This letter presents an analytical procedure for the synthesis of a low-pass prototype filter constituted by the cascade of doublet blocks coupled by inverters or shunt reactances. The considered ...doublet is a second-order resonating structure composed of two resonant and two nonresonant nodes which allow the placement of two finite transmission zeros (TZs) in the frequency response. The considered configuration allows realizing compact fully canonical filters with the maximum number of TZs (the doublets are typically implemented through dual-mode cavities). The proposed procedure introduces for the first time an analytical procedure for synthesizing the low-pass prototype of the cascaded-block topology, overcoming the time consuming and inaccurate procedures currently based on numerical optimization. Two synthesis examples are presented to validate the novel synthesis procedure.
The nature of the inner core (IC) temporal changes is of great importance in understanding the deep earth dynamics. The comment by Tian and Wen (2023, https://doi.org/10.1029/2023gl103173) on our ...previous paper (Yang & Song, 2022, https://doi.org/10.1029/2022gl098393) provided a new observation as evidence against the IC rotation and proposed that our observations are instead from localized rapid changes at the IC surface. Here we argue the opposite to its conclusions. The comment misinterpreted our logic and many of our observations and arguments. Its one new waveform does not contradict with the “rotation” model. The original evidence for the “surface” model is demonstrated to be an artifact from station clock errors and instrument changes. Additionally, the surface model lacks a solid physical and quantitative basis to explain existing seismic evidence. We conclude that the rotation model is currently the best interpretation and the surface model is not a viable alternative.
Plain Language Summary
Seismic waves traversing the Earth's inner core (IC) from repeating earthquakes exhibit significant temporal changes in their arrival times. The intriguing observation has been generally considered as evidence of the IC rotation (relative to the mantle) shifting the IC's laterally varying structures, which is further supported by the compelling evidence in Yang and Song (2022, https://doi.org/10.1029/2022gl098393). In the comment by Tian and Wen (2023, https://doi.org/10.1029/2023gl103173) on our study, they made harsh criticisms of our research and argued against the IC rotation, and proposed instead that the seismic observations result from localized topographic changes at the IC surface. In response, we believe that they misunderstood our logic and misinterpreted a number of our observations and arguments. The only one new example they presented does not contradict with the IC rotation model. Moreover, the original evidence supporting the IC surface change (Wen, 2006, https://doi.org/10.1126/science.1131692) is actually an artifact caused by station clock errors and instrument changes. They neglected substantial evidence that contradicts their proposed model but supports the IC rotation. Their model also lacks a quantitative physical basis. In conclusion, their comment does not diminish our confidence in the rotation model in our original paper and their proposed alternative model is not viable.
Key Points
The comment misinterpreted our logic and arguments and failed to consider a large body of disadvantageous evidence from previous studies
The only one new waveform does not contradict with the inner core (IC) rotation, while all the data from 10 doublets are consistent with it
The model of IC surface change can be ruled out, which is based on misinterpreted evidence and lacks a physical and quantitative basis
The mechanism that allows the axoneme of eukaryotic cilia and flagella to produce both helical and planar beating is an enduring puzzle. The nine outer doublets of eukaryotic cilia and flagella are ...arranged in a circle. Therefore, each doublet pair with its associated dynein motors, should produce torque to bend the flagellum in a different direction. Sequential activation of each doublet pair should, therefore result in a helical bending wave. In reality, most cilia and flagella have a well‐defined bending plane and many exhibit an almost perfectly flat (planar) beating pattern. In this analysis we examine the physics that governs flagellar bending, and arrive at two distinct possibilities that could explain the mechanism of planar beating. Of these, the mechanism with the best observational support is that the flagellum behaves as two ribbons of doublets interacting with a central partition. We also examine the physics of torsion in flagella and conclude that torsion could play a role in transitioning from a planar to a helical beating modality in long flagella. Lastly, we suggest some tests that would provide theoretical and/or experimental evaluation of our proposals.
