spatially periodic phase-modulated potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system’s energy when the potential is stationary. The geometrical resonance solutions represent a local symmetry whose critical breaking leads to a new analytical criterion for the onset of chaotic instabilities. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new physical criterion for the onset of chaotic instabilities is shown to be valid over large regions of parameter space, thus being useful beyond the scope of current mathematical techniques. More importantly, the present theory helps to understand the unreasonable effectiveness of the Melnikov’s method beyond the perturbative regime.

Wave beams, packets and pulses in inhomogeneous non-Hermitian media with dispersive gain or damping

Wave beams, packets or pulses are known to be subject to a drift if the properties of the medium change across their extension. This effect is often analyzed considering the dispersive properties of the oscillation, related to the real part of the dispersion relation. The evolution of Gaussian beams/packets/pulses in nonuniform media in the presence of gain or damping is investigated in detail, with particular emphasis on the role of dispersion on both the real and the imaginary part of the dispersion relation. In the paraxial limit, the influence of a non-Hermitian medium on the evolution of the wave can be treated employing the equations derived by Graefe and Schubert in the frame of non-Hermitian quantum mechanics (Phys. Rev. A 83 060101(R)). Analytic solutions of the corresponding paraxial equations are obtained here for a one-dimensional complex dispersion relation characterized by a linear or quadratic dependence on the transverse coordinate (a space coordinate for beams and packets, the time in the co-moving frame for a pulse). In the presence of a constant gradient in both the real and the imaginary part of the dispersion relation, the contribution of the latter can lead to a faster or slower propagation with respect to the Hermitian case, depending on the parameters. In focusing media, a constant gain can counteract dispersive or inhomogeneous damping producing packets of asymptotically constant shape. The analytic formulas derived in this paper offer a way to predict or control the properties of beams/packets/pulses depending on their initial conditions and on the characteristics of the medium.

A generic impulsive controller for Hamiltonian time-independent systems

In a recent work Briozzo (2021) the author introduced an impulsive Floquet controller for periodic orbits in time-periodic Hamiltonian systems, which expresses the control law analytically in terms of the linearized dynamics about the reference orbit and makes full use of the center manifold enhancing performance by minimizing the energy of the actual orbit in the co-moving frame of the reference one. The purpose of the present work is to introduce an equivalent controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-independent Hamiltonian one about a periodic orbit, so incorporating the presence of a shear manifold associated to energy conservation and the ensuing non-isolation of periodic orbits. Like its preceding version, the controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is repeatedly sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into a shear manifold and saddle, centre, or saddle-focus ones.

Two-dimensional reconstruction of filament temperatures and densities with the thermal helium beam at ASDEX Upgrade

In the scrape-off layer (SOL) of fusion plasmas, radial particle and energy transport is mainly carried by plasma filaments. The plasma parameters of such filaments can be measured by the thermal helium beam diagnostic (THB). By means of an extended collisional radiative model (CRM) used for the evaluation of the diagnostic data, the light intensity response of neutral helium transitions from filaments is studied, which depends on the parameters of the filament and the background. The electron density of the filament is found to be the dominant parameter impacting the line intensities. By applying a numerical reconstruction algorithm based on the CRM, electron temperatures and densities as well as the sizes of experimentally measured filaments are obtained. This method allows for the first time measurements of the temporal decay rates of filament density and temperature in the co-moving frame of the filament and its radial propagation velocity.

