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In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically underpins miscellaneous investigations of phenomenological and quantum extensions of General Relativity. We discuss how it allows quantum field theory to be a theoretical laboratory for testing Einstein's theory of gravity and demonstrate the current state of the art of an efficient and practical scheme for evaluating the classical components of perturbative weak-field scattering amplitudes until the fourth post-Minkowskian order. Such results complement numerical predictions in Einstein's theory of gravity., Comment: 42 pages. 12 figures. Invited chapter for the Section "Effective Quantum Gravity" edited by C. Burgess and J. Donoghue of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Nature, expected in 2023)

A model is proposed for describing the line shape of absorption and dispersion signals from which a recorded signal of nuclear magnetic resonance (NMR) is formed in a weak field. The expediency of using spectral analysis to determine the contributions of absorption and dispersion signals to the recorded NMR signal has been substantiated using a modulation technique. A new method is proposed for determining these contributions. The research results are presented.

The purpose of the present paper is to enquire whether General Relativity (GR) is necessary for the prediction of gravitational waves. It will be shown that in the weak field limit the same predictions come also from the treatment of a zero mass, spin 2 gravitational scattering amplitude. This will also justify the simpler effective vector approach of the author, only the angular distribution differing from that of a tensor theory.

Current limits for exposures to nonionizing electromagnetic fields (EMF) are set, based on relatively short-term exposures. Long-term exposures to weak EMF are not addressed in the current guidelines. Nevertheless, a large and growing amount of evidence indicates that long-term exposure to weak fields can affect biological systems and might have effects on human health. If they do, the public health issues could be important because of the very large fraction of the population worldwide that is exposed. We also discuss research that needs to be done to clarify questions about the effects of weak fields. In addition to the current short-term exposure guidelines, we propose an approach to how weak field exposure guidelines for long-term exposures might be set, in which the responsibility for limiting exposure is divided between the manufacturer, system operator, and individual being exposed. Bioelectromagnetics. © 2020 Bioelectromagnetics Society.

Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems., 5 pages + supplemental material, 7 figures; Updated to reflect published version

Iteration problems such as compound interest calculations have well-specified parameters and aim to derive an exact value. Not all problems offer well-specified parameters, even for well-defined dynamic equations; the linear “weak field approximation” of general relativity is iteratively equivalent to Einstein’s non-linear field equation, but the exact parameters involved in some applications are unknown. This paper develops a theory based on “fuzzy” parameters that must produce exact results. The problem is analyzed and example calculations are produced.

The non-invasive delivery of electric currents through the scalp (transcranial electrical stimulation) is a popular tool for neuromodulation, mostly due to its highly adaptable nature (waveform, montage) and tolerability at low intensities (< 2 mA). Applied rhythmically, transcranial alternating current stimulation (tACS) may entrain neural oscillations in a frequency- and phase-specific manner, providing a causal perspective on brain-behaviour relationships. While the past decade has seen many behavioural and electrophysiological effects of tACS that suggest entrainment-mediated effects in the brain, it has been difficult to reconcile such reports with the weak intracranial field strengths (< 1 V/m) achievable at conventional intensities. In this review, we first describe the ongoing challenges faced by users of tACS. We outline the biophysics of electrical brain stimulation and the factors that contribute to the weak field intensities achievable in the brain. Since the applied current predominantly shunts through the scalp-stimulating the nerves that innervate it-the plausibility of transcutaneous (rather than transcranial) effects of tACS is also discussed. In examining the effects of tACS on brain activity, the complex problem of salvaging electrophysiological recordings from artefacts of tACS is described. Nevertheless, these challenges by no means mark the rise and fall of tACS: the second part of this review outlines the recent advancements in the field. We describe some ways in which artefacts of tACS may be better managed using high-frequency protocols, and describe innovative methods for current interactions within the brain that offer either dynamic or more focal current distributions while also minimising transcutaneous effects.

