Trivial Structure Research Articles

Baroclinic instability in the Eady model for two coupled flows

ABSTRACT The linear instability of baroclinic flows in two superimposed and coupled, immiscible fluids is studied theoretically. These flows are westerlies, and they are thermally or mechanically coupled. The fluids are stably stratified, internally and mutually (the upper fluid is lighter than the lower fluid). In each fluid, two-level surface quasi-geostrophy governs the evolution of the perturbed westerly flow. The perturbations are horizontal normal modes. Firstly, the models are not coupled and the flow instability in each fluid is validated separately against the results of the classical Eady model of baroclinic instability. Secondly, the two fluids are thermally and/or mechanically coupled. With thermal coupling, and for meridionally uniform perturbations, a new mode of instability appears for long waves. This pair of unstable modes converges towards the modes of the uncoupled fluids at medium wavelengths. For perturbations with a non trivial meridional structure, the thermal coupling essentially damps the instability. For an upper flow with a larger deformation radius than in the lower flow, the growth rates of the perturbation are therefore more strongly altered in the former than in the latter. With mechanical coupling, the instability is essentially damped at large to medium scales, while the short-wave cut-off is extended towards smaller waves. When the fluids are both thermally and mechanically coupled, these effects add up. This very idealised study is a first step towards studying more realistic cases.

Phonon-mediated spin transport in quantum paraelectric metals

The concept of ferroelectricity is now often extended to include continuous inversion symmetry-breaking transitions in various metals and doped semiconductors. Paraelectric metals near ferroelectric quantum criticality, which we term ‘quantum paraelectric metals,’ possess soft transverse optical phonons which can have Rashba-type coupling to itinerant electrons in the presence of spin-orbit coupling. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While the spin Hall effect arising from non-trivial electronic band structures has been studied extensively, we find here the presence of the Rashba electron-phonon coupling can give rise to spin current, including spin Hall current, in response to an inhomogeneous electric field even with a completely trivial band structure. Furthermore, this spin conductivity displays unconventional characteristics, such as quadrupolar symmetry associated with the wave vector of the electric field and a thermal activation behavior characterized by scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom.

The gustatory stalk of the Remo flounder exemplifies how complex evolutionary novelties may arise

The appearance of evolutionary novelties is a central issue in biology. Since Darwin’s theory, difficulties in explaining how novel intricate body parts arose have often been used by creationists and other deniers to challenge evolution. Here, we describe the gustatory stalk of the Remo flounder (Oncopterus darwinii), an anatomically and functionally complex organ presumably used as a chemoreceptor probe to detect prey buried in the substrate. We demonstrate that the gustatory stalk is derived from the first dorsal-fin ray, which acquired remarkable modifications in its external morphology, integument, skeleton, muscles, and nerves. Such structural innovations are echoed in both functional and ecological specializations. We reveal that the gustatory stalk arose through the gradual accumulation of changes that evolved at different levels of the phylogenetic tree of ray-finned fishes. At least five preconditions arose in nodes preceding Oncopterus darwinii. This finding constitutes an interesting example of how evolution can deeply remodel body parts to perform entirely new functions. In this case, a trivial support structure primitively used for swimming became a sophisticated sensory tool to uncover hidden prey.

Observation of Multiple Topological edge States in Square-Root electric circuits

Square-root topological states are new topological phases, whose intriguing topological properties are inherited from the parent lattice Hamiltonian. Because of the square-root procedure, the bulk gap of the parent Hamiltonian is doubled. In this letter, we report the observation of the square-root topological insulators (SRTIs) in topological LC circuits, whose squared Hamiltonian includes a Su-Schrieffer-Heeger (SSH) model, a well-known example of topological insulators (TI). The multiple localized edge states falling in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. These edge states with zero energy are manifested by a prominent impedance peak at the midgap frequency and directly observed by impedance measurements. Our work opens up an alternative gateway towards actively controllable topological systems and may bring about new possibilities in topology-driven electronic devices.

A Bi−directional method for evaluating integrals involving higher transcendental functions. HyperRAF: A Julia package for new hyper−radial functions