Variations in the intermediate wind region of the blue supergiant 55 Cygni

Context. The quantitative near-infrared (NIR) spectroscopic synthesis is an important technique for determining wind properties of massive stars. The Brα line is an excellent mass-loss tracer and provides valuable information on the physical conditions of intermediate-wind regions. The knowledge of the wind properties gained by studying the NIR lines could provide extra ingredients to the theory of line-driven winds, mainly because the standard theory does not predict observed properties of blue supergiants, such as high values for the β parameter (β> 2), low terminal velocities, and mass-loss variability. Aims. We seek to enhance our understanding of the wind properties of B supergiants. To this end, we propose analysing their NIR spectra over different epochs to study wind variability and its connection with phenomena arising from regions close to the photosphere. Methods. We present the first sets of multi-epoch high-resolution K- and L-band spectra of 55 Cyg acquired with the Gemini Near-InfraRed Spectrograph (GNIRS). We measured line equivalent widths and modelled the Brα line to derive (unclumped) mass-loss rates. Synthetic line profiles were computed for a homogeneous spherical wind by solving the radiative transfer equations in the co-moving frame for a multi-level atom in non-local thermodynamic equilibrium (NLTE). Results. We observe variations in the spectral lines originating in the upper photosphere and the wind. The perturbations, on average, have periods of ~13 and ~23 days; the latter is similar to that found previously from optical data (22.5 days). The NIR lines observed in 2013 are described with the same wind structure used to model a quasi-simultaneous observation in Hα. By contrast, from observations taken in 2015, we derived a higher mean mass-loss rate. Variations in the mass-loss rate are also detected within a few weeks. Interestingly, we find that the profile shape of the Hu14 line sets constraints on the mass loss. Moreover, we find the Mg II doublet in emission, which suggests a tenuous circumstellar gas ring or shell. Conclusions. The variability detected in the NIR H emission lines of 55 Cyg is related to changes in the mass-loss rate, which doubled its value between 2013 and 2015. Furthermore, the short-term variability (within three weeks) in the spectral lines and mass loss supports the hypothesis of strange-mode oscillations. This pilot project demonstrates the importance of comprehensive monitoring of blue supergiants’ variability to deeply understand the physical properties of their stellar winds and the role of pulsations in recurrently enhancing mass loss.

New predictions for radiation-driven, steady-state mass-loss and wind-momentum from hot, massive stars

Context. Massive stars lose a large fraction of their mass to radiation-driven winds throughout their entire life. These outflows impact both the life and death of these stars and their surroundings. Aims. Theoretical mass-loss rates of hot, massive stars are derived to be used in applications such as stellar evolution. The behaviour of these rates in the OB-star regime is analysed, and their effects on massive-star evolution predictions studied. Methods. Dynamically consistent models are computed by solving the spherically symmetric, steady-state equation-of-motion for a large grid of hot, massive stars with different metallicities. The radiative acceleration is derived from non-local thermodynamic equilibrium radiative transfer in the co-moving frame, and all models cover a large spatial range from deep subsonic atmospheric layers into the radiation-driven and highly supersonic wind outflow. The resulting mass-loss rates are used to derive a simple scaling recipe with stellar parameters (luminosity, mass, effective temperature, and metallicity), and the new recipe is used to evaluate some first impacts upon massive-star evolution tracks. Results. We provide a new prescription for steady-state, radiation-driven mass-loss from hot, massive stars depending on their fundamental parameters. In accordance with our previous work, the rates for O stars are lower a factor of ~3 than the rates typically used in previous stellar-evolution calculations, where differences generally decrease with increasing luminosity and temperature. For cooler B giants/supergiants we find larger discrepancies, of up to one or even two orders of magnitude. This arises because we do not find any systematic increase in mass-loss rates below the so-called bi-stability region; indeed, our results do not show any sign of a significant bi-stability jump within the parameter range covered by the grid (Teff ≥ 15 kK). Due to the lower mass-loss rates we find that massive-star envelopes are not easily stripped by means of standard steady-state winds, making it difficult to create classical Wolf-Rayet stars via this channel. Moreover, since the stars retain more mass right before they die as supernovae, our new rates make it possible to create black holes of higher masses than in previous models, even at Galactic metallicity. However, a remaining key uncertainty regarding these predictions concerns unsteady mass-loss for very high-luminosity stars close to the Eddington limit as well as the impact of non-line-driven winds.

Replicating physical motion with Minkowskian isorefractive spacetime crystals

Abstract Here, we show that isorefractive spacetime crystals with a travelling-wave modulation may mimic rigorously the response of moving material systems. Unlike generic spacetime crystals, which are characterized by a bi-anisotropic coupling in the co-moving frame, isorefractive crystals exhibit an observer-independent response, resulting in isotropic constitutive relations devoid of any bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss the impact of considering either a Galilean or a Lorentz transformation in the homogenization of spacetime crystals, showing that the effective response is independent of the considered transformation.

Optimization of nonlinear enhancement through linear dispersion engineering

We consider nonlinear pulse propagation in media with a dispersion relation exhibiting J periodically spaced identical maxima in a co-moving frame. The nonlinear interactions lead to J pulses centered at each of these frequencies. These pulses propagate at the same group velocity and interfere, leading to a highly non-uniform signal in time. This results in the enhancement of effective nonlinear effects, as we recently demonstrated experimentally [Nat. Phys. 18, 59 (2022)NPAHAX1745-247310.1038/s41567-021-01400-2]. Here we present a detailed theoretical and numerical study of this nonlinear enhancement. We show that the amplitudes of the frequency components approximately follow a simple relation, which allows us to derive that the nonlinear enhancement factor increases as 0.687 J . Hence, enhancements of order 10 can be achieved with 15 frequency components.