BACKGROUND Prostate cancer is a common malignant tumor in males. Prostate cancer grading is an important basis for evaluation of invasion. The purpose of this article was to use dynamic enhanced scan magnetic resonance imaging (MRI) to quantitatively investigate the relationship between tumor oxygenation value and prostate cancer pathological Gleason score. MATERIAL AND METHODS A total of 312 prostate cancer patients diagnosed by needle biopsy who received MRI dynamic enhanced scan were enrolled in this study. Multiparameter oxygen concentration image based on MRI was applied to test pO2 in tumors. Multiple spin resonance image relaxation time edit sequence and weak field diffusion model were used to estimate oxygen saturation level and pO2. hematoxylin and eosin staining and Gleason score were used to determine biological behavior and prognosis. RESULTS According to the Gleason score system, there were 28 cases with a score of 10, 112 cases with a score of 9, 56 cases with a score of 8, and 116 cases with a score lower than 7. The enrolled patients were divided into groups: 116 cases into the middle-to-well differentiation group (Gleason score ≤7) and 196 cases into the poorly differentiation group (Gleason score at 8 to 10). Prostate cancer tumor oxygenation value was positively correlated with Gleason score (r=0.349, P

If a person comes into contact with pathogens on public facilities, there is a threat of contact (skin/wound) infections. More urgently, there are also reports about COVID-19 coronavirus contact infection, which once again reminds that contact infection is a very easily overlooked disease exposure route. Herein, we propose an innovative implantation strategy to fabricate a multi-walled carbon nanotube/polyvinyl alcohol (MWCNT/PVA, MCP) interpenetrating interface to achieve flexibility, anti-damage, and non-contact sensing electronic skin (E-skin). Interestingly, the MCP E-skin had a fascinating non-contact sensing function, which can respond to the finger approaching 0–20 mm through the spatial weak field. This non-contact sensing can be applied urgently to human-machine interactions in public facilities to block pathogen. The scratches of the fruit knife did not damage the MCP E-skin, and can resist chemical corrosion after hydrophobic treatment. In addition, the MCP E-skin was developed to real-time monitor the respiratory and cough for exercise detection and disease diagnosis. Notably, the MCP E-skin has great potential for emergency applications in times of infectious disease pandemics. Electronic Supplementary Material Supplementary material (fabrication of MCP E-skin, laser confocal tomography, parameter optimization, mechanical property characterization, finite element simulation, sensing mechanism, signal processing) is available in the online version of this article at 10.1007/s12274-021-3831-z.

In recent years, Local Defect Resonance (LDR) has generated much interest in development and applications of new resonant acoustic modes for non-destructive testing (NDT) and imaging of planar defects in composite materials. The studies and applications are focused at LDR in composites where the most common defects are delaminations and impacts. This paper considers the mechanism of development and the attributes of LDR for through-thickness cracks in plates. The experiments validate that the LDR is caused by the resonance of the edge waves propagating along the crack faces. The edge wave resonance features weak field decay away from the crack, partial as well as high-order LDR and provides clear opportunities for applications in NDT techniques based on acoustic activation of damage.

We investigate numerically the role of near-field dipole-dipole interactions on the late-emission dynamics of large disordered cold atomic samples driven by a weak field. Previous experimental and numerical studies of subradiance in macroscopic samples have focused on low-density samples of pure two-level atoms, without internal structure, which corresponds to a scalar representation of the light. The cooperative nature of the late emission of light is then governed by the resonant optical depth. Here, by considering the vectorial nature of the light, we show the detrimental role of the near-field terms on cooperativity in higher-density samples. The observed reduction in the subradiant lifetimes is interpreted as a signature of the inhomogeneous broadening due to the near-field contributions, in analogy with the van der Waals dephasing phenomenon for superradiance.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and apply the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma medium as well as non-plasma medium., 13 pages, 4 figures. Accepted for publication in International Journal of Geometric Methods in Modern Physics

Aiming at the problem of servoing task failure caused by the manipulated object deviating from the camera field-of-view (FOV) during the robot manipulator visual servoing (VS) process, a new VS method based on an improved tracking learning detection (TLD) algorithm is proposed in this article, which allows the manipulated object to deviate from the camera FOV in several continuous frames and maintains the smoothness of the robot manipulator motion during VS. Firstly, to implement the robot manipulator visual object tracking task with strong robustness under the weak FOV constraints, an improved TLD algorithm is proposed. Then, the algorithm is used to extract the image features (object in the camera FOV) or predict image features (object out of the camera FOV) of the manipulated object in the current frame. And then, the position of the manipulated object in the current image is further estimated. Finally, the visual sliding mode control law is designed according to the image feature errors to control the motion of the robot manipulator so as to complete the visual tracking task of the robot manipulator to the manipulated object in complex natural scenes with high robustness. Several robot manipulator VS experiments were conducted on a six-degrees-of-freedom MOTOMANSV3 industrial manipulator under different natural scenes. The experimental results show that the proposed robot manipulator VS method can relax the FOV constraint requirements on real-time visibility of manipulated object and effectively solve the problem of servoing task failure caused by the object deviating from the camera FOV during the VS.

