Choice Of Reference Frame Research Articles

How does the choice of reference frame impact the distribution of WBAM components around different anatomical axes?

How does the choice of reference frame impact the distribution of WBAM components around different anatomical axes?

Three Puzzles with Covariance and Supertranslation Invariance of Angular Momentum Flux and Their Solutions.

We describe and solve three puzzles arising in covariant and supertranslation-invariant formulas for the flux of angular momentum and other Lorentz charges in asymptotically flat spacetimes: (i)Supertranslation invariance and covariance imply invariance under spacetime translations; (ii)the flux depends on redundant auxiliary degrees of freedom that cannot be set to zero in all Lorentz frames without breaking Lorentz covariance; (iii)supertranslation-invariant Lorentz charges do not generate the transformations of the Bondi mass aspect implied by the isometries of the asymptotic metric. In this Letter, we solve the first two puzzles by presenting covariant formulas that unambiguously determine the auxiliary degrees of freedom and clarify the last puzzle by explaining the different roles played by covariant and canonical charges. Our construction makes explicit the choice of reference frame underpinning seemingly unambiguous results presented in the current literature.

Quantum Euler angles and agency-dependent space-time

Abstract Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we begin exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws among reference frames in an effective regime. We invoke the quantum group SUq(2) as a description of deformed spatial rotations and interpret states of a representation of its algebra as describing the relative orientation between two reference frames. This leads to a quantization of one of the Euler angles and to an aspect of agency dependence: space is reconstructed as a collection of fuzzy points, exclusive to each agent, which depends on their choice of reference frame. Each agent can choose only one direction in which points can be sharp, while points in all other directions become fuzzy in a way that depends on this choice. Two agents making different choices will thus observe the same points with different degrees of fuzziness.

Gravity theories with local energy-momentum exchange: a closer look at Rastall-like gravity

Einstein’s famous equivalence principle is certainly one of the most striking features of the gravitational interaction. In a strict reading, it states that the effects of gravity can be made to disappear locally by a convenient choice of reference frame. As a consequence, no covariantly-defined net gravitational (point-wise) force should exist and energy-momentum of all matter and interaction fields combined, with gravity excluded, should be locally conserved. Although elegant, this represents a strong constraint on the dynamics of a gravitating system and it is only logical to question its naturality and observational basis. This is the purpose of the present work. For concreteness sake, we analyze, in the context of metric (torsion-free) theories of gravity, the simplest phenomenological model which allows for local energy-momentum exchange between the spacetime and matter/interaction fields while preserving the seemingly more natural principle of general covariance. This concrete model turns out to be a generalization of the socalled Rastall’s theory, with one important advantage: criticisms made to the latter, which are often used to dismiss it as a viable or interesting model, do not apply to the former in a Universe containing ‘dark’ ingredients, such as ours—a connection which seems to have been overlooked thus far. We conclude by exploring the consequences of our Rastall-like model to standard (astrophysical and cosmological) gravitational scenarios.

The choice of reference frame alters interpretations of turning gait and stability

Humans regularly follow curvilinear trajectories during everyday ambulation. However, globally-defined and locally-defined reference frames fall out of alignment during turning gait, which complicates spatiotemporal and biomechanical analyses. Thus, the choice of the locally-defined reference frame is an important methodological consideration. This study investigated how different definitions of reference frame change the results and interpretations of common gait measures during turning. Nine healthy adults completed two walking trials around a circular track. Kinematic data were collected via motion capture and used to calculate step length, step width, anteroposterior margin of stability, and mediolateral margin of stability using three different locally-defined reference frames: walkway-fixed, body-fixed, and trajectory-fixed. Linear-mixed effects models compared the effect of reference frame on each gait measure, and the effect of reference frame on conclusions about a known effect of turning gait – asymmetrical stepping patterns. All four gait measures differed significantly across the three reference frames. A significant interaction of reference frame and step type (i.e. inside vs outside step) on step length (p < 0.001), anteroposterior margin of stability (p < 0.001), and mediolateral margin of stability (p < 0.001) indicated conclusions about asymmetry differed based on the choice of reference frame. The choice of reference frame will change the calculated gait measures and may alter the conclusions of studies investigating turning gait. Care should be taken when comparing studies that used different reference frames, as results cannot be easily harmonized. Future studies of turning gait need to justify and detail their choice of reference frame.