Electron-acoustic solitons and double layers in a non-uniform plasma with field-aligned shear flow

Electron-acoustic solitary waves (EASWs) are investigated in a non-uniform electron plasma with field-aligned shear flow and two electron populations: hot and cold. Hot electrons are assumed to follow kappa distribution and temperature of cold electrons is considered to be less than those of hot electrons , whereas ions provide a stationary background of positive charge. Intermediate frequency drift wave couples with electron-acoustic wave (EAW) due to plasma density inhomogeneity. It is pointed out that the linear phase speed of the waves weakly depend upon the superthermality and temperature ratio of hot to cold electrons. Set of two fluid partial differential equations is reduced to an ordinary differential equation in a co-moving frame which has soliton solution in one limit. This ordinary differential equation can also be expressed in the form of an energy integral equation which admits double layer (DL) solution in another limit under appropriate boundary conditions. The results are applied to broadband electrostatic noise (BEN) in the dayside auroral zone of ionosphere.

Classification of KPI lumps

A large family of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation are investigated. These solutions are constructed via the Gramian method and are identified as points in a complex Grassmannian. Each solution is a traveling wave moving with a uniform background velocity but have multiple peaks which evolve at a slower time scale in the co-moving frame. For large times, these peaks separate and form well-defined wave patterns in the xy-plane. The pattern formation are described by the roots of well-known polynomials arising in the study of rational solutions of Painlevé II and IV equations. This family of solutions are shown to be described by the classical Schur functions associated with partitions of integers and irreducible representations of the symmetric group of N objects. It is then shown that there exists a one-to-one correspondence between the KPI rational solutions considered in this article and partitions of a positive integer N.

Wake characteristics of complex-shaped snow particles: Comparison of numerical simulations with fixed snowflakes to time-resolved particle tracking velocimetry experiments with free-falling analogs

Experimental and numerical approaches have their own advantages and limitations, in particular, when dealing with complex phenomena such as snow particles falling at moderate Reynolds numbers (Re). Time-resolved, three-dimensional particle tracking velocimetry (4D-PTV) experiments of free-falling, three-dimensional (3D)-printed snowflakes' analogs shed light on the elaborate falling dynamics of irregular snow particles but present a lower resolution (tracer seeding density) and a limited field of view (domain size) to fully capture the wake flow. Delayed-detached eddy simulations of fixed snow particles do not realistically represent all the physics of a falling ice particle, especially for cases with unsteady falling attitudes, but accurately predict the drag coefficient and capture the wake characteristics for steadily falling snowflakes. In this work, we compare both approaches on time- and space-averaged flow quantities in the snowflake wake. First, we cross validate the two approaches for low Re cases, where close agreement of the wake features is expected, and second, we assess how strongly the unsteady falling motion perturbs the average wake pattern as compared to a fixed particle at higher Re. For steadily falling snowflakes, the fixed-particle model can properly represent the wake flow with errors within the experimental uncertainty (±15%). At moderate/high Re (unsteady falling motion), larger differences are present. Applying a co-moving frame to the experimental data to account for the particle movement or filtering the numerical data on larger grids reduces these differences only to some extent, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.

Inducing a bound state between active particles.

We show that two active particles can form a bound state by coupling to a driven nonequilibrium environment. We specifically investigate the case of two mutually noninteracting run-and-tumble probes moving on a ring, each in short-range interaction with driven colloids. Under conditions of timescale separation, these active probes become trapped in bound states. In fact, the bound state appears at high enough persistence (low effective temperature). From the perspective of a comoving frame, where colloids are in thermal equilibrium and the probes are active and driven, an appealing analogy appears with Cooper pairing, as electrons can be viewed as run-and-tumble particles in a pilot-wave picture.

Simulation and modeling of radio-frequency atmospheric pressure plasmas in the non-neutral regime

Radio-frequency-driven atmospheric pressure plasma jets (RF APPJs) play an essential role in many technological applications. This work studies the characteristics of these discharges in the so-called non-neutral regime where the conventional structure of a quasi-neutral bulk and an electron depleted sheath does not develop, and the electrons are instead organized in a drift-soliton-like structure that never reaches quasi-neutrality. A hybrid particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation is set up, which combines a fully kinetic electron model via the PIC/MCC algorithm with a drift-diffusion model for the ions. In addition, an analytical model for the electron dynamics is formulated. The formation of the soliton-like structure and the connection between the soliton and the electron dynamics are investigated. The location of the electron group follows a drift equation, while the spatial shape can be described by Poisson–Boltzmann equilibrium in a co-moving frame. A stability analysis is conducted using the Lyapunov method and a linear stability analysis. A comparison of the numerical simulation with the analytical models yields a good agreement.

