Uniqueness of the Inflationary Higgs Scalar for Neutron Stars and Failure of Non-Inflationary Approximations

Neutron stars are perfect candidates to investigate the effects of a modified gravity theory, since the curvature effects are significant and more importantly, potentially testable. In most cases studied in the literature in the context of massive scalar-tensor theories, inflationary models were examined. The most important of scalar-tensor models is the Higgs model, which, depending on the values of the scalar field, can be approximated by different scalar potentials, one of which is the inflationary. Since it is not certain how large the values of the scalar field will be at the near vicinity and inside a neutron star, in this work we will answer the question, which potential form of the Higgs model is more appropriate in order for it to describe consistently a static neutron star. As we will show numerically, the non-inflationary Higgs potential, which is valid for certain values of the scalar field in the Jordan frame, leads to extremely large maximum neutron star masses; however, the model is not self-consistent, because the scalar field approximation used for the derivation of the potential, is violated both at the center and at the surface of the star. These results shows the uniqueness of the inflationary Higgs potential, since it is the only approximation for the Higgs model, that provides self-consistent results.

Effects of Rotation on Transient Fluid Flow and Heat Transfer Through a Curved Square Duct: The Case of Negative Rotation

The fluid flow and heat transfer through a rotating curved duct has received much attention in recent years because of vast applications in mechanical devices. It is noticed that there occur two different types of rotations in a rotating curved duct such as positive and negative rotation. The positive rotation through the curved duct is widely investigated while the investigation on the negative rotation is rarely available. The paper investigates the influence of negative rotation for a wide range of Taylor number (−10 ≤ Tr ≤ −2500) when the duct itself rotates about the center of curvature. Due to the rotation, three types of forces including Coriolis, centrifugal, and buoyancy forces are generated. The study focuses and explains the combined effect of these forces on the fluid flow in details. First, the linear stability of the steady solution is performed. An unsteady solution is then obtained by time-evolution calculation and flow transition is determined by calculating phase space and power spectrum. When Tr is raised in the negative direction, the flow behavior shows different flow instabilities including steady-state, periodic, multi-periodic, and chaotic oscillations. Furthermore, the pattern variations of axial and secondary flow velocity and isotherms are obtained, and it is found that there is a strong interaction between the flow velocities and the isotherms. Then temperature gradients are calculated which show that the fluid mixing and the acts of secondary flow have a strong influence on heat transfer in the fluid. Diagrams of unsteady flow and vortex structure are further sketched and precisely elucidate the curvature effects on unsteady fluid flow. Finally, a comparison between the numerical and experimental data is discussed which demonstrates that both data coincide with each other.

Turbulent flow in curved channels

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

Dynamic aerosol and dynamic air-water interface curvature effects on a 2-Gbit/s free-space optical link using orbital-angular-momentum multiplexing

When an orbital-angular-momentum (OAM) beam propagates through the dynamic air–water interface, the aerosol above the water and the water surface curvature could induce various degradations (e.g., wavefront distortion, beam wandering, scattering, and absorption). Such time-varying degradations could affect the received intensity and phase profiles of the OAM beams, resulting in dynamic modal power loss and modal power coupling. We experimentally investigate the degradation for a single OAM beam under dynamic aerosol, dynamic curvature, and their comprehensive effects. Our results show the following: (i) with the increase of the aerosol strength (characterized by the attenuation coefficient) from ∼0 to ∼0.7–1.3 dB/cm over ∼7 cm, the power coupling ratio from OAM −1 to +2 increases by 4 dB, which might be due to the amplitude and phase distortion caused by spatially dependent scattering and absorption. (ii) With the increase of the curvature strength (characterized by the variance of curvature slope over time) from ∼0 to ∼2 × 10−5 rad2, the power coupling ratio from OAM −1 to +2 increases by 11 dB. This could be caused by both the wavefront distortion and the beam wandering. (iii) Under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2), there is an up to 2 dB higher modal power loss as compared with the single-effect cases. (iv) The received power on OAM −1 fluctuates in a range of ∼6 dB within a 220 ms measurement time under aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2) effects due to the dynamic degradations. We also demonstrate an OAM −1 and +2 multiplexed 2-Gbit/s on–off-keying link under dynamic aerosol and curvature effects. The results show a power penalty of ∼3 dB for the bit-error-rate at the 7% forward-error-correction limit under the comprehensive effect of aerosol (∼0.1–0.6 dB/cm) and curvature (∼6 × 10−7 rad2), compared with the no-effect case.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.

Diffusive effects in local instabilities of a baroclinic axisymmetric vortex

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$ ), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$ ), and (ii) an oscillatory instability (absent at $Sc = 1$ ). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$ ) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$ , monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.

Coupling and Optical Analysis of a Round-Cornered Square-Shaped Microresonator

An on-chip structure consisting of a round-cornered square-shaped (RCSS) resonator as an optical filter is studied via optical experiments, analytical modeling, and numerical techniques. A general coupling model is shown to accurately represent the entire spectral response; the model also provides an understanding of the influence of geometrical and coupling parameters on the resonance characteristics of the RCSS microresonators. The selection of an optimum radius of curvature for rounding off the sharp corners of square microresonators can provide higher quality factors than that of conventional circular resonators. The rotation of the RCSS at the central corner coupling point is also shown to improve the quality factor and remove the minimal phase mismatch requirement and dependency on interaction length. The model results are validated with an electromagnetic finite domain analysis (EMFD) and optical experiments, for which an RCSS on a silicon-on-insulator platform is fabricated. It is shown that the optical performance characteristics (quality factor, transmission ratio, and extinction ratio) of the microresonators are very sensitive to the coupling parameters and must be carefully considered in addition to geometrical length, rotation, and curvature effects. Due to the change in coupling introduced by rotation, the quality factor of the round-cornered square-shaped microresonator can be significantly larger than a circular ring with the same size, thereby establishing RCSS as a competitive alternative to circular microresonators.