A framework to understand the role of biological time in responses to fluctuating climate drivers

Understanding biological responses to environmental fluctuations (e.g. heatwaves) is a critical goal in ecology. Biological responses (e.g. survival) are usually measured with respect to different time reference frames, i.e. at specific chronological times (e.g. at specific dates) or biological times (e.g. at reproduction). Measuring responses on the biological frame is central to understand how environmental fluctuation modifies fitness and population persistence. We use a framework, based on partial differential equations (PDEs) to explore how responses to the time scale and magnitude of fluctuations in environmental variables (= drivers) depend on the choice of reference frame. The PDEs and simulations enabled us to identify different components, responsible for the phenological and eco-physiological effects of each driver on the response. The PDEs also highlight the conditions when the choice of reference frame affects the sensitivity of the response to a driver and the type of join effect of two drivers (additive or interactive) on the response. Experiments highlighted the importance of studying how environmental fluctuations affect biological time keeping mechanisms, to develop mechanistic models. Our main result, that the effect of the environmental fluctuations on the response depends on the scale used to measure time, applies to both field and laboratory conditions. In addition, our approach, applied to experimental conditions, can helps us quantify how biological time mediates the response of organisms to environmental fluctuations.

Ковариантный формализм гидродинамики гамильтоновых систем

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis R. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.

S-wave single heavy baryons with spin-3/2 at finite temperature

The thermal behavior of the spectroscopic parameters of the S-wave single heavy baryons Sigma _{Q}^{*}, Xi _{Q}^{*} and Omega _{Q}^{*} with spin-3/2 are investigated in QCD at finite temperature. We analyze the variations of the mass and residue of these baryons taking into consideration the contributions of QCD thermal condensates up to dimension eight in Wilson expansion. At finite temperature, due to the breakdown of the Lorentz invariance by the choice of reference frame and presence of an extra O(3) symmetry, some new four-dimensional operators come out in the form of the fermionic and gluonic parts of the energy momentum tensor that are taken into account in the calculations. Our analyses show that at lower temperatures, the parameters of baryons under consideration are not affected by the medium. These parameters, however, show rapid variations with respect to temperature at higher temperatures near to a pseudo-critical temperature, after which the baryons are melted. The results of the masses and residues at Trightarrow 0 limit are compatible with the available experimental data and predictions of other theoretical studies.

Can an infinitely long object fit in an expanding universe?

AbstractDoes space stretch its contents as the universe expands? Usually, we say the answer is no—the stretching of space is not like the stretching of a rubber sheet that might drag things with it. In this paper, we explore a potential counterexample—namely, we show that it is impossible to make an arbitrarily long object in an expanding universe, because it is impossible to hold the distant end of the object ‘stationary’ with respect to us (as defined in the Friedmann–Lemaître–Robertson–Walker metric). We show that this does not mean that expanding space has a force associated with it, rather, some fictitious forces arise due to our choice of reference frame. By choosing our usual time slice (where all comoving observers agree on the age of the universe), we choose a global frame that does not correspond to the frame of any inertial observer. As a result, simple relativistic velocity transforms generate an apparent acceleration, even where no force exists. This effect is similar to the fictitious forces that arise in describing objects in rotating reference frames, as in the case of the Coriolis effect.

Rattlebacks for the rest of us

Rattlebacks are semi-ellipsoidal tops that have a preferred direction of spin (i.e., a spin-bias). If spun in one direction, the rattleback will exhibit seemingly stable rotary motion. If spun in the other direction, the rattleback will being to wobble and subsequently reverse its spin direction. This behavior is often counter-intuitive for physics and engineering students when they first encounter a rattleback, because it appears to oppose the laws of conservation of momenta, thus this simple toy can be a motivator for further study. This paper develops an accurate dynamic model of a rattleback, in a manner accessible to undergraduate physics and engineering students, using concepts from introductory dynamics, calculus, and numerical methods classes. Starting with a simpler, 2D planar rocking semi-ellipse example, we discuss all necessary steps in detail, including computing the mass moment of inertia tensor, choice of reference frame, conservation of momenta equations, application of kinematic constraints, and accounting for slip via a Coulomb friction model. Basic numerical techniques like numerical derivatives and time-stepping algorithms are employed to predict the temporal response of the system. We also present a simple and intuitive explanation for the mechanism causing the spin-bias of the rattleback. It requires no equations and only a basic understanding of particle dynamics, and thus can be used to explain the intriguing rattleback behavior to students at any level of expertise.