The Pulsar Gamma-Ray Emission from High-resolution Dissipative Magnetospheres

Abstract The pulsar light curves and energy spectra in dissipative pulsar magnetospheres are explored with Aristotelian electrodynamics (AE), where particle acceleration is fully balanced with the radiation reaction. AE magnetospheres with nonzero pair multiplicity are computed using a pseudo-spectral method in the co-moving frame. The dissipative region near the current sheet outside the light cylinder is accurately captured by a high-resolution simulation. The pulsar light curves and spectra are computed using the test particle trajectory method, including the influence of both the consistent accelerating electric field and radiation reaction. Our results can generally reproduce the double-peak light curves and the GeV cutoff energy spectra in agreement with the Fermi observations for the pair multiplicity κ ≳ 1.

Bloch theorem in the presence of an additional conserved charge

The Bloch theorem is a general theorem restricting the persistent current associated with a conserved U(1) charge in a ground state or in a thermal equilibrium. It gives an upper bound of the magnitude of the current density, which is inversely proportional to the system size. In a recent paper, Else and Senthil applied the argument for the Bloch theorem to a generalized Gibbs ensemble, assuming the presence of an additional conserved charge, and predicted a nonzero current density in the nonthermal steady state [D. V. Else and T. Senthil, Phys. Rev. B 104, 205132 (2021)]. In this work, we provide a complementary derivation based on the canonical ensemble, given that the additional charge is strictly conserved within the system by itself. Furthermore, using the example where the additional conserved charge is the momentum operator, we discuss that the persistent current tends to vanish when the system is in contact with an external momentum reservoir in the co-moving frame of the reservoir.

Spectral and polarization properties of reflected X-ray emission from black hole accretion discs

ABSTRACTX-ray polarimetric missions planned for this decade will significantly enhance our knowledge of compact accreting sources. Observations of the X-ray polarization signal from active galactic nuclei (AGNs) or X-ray binary systems (XRBs) will bring new means to study inner accretion flow in these objects that, together with currently used spectroscopic and timing techniques, will help us to determine better their properties, such as their inclination, orientation, shape, and size of their corona as well as the black hole spin. In this work, we present a yet missing piece in the global polarization models of black hole accretion discs. We compute the reflected X-ray emission from the disc in a local co-moving frame using (1) the radiative transfer code titan to obtain the ionization structure of the disc and (2) the Monte Carlo code stokes that incorporates the physics of absorption, re-emission, and Compton scattering to produce a complete spectropolarimetric output. We present the final Stokes parameters I, Q, and U for a set of photon-indices of the incident primary power-law radiation, the disc ionization parameters, incident and emission angles, for three independent polarization states of the incident coronal X-ray photons with a sufficient resolution in energy to allow for sharp discussion of spectral and polarization properties. We show that the spectral component matches well literature predictions. The polarization degree and angle are in agreement with analytical approximations previously appearing in reflection models and we demonstrate that the polarized reflected X-ray emission can be, locally, quite large in the $2{\!-\!}12\,$ keV band.

Violation of generalized fluctuation-dissipation theorem in biological limit cycle oscillators with state-dependent internal drives: Applications to hair cell oscillations

The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on the current state of the system. We study fluctuation dissipation relations in such adaptively-driven, nonequilibrium limit-cycle oscillators. We observe the expected violation of the well-known, equilibrium fluctuation-dissipation theorem (FDT), and verify the existence of a generalized fluctuation-dissipation theorem (GFDT) in the non-adaptively driven model of the hair cell oscillator. This generalized fluctuation theorem requires the system to be analyzed in the co-moving frame associated with the mean limit cycle of the stochastic oscillator. We then demonstrate, via numerical simulations and analytic calculations, that the adaptively-driven dynamical hair cell model violates both the FDT and the GFDT. We go on to show, using stochastic, finite-state, dynamical models, that such a feedback-controlled drive in stochastic limit cycle oscillators generically violates both the FDT and GFDT. We propose that one may in fact use the breakdown of the GFDT as a tool to more broadly look for and quantify the effect of adaptive, feedback mechanisms associated with driven (nonequilibrium) biological dynamics.