We consider an extension of the standard model (SM) with three SU(2) scalar doublets and discrete S3⊗Z2 symmetries. The irreducible representation of S3 has a singlet and a doublet, and here we show ...that the singlet corresponds to the SM-like Higgs and the two additional SU(2) doublets forming a S3 doublet are inert. In general, in a three scalar doublet model, with or without S3 symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model.
•Inner core differential rotation is highly time-varying during 1991–2017.•Inner core was nearly locked to mantle before 2001 and after 2003.•Inner core experienced a burst of differential rotation ...during 2001–2003.•The burst may have excited the six-year oscillation in length-of-day.
The nature of any differential rotation between Earth's inner core and mantle is important for understanding Earth's magnetic field and intradecadal variations in the length-of-day; however, a consensus on the existence and rate of differential rotation is still lacking after 25 years. The reported model for inner core differential rotation from seismic body waves is controversial and might be explained by non–rotational processes. Here, we explore inner core differential rotation using the decorrelation of inner-core sensitive coda waves from 123 earthquake doublets recorded during 1991–2017. We find that the inner core was nearly locked to the mantle before 2001 and after 2003 with relatively small motion about an equilibrium position. During 2001–2003 the inner core experienced a burst of differential rotation, possibly in response to a magnetic torque induced by the expulsion of light elements from the inner core. We suggest that this fleeting bit of differential rotational helped excite an inner core rotational oscillation, consequently exciting the six-year-oscillation in the length-of-day.
Multilayered plasmonic metasurfaces have been previously shown to enable multifunctional control of full‐space electromagnetic waves, which are of great importance to the development of compact ...optical systems. While this structural configuration is practical for acquiring metasurfaces working in microwave frequency, it will inevitably become lossy and highly challenging to fabricate when entering the visible band. Here, an efficient yet facile approach to address this issue by resorting to a dielectric metasurface doublet (DMD) based on two vertically integrated polarization‐filtering meta‐atoms (PFMs) is presented. The PFMs exhibit polarization‐dependent high transmission and reflection, as well as independent and full 2π phase control characteristics, empowering the DMD to realize three distinct incidence‐direction and polarization‐triggered wavefront‐shaping functionalities, including anomalous beam deflection, light focusing, vortex beam generation, and holographic image projection as it is investigated either numerically or experimentally. The presented DMD undoubtedly holds several salient features compared with the multilayered metallic metasurfaces in aspects of design complexity, efficiency, and fabrication. Furthermore, as dielectric meta‐atoms with distinct polarization responses can be deployed to construct the DMD, it is anticipated that diverse full‐space metasurfaces equipped with versatile functionalities can be demonstrated in the future, which will greatly advance the development of multifunctional meta‐optics.
A dielectric metasurface doublet incorporating two vertically integrated polarization‐filtering meta‐atoms allowing two orthogonal linear polarizations to be, respectively, transmitted and reflected with high efficiency and independent 2π‐phase tuning ability, is demonstrated to empower trifunctional control of full‐space visible light. By selecting incidence direction and polarization, various functionalities including beam deflection, light focusing, vortex beam generation, and holographic images are realized.
We investigate Andreev reflection properties contributed by the Majorana doublets, by introducing two ferromagnetic leads coupled to the ends of the time-reversal-invariant topological ...superconducting nanowire. It is found that the local and crossed Andreev reflections are influenced by the polarization strengths and directions in the ferromagnetic leads. This directly leads to the dependence of the shot noise Fano factors on the ferromagnetic leads, as well as their correspondence to the Andreev conductances. In addition, the coupling manners between the Majorana doublets and leads take effects to the conductance and Fano factors. This work provides useful information for the understanding of the Andreev reflection properties of Majorana doublets.
•We investigate Andreev reflection properties contributed by Majorana doublets, by introducing two ferromagnetic leads.•Local and crossed Andreev reflections are influenced by polarization strengths and directions in ferromagnetic leads.•Shot noise Fano factors and their relations to conductance depend on the ferromagnetic leads.•Coupling manners between Majorana doublets and leads take effects to the conductance and Fano factors.•This work provides useful information for understanding the Andreev reflection properties of Majorana doublets.
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