Generalised model-independent characterisation of strong gravitational lenses – VI. The origin of the formalism intrinsic degeneracies and their influence on H0

We give a physical interpretation of the formalism intrinsic degeneracies of the gravitational lensing formalism that we derived on a mathematical basis in part IV of this series. We find that all degeneracies occur due to the partition of the mass density along the line of sight. Usually, it is partitioned into a background (cosmic) density and a foreground deflecting object. The latter can be further partitioned into a main deflecting object and perturbers. Weak deflecting objects along the line of sight are also added, either to the deflecting object or as a correction of the angular diameter distances, perturbing the cosmological background density. A priori, this is an arbitrary choice of reference frame and partition. They can be redefined without changing the lensing observables which are sensitive to the integrated deflecting mass density along the entire line of sight. Reformulating the time delay equation such that this interpretation of the degeneracies becomes easily visible, we note that the source can be eliminated from this formulation, which simplifies reconstructions of the deflecting mass distribution or the inference of the Hubble constant, $H_0$. Subsequently, we list necessary conditions to break the formalism intrinsic degeneracies and discuss ways to break them by model choices or including non-lensing observables like velocity dispersions along the line of sight with their advantages and disadvantages. We conclude with a systematic summary of all formalism intrinsic degeneracies and possibilities to break them.

Cued by What We See and Hear: Spatial Reference Frame Use in Language.

To what extent is the choice of what to say driven by seemingly irrelevant cues in the visual world being described? Among such cues, how does prior description affect how we process spatial scenes? When people describe where objects are located their use of spatial language is often associated with a choice of reference frame. Two experiments employing between-participants designs (N = 490) examined the effects of visual cueing and previous description on reference frame choice as reflected in spatial prepositions (in front of, to the left of, etc.) to describe pictures of object pairs. Experiment 1 examined the effects of visual and linguistic cues on spatial description choice through movement of object(s) in spatial scenes, showing sizeable effects of visual cueing on reference frame choice. Experiment 2 monitored eye movements of participants following a linguistic example description, revealing two findings: eye movement “signatures” associated with distinct reference frames as expressed in language, and transfer of these eye movement patterns just prior to spatial description for different (later) picture descriptions. Both verbal description and visual cueing similarly influence language production choice through manipulation of visual attention, suggesting a unified theory of constraints affecting spatial language choice.

Comparison of Moment-Based Methods for Representing Droplet Size Distributions in Supersonic Nucleating Flows of Steam

This paper investigates the performance of moment-based methods and a monodispersed model (Mono) in predicting the droplet size distribution and behavior of wet-steam flows. The studied moment-based methods are a conventional method of moments (MOM) along with its enhanced version using Gaussian quadrature, namely the quadrature method of moments (QMOM). The comparisons of models are based on the results of an Eulerian–Lagrangian (E–L) method, as the benchmark calculations, providing the full spectrum of droplet size. In contrast, for the MOM, QMOM, and Mono an Eulerian reference frame is chosen to cast all the equations governing the phase transition and fluid motion. This choice of reference frame is essential to draw a meaningful comparison regarding complex flows in wet-steam turbines as the most important advantage of the moment-based methods is that the moment-transport equations can be conveniently solved in an Eulerian frame. Thus, the moment-based method can avoid the burdensome challenges in working with a Lagrangian framework for complicated flows. The main focus is on the accuracy of the QMOM and MOM in representing the water droplet size distribution. The comparisons between models are made for two supersonic low-pressure nozzle experiments reported in the literature. Results show that the QMOM, particularly inside the nucleation zone, predicts moments closer to those of the E–L method. Therefore, for the test case in which the nucleation is significant over a large proportion of the domain, the QMOM provides results in clearly better agreements with the E–L method in comparison with the MOM.

Determining the impact of cell mixing on signaling during development.

