Comoving Reference Frame Research Articles

Time-lapse Very Long Baseline Interferometry Imaging of the Close Active Binary HR 1099

We report multiepoch astrometric very long baseline interferometry observations of the chromospherically active binary HR 1099 (V711 Tau, HD 22468) at six epochs over 63 days using the Very Long Baseline Array at 22.2 GHz. We determined hourly radio positions at each epoch with a positional uncertainty significantly smaller than the component separation. The aggregate radio positions at all epochs define an ellipse in the comoving reference frame with an inclination i=39.°5−3.°5+3.°6 and longitude of ascending node Ω = 212° ± 22°. The ellipse center is offset from the Third Gaia Celestial Reference Frame position by Δα = −0.81−0.37+0.25 , Δδ = 0.45−0.25+0.23 mas. All radio centroids are well displaced from the binary center of mass at all epochs, ruling out emission from the interbinary region. We examined the motion of the radio centroids within each epoch by comparing hourly positions over several hours. The measured speeds were not statistically significant for five of the six epochs, with 2σ upper limits in the range 200–1000 km s−1. However, for one flaring epoch, there was a 3σ detection v ⊥ = 228 ± 85 km s−1. This speed is comparable to the mean speed of observed coronal mass ejections on the Sun.

Eulerian discrete kinetic framework in comoving reference frame for hypersonic flows

Flow physics vary in different regimes across the full Mach number range, with our knowledge being particularly poor about the hypersonic regime. An Eulerian realization of the particles on demand method, a kinetic model formulated in the comoving reference frame, is proposed to simulate hypersonic compressible flows. The present model allows for flux evaluation in different reference frames, in this case rescaled and shifted by local macroscopic quantities, i.e. fluid speed and temperature. The resulting system of coupled hyperbolic equations is discretized in physical space with a finite volume scheme ensuring exact conservation properties. Regularization via Grad expansion is introduced to implement distribution function and flux transformation between different reference frames. It is shown that the proposed method possesses Galilean invariance at a Mach number up to $100$ . Different benchmarks including both inviscid and viscous flows are reproduced with the Mach number up to $198$ and pressure ratio up to $10^5$ . Finally, the new model is demonstrated to be capable of simulating hypersonic reactive flows, including one-dimensional and two-dimensional detonations. The developed methodology opens up possibilities for the simulation of the full range of compressible flows, without or with chemical reactions, from the subsonic to hypersonic regimes, leading to enhanced understanding of flow behaviours across the full Mach number range.

Modeling multi-loop atom interferometers with Co-moving Reference Theory

With the rapid development of atom interferometry, atom interferometers have been widely used in inertial navigation, resource exploration, basic physics and other fields. For precise measurement experiments with multi-loop atom interferometer configuration, it is urgent to establish a high-precision theoretical model charactering the relationship between target measurement quantities and measurement results. Based on this, we adopt the idea of co-moving reference frame, so as to transfer the gravity, gravity gradient and Earth’s rotation effects to the laser light field interacting with atoms by translating, rotating and stretching the background spacetime. With this method, we not only can simplify the analysis process of the experimental principle, but also give the analytical results of the high-order interference phase of the multi-loop atom interferometer containing the gravity gradient and Earth’s rotation. This work will lay a certain theoretical foundation for higher-precision experiment, and will also help to clearly guide the implementation of the experiment.

Statistics of geometrical invariants of magnetic field gradient tensors in the turbulent magnetosheath based on magnetospheric multiscale mission

Geometrical invariants of magnetic field gradient tensors are used to classify the topological structures of a magnetic field. This study presents a statistical analysis on the geometrical invariants of magnetic field gradient based on high-quality data measured by magnetospheric multiscale mission in turbulent magnetosheath. The method for the classification of velocity field topologies cannot be applied to magnetic field with strong intensity directly because the magnetic field cannot be transformed to zero by selecting a co-moving reference frame in which the velocity is zero. During a strong magnetic field, flux ropes and tubes are the most possible magnetic structures. Statistics in the plane formed by geometrical invariants show that about 23% are force-free structures comprised of 20.5% flux tubes and 79.5% flux ropes. The remaining actively evolved structures are comprised of 30% flux tubes and 70% flux ropes. Moreover, the conditional average of current density and Lorentz force decomposition in geometrical invariants plane are investigated. The results show that flux ropes carried more current density than flux tubes for the same geometrical invariants, and flux ropes tend to associate with magnetic pressure force and flux tubes tend to associate with magnetic tension.