This paper presents a new concept of dual-band circulators using a weak field biased ferrite. Two prototypes were designed and measured, one with the same circulation direction between the first and the second band (unidirectional circulator) and the other one with an opposite circulation direction (bidirectional circulator). These new designs allow a control of the two operating frequencies and a widening of bandwidths.

Using the previous results on static Green functions we will demonstrate in this chapter how we can utilize them to construct the gravitational field of static and stationary mass distributions in the weak-field limit of non-local ghost-free gravity. This chapter is based on Boos et al. (Phys. Rev. D 97(8), 084021 (2018); Int. J. Mod. Phys. D 27(14), 1847022 (2018); Int. J. Mod. Phys. D 29(14), 2043027 (2020); Phys. Rev. D 101(12), 124065 (2020)).

International audience; From 1949, the Adenauer government has a government communication service. In fact, a State apparatus has been built and institutionalized since 1918. This practice was built through a long process of institutionalization of the government’s symbolic policy. This paper is based on an analysis of the trajectories of the actors of the post-war German governmental communication. Although it is institutionalized, the conclusions may be surprising. Looking at the careers of the actors who occupy the positions in this field, everything suggests the incomplete professionalization of the actors in this field. No occupational group seems to have its own recruitment, exit and maintenance mechanisms, or even to maintain activity.; Desde 1949, el gobierno de Adenauer dispone de un portavoz et fomenta la práctica de la comunicación social del gobierno. Esta práctica de la comunicación se apoya en un Estado construido y consolidado desde 1918, así que esa práctica se ha construido a lo largo de un proceso de institucionalización de la política simbólica del gobierno. El balance que se hace desde el análisis de las trayectorias de los actores de la comunicación gubernamental de la posguerra, puede sorprender. A pesar de que este campo es institucionalizado, no es el caso de las trayectorias profesionales de los propios actores. Pues, ningún grupo profesional ha logrado imponer sus propios mecanismos de reclutamiento, de entrada y de salida de la profesión o incluso de desempeño de la actividad de la comunicación gubernamental.; Dès 1949, le gouvernement d’Adenauer dispose et assoie la pratique d’un porte-parolat et d’un service de communication gouvernementale. Plus exactement, il dispose d’un appareil d’État construit et consolidé dès 1918. Cette pratique s’est construite par un long processus d’institutionnalisation de la politique symbolique gouvernementale. A partir d’une analyse des trajectoires des acteurs de la communication gouvernementale d’après-guerre, le constat peut surprendre. Bien qu’institutionnalisé, au regard des carrières des acteurs qui l’occupent, tout laisse à penser à l’incomplétude de la professionnalisation des acteurs de ce champ. Aucun groupe professionnel ne semble avoir imposé ses propres mécanismes de recrutement, d’entrée et de sortie voire de maintien dans cette activité de communication gouvernementale.

We study light deflection from a Reissner-Nordstr\"om-de Sitter black hole in the gravitational monopole background. We first calculate the orbit equation and the contribution of the monopole and black hole parameters to the deflection angle up to second-order for the vanishing cosmological constant case using the Rindler-Ishak method. We also obtain the contribution of the cosmological constant to light deflection in this geometry in the weak field limit using the same method., Comment: v2: 10 pages, 2 figures, matches the published version