Cell movement and intercellular signaling occur simultaneously to organize morphogenesis during embryonic development. Cell movement can cause relative positional changes between neighboring cells. When intercellular signals are local such cell mixing may affect signaling, changing the flow of information in developing tissues. Little is known about the effect of cell mixing on intercellular signaling in collective cellular behaviors and methods to quantify its impact are lacking. Here we discuss how to determine the impact of cell mixing on cell signaling drawing an example from vertebrate embryogenesis: the segmentation clock, a collective rhythm of interacting genetic oscillators. We argue that comparing cell mixing and signaling timescales is key to determining the influence of mixing. A signaling timescale can be estimated by combining theoretical models with cell signaling perturbation experiments. A mixing timescale can be obtained by analysis of cell trajectories from live imaging. After comparing cell movement analyses in different experimental settings, we highlight challenges in quantifying cell mixing from embryonic timelapse experiments, especially a reference frame problem due to embryonic motions and shape changes. We propose statistical observables characterizing cell mixing that do not depend on the choice of reference frames. Finally, we consider situations in which both cell mixing and signaling involve multiple timescales, precluding a direct comparison between single characteristic timescales. In such situations, physical models based on observables of cell mixing and signaling can simulate the flow of information in tissues and reveal the impact of observed cell mixing on signaling.

Anomalies of the entanglement entropy in chiral theories

We study entanglement entropy in theories with gravitational or mixed U(1) gauge-gravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and self-dual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems. In two and four dimensions we use anomalous Ward identities to find general expressions for the transformation of the entanglement entropy under a diffeomorphism. (In the case of a mixed anomaly there is an alternative presentation of the theory in which the entanglement entropy is not invariant under a U(1) gauge transformation. The free-field manifestation of this phenomenon involves a novel kind of fermion zero mode on a gravitational background with a twist in the normal bundle to the entangling surface.) We also study d-dimensional anomalous systems as the boundaries of d + 1 dimensional gapped Hall phases. Here the full system is non-anomalous, but the boundary anomaly manifests itself in a change in the entanglement entropy when the boundary metric is sheared relative to the bulk.

О ГЕОМЕТРИЧЕСКИ НЕЛИНЕЙНЫХ ОПРЕДЕЛЯЮЩИХ СООТНОШЕНИЯХ УПРУГОГО МАТЕРИАЛА

In the field of solid mechanics it is often necessary to use constitutive (physical) relations in the rate form, for example, for formulation of the boundary value problem in the rate form with contact conditions when a contact area is a priori unknown and changes in a deformation process. The paper considers some questions of formulating geometrically nonlinear constitutive relations of elastic material in the rate form and the relationship of these equations and the constitutive relations in the finite form. In many existing elastic and elasto-plastic models Hooke's law (written in terms of the actual configuration) is used as the constitutive relation. As a rule, the rate measure of the strain is deformation rate tensor (the symmetrical part of velocity gradient) and the stress rate measure is some objective derivative (convective or corotational) of weighted Kirchhoff stress tensor. The use of the convective derivative leads to certain difficulties, for example, analysis of evolution stress state in a deformable basis is complicated; consequently, convective derivatives are excluded from consideration. Using a stress tensor corotational derivative instead of the material derivative (derivative by time) allows satisfying the principle of material indifference (the principle of independence of constitutive relation from the choice of reference frame), however a choice of the derivative type can be implemented by many ways. An arbitrary selection of stress corotational derivative leads to undesirable effects: stress oscillations for the simple shear monotonic loading (for example, for Jaumann derivative), “not closed” stress trajectories and nonzero stress work for a closed deformation trajectory. In papers of A. Meyers, H. Xiao, O. Bruhns corotational derivative (with logarithmic spin or logspin) was proposed.The derivative of the right Hencky's strain tensor is exactly equal to deformation rate tensor. When using this derivative in the constitutive relation the described effects are missing, on the basis of this remarked logspin authors state the logspin exclusivity and recommend it only for using in rate form constitutive relations. The article shows full compliance between Hooke's law in the rate and finite form under conditions: existence of the material basis in which properties of the body (in this case - elastic) remain unchanged and the use of the same type corotational derivative for stress and strain measures. Computational experiments for illustration of the proved assertion about the equivalence of different Hooke's law forms were conducted: various measures of strain state and their corotational derivatives are considered; a kinematic loading in a closed cycle (in the space of deformations) is applied. It is shown for isotropic elastic materials that stress trajectories are closed. When using work-conjugacy stress and strain measures the dissipation energy is absent. Thus it is possible to question the exclusive choice of logarithmic spin and the above-mentioned commonly used measures of stress-strain state. In formulating and solving the problems of solid mechanics there should be an opportunity to use different stress-strain measures and their objective derivatives, the choice of measures and constitutive relations should be justified from the point of physical analysis of the process.