Emergence of Gloomy Eyelet inside DNA

The purpose of this article is to study gloomy eyelet (GE) inside the cell nucleus by using models of warp drive hydro (WDH), swinging spring, Rankine, co-moving reference frame, and Poincare. The beat wave frequency (ω) of blood pressure on the vessel and the swinging spring frequency (Ω) of DNA coincide together on the Rankine model. In this case, it leads to appearing as a sudden pressure drop and an accelerated cavity in the medium of the warp drive hydro (WDH) model. In transient conditions, the vortex flow inside WDH can generate gloomy eyelet (GE), and the tiny distortion of nano space–time revealed inside the gloomy eyelet (GE) inside DNA and the tiny distortion of nano space–time revealed inside the co-moving reference frame (CMRF) model of the gloomy eyelet (GE). The space–time distortion can act as a hidden potential for the cell nucleus and some behaviors of gloomy eyelet can be traced by the frequency responses of human body organs. The interactions between two adjacent different mediums such as the normal cells and abnormal cells, earth’s gravitational effects can lead to changes in the distortion of space–time inside the cell nucleus. Transient bonds between particles can be expected to appear in the gloomy eyelet inside DNA. Identifying the range of changes in the frequency responses and the transient bonds inside the cell nucleus can be introduced as one of the health indicators.

On the Channeling Phenomenon as 1D and 2D Atomic Models in the Comoving Reference Frame

On the Channeling Phenomenon as 1D and 2D Atomic Models in the Comoving Reference Frame

Extensions to the Navier–Stokes equations

Historically, the mass conservation and the classical Navier–Stokes equations were derived in the co-moving reference frame. It is shown that the mass conservation and Navier–Stokes equations are Galilean invariant—they are valid in any arbitrary inertial reference frame. From the mass conservation and Navier–Stokes equations, we can derive a wave equation, which contains the speed of pressure wave as its parameter. This parameter is independent of the speed of the source—the fluid element velocity. The speed of pressure wave is determined from the thermodynamic equation of state of the fluid, which is reference frame independent. It is well known that Lorentz transformation ensures wave speed invariant in all inertial frames, and the Lorentz invariance holds for different inertial observers. Based on these arguments, general Navier–Stokes equations (conservation law for the energy–momentum) can be written in any arbitrary inertial reference frame, they are transformed from one reference frame into another with the help of the Lorentz transformation. The key issue is that the Lorentz factor is parametrized by the local Mach number. In the instantaneous co-moving reference frame, these equations will degrade to the classical Navier–Stokes equations—the limit of the non-relativistic ones. These extended equations contain a square of the Lorentz factor. When the local Mach number is equal to one (the Lorentz factor approaches infinity), the extended Navier–Stokes equations will embody an intrinsic singularity, meaning that the transitions from the subsonic flow to the supersonic flow will happen. For the subsonic flow, the square of the Lorentz factor is positive, while for the supersonic flow, the square of the Lorentz factor becomes a negative number, which represents that the speed of sound cannot travel upstream faster than the flow velocity.

Magnetized Dusty Black Holes and Wormholes

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions f(R), F(R) and τ0(R), where R is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (f>0), parabolic (f=0) and elliptic (f<0) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.

Multiscale semi-Lagrangian lattice Boltzmann method.

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets of lower and higher order are consistently and efficiently coupled, allowing us to use the higher-order model only when and where needed. This includes regions of high Mach or high Knudsen numbers. The coupling procedure of discrete velocity sets consists of either a projection of the higher-order populations onto the lower-order lattice or lifting of the lower-order populations to the higher-order velocity space. Both lifting and projection are local operations, which enable a flexible adaptive velocity set. The proposed scheme is formulated for both a static and an optimal, co-moving reference frame, in the spirit of the recently introduced Particles on Demand method. The multi-scale scheme is validated with an advection of an athermal vortex and in a jet flow setup. The performance of the proposed scheme is further investigated in the shock structure problem and a high-Knudsen-number Couette flow, typical examples of highly non-equilibrium flows in which the order of the velocity set plays a decisive role. The results demonstrate that the proposed multi-scale scheme can operate accurately, with flexibility in terms of the underlying models and with reduced computational requirements.