The role of magnetic fields in the chromospheric heating problem remains greatly unconstrained. Most theoretical predictions from numerical models rely on a magnetic configuration, field strength and connectivity whose details have not been well established with observational studies. High-resolution studies of chromospheric magnetic fields in plage are very scarce or non-existent in general. Our aim is to study the stratification of the magnetic field vector in plage regions. We use high-spatial resolution full-Stokes observations acquired with CRISP instrument at the Swedish 1-m Solar Telescope in the Mg I $\lambda$5173, Na I $\lambda$5896 and Ca II $\lambda$8542 lines. We have developed a spatially-regularized weak-field approximation (WFA) method based on the idea of spatial regularization. This method allows for a fast computation of magnetic field maps for an extended field of view. The fidelity of this new technique has been assessed using a snapshot from a realistic 3D magnetohydrodynamics simulation. We have derived the depth-stratification of the line-of-sight component of the magnetic field from the photosphere to the chromosphere in a plage region. The magnetic fields are concentrated in the intergranular lanes in the photosphere and expand horizontally toward the chromosphere, filling all the space and forming a canopy. Our results suggest that the lower boundary of this canopy must be located around 400-600 km from the photosphere. The mean canopy total magnetic field strength in the lower chromosphere ($z\approx760$ km) is 658 G. At $z=1160$ km we estimate $\approx 417$ G. We propose a modification to the WFA that improves its applicability to data with worse signal-to-noise ratio. These methods provide a quick and reliable way of studying multi-layer magnetic field observations without the many difficulties inherent to other inversion methods., Comment: Accepted for publication on 2020-08-27

International audience; We present paleomagnetic and geochronological data of twenty-five stacked lava flows from São Miguel Island (Azores) that were emplaced during the last geomagnetic reversal (Matuyama-Brunhes, M-B). The characteristic direction of natural remanent magnetization was isolated through alternating field and/or thermal demagnetization. From bottom to top, the directional changes display a first phase with reverse, transitional and normal directions which is followed by a second phase with transitional and normal directions. Dating by Potassium-Argon (K-Ar) of fresh separated groundmass provide ages of 768 ± 5 ka and 765 ± 5 ka (1σ) for the first and second transitional episodes, respectively. We infer that this sequence recorded the last reversal and reveal the presence of a rebound that occurred soon after the transition. The age of the transition is 5-15 kyr younger than at other volcanic localities, but in agreement with astronomical ages that were recently proposed for the transitional interval. The reversal is characterized by weak field intensity during the transition, a recovery phase and a subsequent decrease during the rebound. The two transitional virtual geomagnetic poles (VGPs) that characterize the transition are found above the South Atlantic and the North Pacific. When compared to other M-B records, no VGP is found above preferred locations.

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field., Comment: 12 pages. Accepted for publication in Physical Review D (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.103521)

We study numerically the thermodynamic properties of the spin nematic phases in a magnetic field in the spin-1 bilinear-biquadratic model. When the field is applied, the phase transition temperature once goes up and then decreases rapidly toward zero, which is detected by the peak-shift in the specific heat. The underlying mechanism of the reentrant behavior is the entropic effect. In a weak field the high temperature paramagnetic phase rapidly loses its entropy while the ferroquadrupolar nematic phase remains robust by modifying the shape of the ferroquadrupolar moment. This feature serves as a fingerprint of generic ferroquadrupolar phases, while it is not observed for the case of antiferroquadrupoles., 6 pages, 4 figures + supplemental material

We study the dissipative conductivity $\sigma_1$ of a dirty superconductor with a finite Dynes parameter $\Gamma$ under a dc-biased weak time-dependent field. The Usadel equation for the current-carrying state is solved to calculate the pair potential, penetration depth, supercurrent density, and quasiparticle spectrum. It is shown that, while the depairing current density $j_d$ for $\Gamma=0$ is coincident with the Kupriyanov-Lukichev theory, a finite $\Gamma$ decreases the superfluid density, resulting in a reduction of $j_d$. The broadening of the peaks of the quasiparticle density of states induced by a combination of a finite $\Gamma$ and a dc bias can reduce $\sigma_1$ below that for the ideal dirty BCS superconductor with $\Gamma=0$, while subgap states at Fermi level proportional to $\Gamma$ results in a residual conductivity at $T\to 0$. We find the optimum combination of $\Gamma$ and the dc bias to minimize $\sigma_1$ by scanning all $\Gamma$ and all currents up to $j_d$. By using the results, it is possible to improve $j_d$ and reduce electromagnetic dissipation in various superconducting quantum devices., Comment: 9 pages, 8 figures