Effect of Laterally Wedged Insoles on the External Knee Adduction Moment across Different Reference Frames.

ObjectiveBiomechanical effects of laterally wedged insoles are assessed by reduction in the knee adduction moment. However, the degree of reduction may vary depending on the reference frame with which it is calculated. The purpose of this study was to clarify the effect of reference frame on the reduction in the knee adduction moment by laterally wedged insoles.MethodsTwenty-nine healthy participants performed gait trials with a laterally wedged insole and with a flat insole as a control. The knee adduction moment, including the first and second peaks and the angular impulse, were calculated using four different reference frames: the femoral frame, tibial frame, laboratory frame and the Joint Coordinate System.ResultsThere were significant effects of reference frame on the knee adduction moment first and second peaks (P < 0.001 for both variables), while the effect was not significant for the angular impulse (P = 0.84). No significant interaction between the gait condition and reference frame was found in either of the knee adduction moment variables (P = 0.99 for all variables), indicating that the effects of laterally wedged insole on the knee adduction moments were similar across the four reference frames. On the other hand, the average percent changes ranged from 9% to 16% for the first peak, from 16% to 18% for the second peak and from 17% to 21% for the angular impulse when using the different reference frames.ConclusionThe effects of laterally wedged insole on the reduction in the knee adduction moment were similar across the reference frames. On the other hand, Researchers need to recognize that when the percent change was used as the parameter of the efficacy of laterally wedged insole, the choice of reference frame may influence the interpretation of how laterally wedged insoles affect the knee adduction moment.

Lagrangian vortices in developing tropical cyclones

Tracking pre‐genesis tropical cyclones is important for earlier detection of developing systems as well as targeting potential locations for dropsondes in field experiments. The use of a reference frame moving with the disturbance gives a more accurate depiction of streamlines and closed circulation than the Earth‐relative frame. However, identification of recirculating regions does not require a choice of reference frame when marked by the Galilean invariant Eulerian Okubo–Weiss (OW) parameter. While the Eulerian OW parameter is generally effective at identifying vortex cores at a given place and a given time, it has its limitations in weak disturbances and in time‐dependent flows. Integrating the eigenvalue of the velocity gradient tensor along particle trajectories provides a time‐smoothing of the Eulerian OW parameter, and provides earlier detection with fewer false alarms. We refer to this integration along trajectories as the Lagrangian OW parameter. When mapped to a horizontal grid it becomes a Lagrangian OW field.The Lagrangian OW field has advantages over the Eulerian OW field in the detail of additional flow structures that it identifies. The Lagrangian OW field shows the Lagrangian boundaries that are present as a disturbance develops from an easterly wave, and a shear sheath that forms when a disturbance becomes self‐sustaining, typically at tropical storm strength. Since all of these structures are Lagrangian, they are advected with the flow field, and display the continuous evolution of coherent flow features as the fluid evolves.Examples of the use of the Lagrangian OW field are given for ECMWF forecast data from the 2014 Atlantic hurricane season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones. The Lagrangian OW field also shows additional details of vortex mergers, and is used to identify a stable crystal lattice configuration in which vorticity does not aggregate.

Reference frames in virtual spatial navigation are viewpoint dependent.

Spatial navigation in the mammalian brain relies on a cognitive map of the environment. Such cognitive maps enable us, for example, to take the optimal route from a given location to a known target. The formation of these maps is naturally influenced by our perception of the environment, meaning it is dependent on factors such as our viewpoint and choice of reference frame. Yet, it is unknown how these factors influence the construction of cognitive maps. Here, we evaluated how various combinations of viewpoints and reference frames affect subjects' performance when they navigated in a bounded virtual environment without landmarks. We measured both their path length and time efficiency and found that (1) ground perspective was associated with egocentric frame of reference, (2) aerial perspective was associated with allocentric frame of reference, (3) there was no appreciable performance difference between first and third person egocentric viewing positions and (4) while none of these effects were dependent on gender, males tended to perform better in general. Our study provides evidence that there are inherent associations between visual perspectives and cognitive reference frames. This result has implications about the mechanisms of path integration in the human brain and may also inspire designs of virtual reality applications. Lastly, we demonstrated the effective use of a tablet PC and spatial navigation tasks for studying spatial and cognitive aspects of human memory.

A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves

Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary's gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.