Disintegration and expansion of wormholes

We consider the process of catastrophic expansion of a spacelike wormhole after a violation of its equilibrium state. The dynamics of deformation of the comoving reference frame is investigated. We show that the deformation has a very specific anisotropic feature. The statement made earlier by other authors, that in the process of expanding the wormhole connecting two universes these universes ultimately unite into one universe, is not correct. We show that the transverse size of the wormhole (its throat) increases and the length of the corridor decreases which does not correspond to the de Sitter model.

Accurate numerical determination of a self-preserving quantum vortex ring

We compute simultaneously the translational speed, the magnitude and the phase of a quantum vortex ring for a wide range of radii, within the Gross–Pitaevskii model, by imposing its self preservation in a co-moving reference frame. By providing such a solution as the initial condition for the time-dependent Gross–Pitaevskii equation, we verify a posteriori that the ring’s radius and speed are well maintained in the reference frame moving at the computed speed. Convergence to the numerical solution is fast for large values of the radius, as the wavefunction tends to that of a straight vortex, whereas a continuation technique and interpolation of rough solutions are needed to reach convergence as the ring tends to a disk. Comparison with other strategies for generating a quantum ring reveals that all of them seem to capture quite well the translational speed, whereas none of them seems to preserve the radius with the accuracy reached in the present work.

Speed Measurement in an Accomoving Reference System

A method of direct measurement of the observer's velocity (peculiar velocity) relative to the accompanying reference system is proposed and investigated. To measure peculiar velocity, it is proposed to use the measurement of stellar light aberration. A comparison of the use of light aberration and the Doppler Effect for measuring velocity relative to relic radiation was made. When using the Doppler Effect, the total speed of the observer was measured - the Hubble speed and the radial component of the peculiar speed of the observer. As a result of the analysis of the components of the observer's velocity in the comoving reference frame, the Hubble and peculiar velocities of the observer, their essential features are formulated. The analysis of the shape of the wave fronts of the CMB radiation, the radiation of quasars, the radiation of stars and the radiation of ground sources is given. As a consequence of this analysis, the decisive influence of the shape of their wave fronts on the possibilities of measuring stellar aberration and the absence of such an effect when measuring velocity using the Doppler Effect are shown. Measurement of light aberration in an inertial system enables direct measurement of the observer's peculiar velocity in an comoving reference frame. Knowing the observer's peculiar velocity is important for increasing the accuracy of determining the Hubble velocity of especially objects of relatively small remoteness. The proposed structures of devices for measuring the peculiar velocity of an inertial reference system were investigated. Peculiar speed is determined by the measured light aberration without switching to another frame of reference. Their expected accuracy and reliability were evaluated. The practical use of the proposed structures is possible in astronomy and spacecraft.

Extensive analysis of the lattice Boltzmann method on shifted stencils.

Standard lattice Boltzmann methods (LBMs) are based on a symmetric discretization of the phase space, which amounts to study the evolution of particle distribution functions (PDFs) in a reference frame at rest. This choice induces a number of limitations when the simulated flow speed gets closer to the sound speed, such as velocity-dependent transport coefficients. The latter issue is usually referred to as a Galilean invariance defect. To restore the Galilean invariance of LBMs, it was proposed to study the evolution of PDFs in a comoving reference frame by relying on asymmetric shifted lattices [N. Frapolli, S.S. Chikatamarla, and I.V. Karlin, Phys. Rev. Lett. 117, 010604 (2016)].PRLTAO0031-900710.1103/PhysRevLett.117.010604 From the numerical viewpoint, this corresponds to overcoming the rather restrictive Courant-Friedrichs-Lewy conditions on standard LBMs and modeling compressible flows while keeping memory consumption and processing costs to a minimum (therefore using the standard first-neighbor stencils). In the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions (EDFs) and collision models. Thanks to them, it is possible to (1) better understand the effect of this solution on both physics and stability, (2) assess its viability as a way to extend the validity range of LBMs, and (3) quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path. The results clearly show that, in theory, the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity. Furthermore, just like the zero-Mach flow for the standard stencils, it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties. In addition, a detailed analysis of the obtained results shows that the properties of different collision models and EDFs remain unchanged under the shift of stencil. In other words, by introducing a velocity shift in the stencil, the optimal operating point, in terms of physics and numerics, will also be shifted by the same vector regardless of the EDF or collision model considered. Eventually, while limited to the D2Q9 stencil with the nine possible first-neighbor shifts, the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner.