A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: \[ \begin{array}{lll} {\bf{\nabla}^{2}\Phi}=4\pi G \rho+\bf{H}{\bf{\cdot}}\bf{H}\,, \quad&\qquad\bf{\nabla}\bf{\cdot}\bf{H}=0\,, \quad&\qquad {\bf{\nabla}\bf{\times}\bf{H}}=4\pi G\, \bf{K}\,. \end{array} \] Not only the mass density $\rho$ but also the current density $\mathbf{K}$ is intrinsic to matter. Sourcing $\mathbf{H}$ which is of NS-NS $H$-flux origin, $\mathbf{K}$ is nontrivial if the matter is `stringy'. $\mathbf{H}$ contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e. $\bf{\ddot{x}}=-\bf{\nabla}\Phi$. We define `stringization' analogous to magnetization and discuss regular as well as monopole-like singular solutions., Comment: 6 pages, No figure, v2) Refs added

The present study outlines discursive work in a weak field mandate event. The case is a conference focussed on assistive technologies that may help persons with disabilities gain better access to educational and employment spaces in India. Findings highlight three mechanisms which underpinned event-specific discursive work – discursive clarity, alignment, and coordination. In outlining such discursive work, the present study indicates how actors, who congregate as a group without high symbolic or resource support from powerful institutional elites, attempt to influence broader processes of institutionalisation. Keywords: Discourse, Field-level events, Disability, Assistive technologies

We show that in the weak field limit the light deflection alone cannot distinguish between different R + F [ g ( □ ) R ] models of gravity, where F and g are arbitrary functions. This does not imply, however, that in all these theories an observer will see the same deflection angle. Owed to the need to calibrate the Newton constant, the deflection angle may be model-dependent after all necessary types of measurements are taken into account.

A compact design of a rapid-response nuclear magnetic spectrometer for investigation of condensed media in weak fields is reported. As a result of investigation of different condensed media, special features of recording a nuclear magnetic resonance (NMR) signal in a weak magnetic field from a small volume of the medium under study are established. For the first time the NMR absorption spectra of condensed media in a weak field are collected. Based on the results of experimental studies, the potential of using a compact NMR-spectrometer for condensed media monitoring in a rapid response mode is determined.

A new construction of a magnetic system and a circuit for detecting the signal of nuclear magnetic resonance (NMR) in a weak magnetic field are described. The features of NMR-signal detection from a small volume (less than 0.3 mL) of liquid medium in a weak field using the modulation method are determined. Taking these features into account in the new design of the compact NMR spectrometer has made it possible to provide detection of signals from different nuclei of a condensed medium that possess a magnetic moment. The results of the experimental investigations of various condensed media are presented.

Gravitational waves are regarded as linear waves in the weak field approximation, which ignores the spacetime singularity. In this paper, we analyze singularities in exact gravitational wave solutions. We provide an exact general solution of the gravitational wave with cylindrical symmetry. The general solution includes some known cylindrical wave solutions as special cases. We show that there are two kinds of singularities in the cylindrical gravitational wave solution. The first kind of singularity corresponds to a singular source. The second kind of singularity corresponds to a resonance between different gravitational waves. When two gravitational waves coexist, the interference term in the source may vanish in the sense of time averaging.

The characteristics of signal registration of nuclear-magnetic resonance in a weak magnetic field from a small volume of an investigated medium have been considered. The consideration of the characteristics revealed in a new developed design of a magnetic system for a compact nuclear-magnetic spectrometer, and also in the NMR-signal registration method allows significant extension of the possibility to use the phenomenon of nuclear-magnetic resonance for the study of condensed medium in an express mode. The experimental results of different media studies have been presented.

Temperature-dependent magnetization was measured for CuCr2–x Sb x Sе4 solid solutions in the range 300–5 K in a weak field (50 Oe) and a strong field (10 kOe) and in an ac magnetic field having a frequency of 100–10000 Hz and an amplitude of Н = 1 Oe. The type and character of magnetic transitions under investigation in the system were determined, and its magnetic phase diagram was constructed.