Asymmetric population of momentum distribution by quasi-periodically driving a triangular optical lattice.

Ultracold atoms in periodical-driven optical lattices enable us to investigate novel band structures and explore the topology of the bands. In this work, we investigate the impact of the ramping process of the driving signal and propose a simple but effective method to realize desired asymmetric population in momentum distribution by controlling the initial phase of the driving signal. A quasi-momentum oscillation along the shaking direction in the frame of reference co-moving with the lattice is formed, causing the formation of the mix of ground energy band and first excited band in laboratory frame, within the regime that the driving frequency is far less than the coupling frequency between ground band and higher energy bands. This method avoids the construction of intricate lattices or complex control sequence. With a triangular lattice, we experimentally investigate the influence of the initial phase, frequency, amplitude of the driving signal on the population difference and observe good agreement with our theoretical model. This provides guidance on how to load a driving signal in driven optical lattice experiment and also potentially supplies a useful tool to form a qubit that can be used in quantum computation.

The Schwarzschild Mass in General Relativity

The central (surface) energy-density, <i>E₀</i> (<i>E_R</i>), which appears in the expression of total static and spherical mass, <i>M</i> (corresponding to the total radius <i>R</i>) is defined as the density measured only by one observer located at the centre (surface) in the Momentarily Co-moving Reference Frame (MCRF). Since the mass, <i>M</i>, depends only on the central (surface) density for most of the equations of state (EOSs) and/or exact analytic solutions of Einstein’s field equations available in the literature, the central (surface) density measured in the preferred frame (that is, in the MCRF) appears to be not in agreement with the coordinate invariant form of the field equations that result for the source mass, <i>M</i>. In order to overcome the use of any preferred coordinate system (the MCRF) defined for the central (surface) density in the literature, we argue for the first time that the said density may be defined in the coordinate invariant form, that is, in the form of the average density, (3<i>M</i>/4<i>πR</i>³), of the configuration which turns out to be independent of the radial coordinate <i>r</i> and depends only on the central (surface) density of the configuration. In this connection, we further argue that the central (surface) density of the structure should be independent of the density measured on the other boundary (surface/central) because there exists no a priori relation between the radial coordinate <i>r</i> and the proper distance from the centre of the sphere to its surface [1]. In the light of this reasoning, the various EOSs and analytic solutions of Einstein’s field equations in which the central and the surface density are interdependent can not fulfill the definition of central (surface) density measured only by one observer located in the MCRF at the centre (surface) of the configuration.

Marker-Free Tracking for Motion Artifact Compensation and Deformation Measurements in Optical Mapping Videos of Contracting Hearts.

Optical mapping is a high-resolution fluorescence imaging technique, which provides highly detailed visualizations of the electrophysiological wave phenomena, which trigger the beating of the heart. Recent advancements in optical mapping have demonstrated that the technique can now be performed with moving and contracting hearts and that motion and motion artifacts, once a major limitation, can now be overcome by numerically tracking and stabilizing the heart's motion. As a result, the optical measurement of electrical activity can be obtained from the moving heart surface in a co-moving frame of reference and motion artifacts can be reduced substantially. The aim of this study is to assess and validate the performance of a 2D marker-free motion tracking algorithm, which tracks motion and non-rigid deformations in video images. Because the tracking algorithm does not require markers to be attached to the tissue, it is necessary to verify that it accurately tracks the displacements of the cardiac tissue surface, which not only contracts and deforms, but also fluoresces and exhibits spatio-temporal physiology-related intensity changes. We used computer simulations to generate synthetic optical mapping videos, which show the contracting and fluorescing ventricular heart surface. The synthetic data reproduces experimental data as closely as possible and shows electrical waves propagating across the deforming tissue surface, as seen during voltage-sensitive imaging. We then tested the motion tracking and motion-stabilization algorithm on the synthetic as well as on experimental data. The motion tracking and motion-stabilization algorithm decreases motion artifacts approximately by 80% and achieves sub-pixel precision when tracking motion of 1–10 pixels (in a video image with 100 by 100 pixels), effectively inhibiting motion such that little residual motion remains after tracking and motion-stabilization. To demonstrate the performance of the algorithm, we present optical maps with a substantial reduction in motion artifacts showing action potential waves propagating across the moving and strongly deforming ventricular heart surface. The tracking algorithm reliably tracks motion if the tissue surface is illuminated homogeneously and shows sufficient contrast or texture which can be tracked or if the contrast is artificially or numerically enhanced. In this study, we also show how a reduction in dissociation-related motion artifacts can be quantified and linked to tracking precision. Our results can be used to advance optical mapping techniques, enabling them to image contracting hearts, with the ultimate goal of studying the mutual coupling of electrical and mechanical phenomena in healthy and diseased hearts.