Photochemistry induced by phase-coherent laser light is an intriguing topic. The possibility of weak-field (one-photon) phase-only control of photoisomerization is controversial. Experimental studies on the weak-field coherent control of cis-trans isomerization have led to conflicting results. Here we address this issue by quantum dynamical calculations, focusing on a mechanism where different "phase-shaped" wave packets are quickly stabilized ("dumped") in the trans configuration because of prompt energy dissipation. We systematically investigate different relaxation rates with the system-bath dynamics described within the time-dependent Hartree approximation leading to a friction-type force. We find evidence for phase control of trans-isomer yields (about 5%) in this model with pure energy dissipation given sufficiently strong dampening.

We explore the implementation of weak field asymptotic theory using orbitals and potentials calculated via Density Functional Theory. This provides a way to calculate strong field ionization rates by assuming that the field is constant.

In this paper we examine the possibility of a Josephson AC effect between two superconductors induced by the Earth's gravitational field, making use of the gravito-Maxwell formalism. The theoretical framework exploits the symmetry between the weak field expansion of the gravitational field and the standard Maxwell formulation, combined with the Josephson junction physics. We also suggest a suitable experimental setup, analysing also the related possible difficulties in measurements., 9 pages, 3 figures

We show that fundamental plane of elliptical galaxies can be used to obtain observational constraints on metric theories of gravity. Being it connected to global properties of ellipticals, it can fix parameters of modified gravity. Specifically, we use fundamental plane to constrain modified theories of gravity with Yukawa-like corrections which commonly emerge in the post-Newtonian limit. After giving examples on how these corrections are derived, we first analyze the velocity distribution of elliptical galaxies comparing theoretical results of modified gravity with Yukawa-like corrections with astronomical data. According to these results, it is possible to constrain the parameters of the corrections discriminating among classes of models compatible with astronomical observations. We conclude that fundamental plane can be used as a standard tool to probe different theories of gravity in the weak field limit., Comment: 13 pages, 7 figures, to be published in Phys. Dark. Univ. (2020)

It was pointed out long ago by Vainshtein [Phys. Lett. 39B, 393 (1972)] that the weak-field perturbation expansion of generic theories (of the nonlinear Fierz-Pauli type) involving massive spin-2 excitations breaks down below a certain distance around a material source ("Vainshtein radius"), scaling as some inverse power of the spin-2 mass $m_2$, i.e., some positive power of the range $m_2^{-1}$. Here we prove that this conclusion does not apply in a generalized Einstein-Cartan theory (called "torsion bigravity") whose spectrum is made (like that of bimetric gravity) of a massless spin-2 excitation and a massive spin-2 one. Working within a static spherically symmetric ansatz, we prove, by reformulating the field equations in terms of new variables, that one can construct an all-order weak-field perturbative expansion where no denominators involving $m_2$ ever appear in the region $r \ll m_2^{-1}$. In particular, we show how the formal large-range limit, $m_2 \to 0$, leads to a well-defined, finite perturbation expansion, whose all-order structure is discussed in some detail., 18 pages, no figures

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts which can be used as a guide for creating learning tools to help students develop a functional understanding of concepts involving the corrections to the energy spectrum due to the Zeeman effect., Comment: Physics Education Research Conference Proceedings. arXiv admin note: text overlap with arXiv:2006.05000

Accurate cosmological simulations that include the effect of non-linear matter clustering as well as of massive neutrinos are essential for measuring the neutrino mass scale from upcoming galaxy surveys. Typically, Newtonian simulations are employed and the neutrino distribution is sampled with a large number of particles in order to beat down the shot noise. Here we perform very efficient simulations with light massive neutrinos which require virtually no extra cost over matter-only simulations, and furthermore do not require tracer particles for the neutrinos. Instead, we use a weak-field dictionary based on the recently developed Newtonion motion approach, where Newtonian simulations for matter are paired with a linear relativistic Boltzmann code to allow for an absorption of the neutrino evolution into a time-dependent coordinate transformation. For this, only minimal modifications in existing N-body codes are required, which we have explicitly implemented in $\textit{gevolution}$ and $\textit{gadget-2}$. Our fast method determines the non-linear matter power spectrum to permille-level precision when compared against state-of-the-art simulations that have been performed for $0.1\,{\rm eV} \leq \sum m_\nu \leq 0.3\,$eV., Comment: v2, matches published version at JCAP