Phantom Dirac-Born-Infeld dark energy

Motivated by the apparent discrepancy between Cosmic Microwave Background measurements of the Hubble constant and measurements from Type-Ia supernovae, we construct a model for Dark Energy with equation of state $w = p / \rho < -1$, violating the Null Energy Condition. Naive canonical models of so-called "Phantom" Dark Energy require a negative scalar kinetic term, resulting in a Hamiltonian unbounded from below and associated vacuum instability. We construct a scalar field model for Dark Energy with $w < -1$, which nonetheless has a Hamiltonian bounded from below in the comoving reference frame, {\it i.e.} in the rest frame of the fluid. We demonstrate that the solution is a cosmological attractor, and find that early-time cosmological boundary conditions consist of a "frozen" scalar field, which relaxes to the attractor solution once the Dark Energy component dominates the cosmological energy density. We consider the model in an arbitrary choice of gauge, and find that, unlike the case of comoving gauge, the fluid Hamiltonian is in fact unbounded from below in the reference frame of a highly boosted observer, corresponding to a nonlinear gradient instability. We discuss this in the context of general NEC-violating perfect fluids, for which this instability is a general property.

Redshift of a compact binary star in the neighborhood of a supermassive black hole

We present a method that allows to calculate the redshift of a compact binary star which moves in a strong external gravitational field, e.g. the field of a supermassive black hole. If the binary is close enough to the field center, its motion can be relativistic, while the relative motion of the stars in the binary is still non-relativistic. The latter can be computed in a co-moving reference frame. We calculate the redshift in a co-moving frame in Fermi coordinates as a series in the size of the binary $$\varrho $$ . The obtained expression is written in a covariant form up to linear terms in $$\varrho $$ . Using the equations of motion that have been obtained in a previous paper, we present the method of calculation of the redshift of a sample binary star moving in the field of a black hole. We illustrate this method by numerical model for the case of spherically-symmetric (Schwarzschild) black hole. The method can be applied to the analysis of the timing data of pulsars in the vicinity of the Galactic Center, and to the reconstruction of the binary star motion by its redshift.

Controlling straight line motion up to quantum levels by quantum measurements

Abstract A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrodinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.

On the internal structure of the current sheet in the pulsar wind

We investigate the internal structure of the current sheet in the pulsar wind within force-free and two-fluid MHD approximations. Within the force-free approximation we obtain general asymptotic solution of the Grad-Shafranov equation for quasi-spherical pulsar wind up to the second order in small parameter $\varepsilon = (\Omega r/c)^{-1}$. The solution allows an arbitrary latitudinal structure of the radial magnetic field, including that obtained in the numerical simulations of oblique rotators. It is also shown that the shape of the current sheet does not depend on the latitudinal structure. For the internal region of the current sheet outside the fast magnetosonic surface where the force-free approximation is not valid we use two-fluid MHD approximation. Carrying out calculations in the comoving reference frame we succeed in determining intrinsic electric and magnetic fields of a sheet. It allows us to analyze time-dependent effects which were not investigated up to now. In particular, we estimate the efficiency of the particle acceleration inside the sheet. Finally, after investigating the motion of individual particles in the time-dependent current sheet, we find self-consistently the width of the sheet and its time evolution.