The electron repulsion integrals over Slater−type orbitals with non−integer principal quantum numbers are investigated. These integrals are useful in both non−relativistic and relativistic calculations of many−electron systems. They involve hyper−geometric functions that are practically difficult to compute. Relationships free from hyper−geometric functions for expectation values of Coulomb potential (r21−1) are derived. These relationships are new and show that the complication coming from two−range nature of Laplace expansion for the Coulomb potential is removed. This is achieved by utilizing auxiliary functions represented in finite power series. They serve as essential components in deriving straightforward recurrence relationships for electron repulsion integrals. In the context of computing the expectation values of potentials with arbitrary power, the methodology presented here for evaluation of these integrals forms the initial condition. It is also adapted to multi−center integrals. Program summaryProgram Title: HyperRAFCPC Library link to program files:https://doi.org/10.17632/6pbv2y7s42.1Developer's repository link:https://github.com/abagciphys/HyperRAF.gitLicensing provisions: MITProgramming language:Julia Programming Language [1]Supplementary material: An exploratory variant of the software program written in the Mathematica Programming Language [2].External routines/libraries:Nemo, a computer algebra package for the Julia programming language [3], JRAF, a Julia package for computation of relativistic molecular auxiliary functions [4].Nature of problem: Definite integrals involving higher transcendental functions given by,fmn1(a,b,x)=xm−1e−bxΓ[n,ax], andfmn2(a,b,x)=xm−1e−bxγ[n,ax] are frequently encountered in atomic physics, with the electron repulsion integral being a notable illustration.For exclusive solutions to these integrals, one can refer to Erdélyi's [5] or Gradshteyn and Ryzhik's [6] books. The solutions are obtained by using the series representation of incomplete gamma functions. The result is hyper−geometric functions of the form F12[1,b,c;z], where b=m+n, c=m+1, z=b/(a+b) for fmn1(a,b,x) and c=n+1, z=a/(a+b) for fmn2(a,b,x), respectively. Due to the non−trivial structure of infinite series that are used to define them, the computation for hyper−geometric poses challenges. Convergence of their series strictly depends on the values of parameters. Computational issues such as cancellation or round−off error emerge.Solution method: This research introduces novel bi−directional hyper−radial functions that are used to establish fresh recurrence relationships for electron repulsion integrals, eliminating the dependence on hyper−geometric functions. Dual functionality is inherent in the hyper−radial functions as they offer alternative solutions for definite integrals involving higher transcendental functions. Additionally, they transform the representation of the hyper−geometric functions into finite power series.

Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe.

Femtosecond pulses have been used to reveal hidden broken symmetry states and induce transitions to metastable states. However, these states are mostly transient and disappear after laser removal. Photoinduced phase transitions toward crystalline metastable states with a change of topological order are rare and difficult to predict and realize experimentally. Here, by using constrained density functional perturbation theory and accounting for light-induced quantum anharmonicity, we show that ultrafast lasers can permanently transform the topologically trivial orthorhombic structure of SnSe into the topological crystalline insulating rocksalt phase via a first-order nonthermal phase transition. We describe the reaction path and evaluate the critical fluence and possible decay channels after photoexcitation. Our simulations of the photoexcited structural and vibrational properties are in excellent agreement with recent pump-probe data in the intermediate fluence regime below the transition with an error on the curvature of the quantum free energy of the photoexcited state that is smaller than 2%.

Observation of a Topological Edge State Stabilized by Dissipation.

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated.

Homogeneous spaces with invariant Koszul-Vinberg structures

Let M be a manifold endowed with a flat torsionless connection ∇. A symmetric bivector field h on (M,∇) is said to be a Koszul-Vinberg (K-V for short) bivector field if it satisfies: (∇α#h)(β,γ)=(∇β#h)(α,γ), where α#:=h#(α) and h#:T⁎M→TM is the contraction of h. The pair (∇,h) is called a K-V structure and the triple (M,∇,h) is called a K-V manifold. When h is non-degenerate, (M,∇,h−1) is a pseudo-Hessian manifold, otherwise, we have a singular foliation defined by Imh# called the associated affine foliation whose leaves are pseudo-Hessian manifolds. In this paper, we study invariant K-V structures on homogeneous spaces. More precisely, we give an algebraic characterization of these structures in the same spirit of Nomizu's theorem on invariant connections on homogeneous spaces, and we give many classes of examples mainly for reductive or symmetric pairs (G,H). We establish many properties of pseudo-Hessian homogeneous manifolds, in particular, we show that when G is a semi-simple Lie group then G/H does not admit any non trivial G-invariant pseudo-Hessian structure. Finally, we show that the leaves of the affine foliation associated to an invariant K-V structure are homogeneous pseudo-Hessian manifolds.

The Stylistic Term of Liberal-Exotic Nature and Structure: between Functionalism and Lexicography

In the last fifteen years the modern French literature and language has featured the emergence of two works by Charles Dantzig: Dictionnaire egoïste de la littérature française (-Paris: Grasset et le Livre de Poche, 2005. 1154-p.) and Dictionnaire egoïste de la littérature mondiale (-Paris: Grasset, 2019. 1244 p. -), both of them being highly appreciated by literary critics and won valuable prizes. Dantzig’s dictionaries have challenged and annihilated many dogmas and axioms which used to belong to the traditional lexicography. The aforementioned works have suggested the topic of our article i.e. The Stylistic Term of Liberal-Exotic Nature and Structure, which is vastly appreciated and updated by Dantzig. Before him we have encountered several examples in lexicographers, when a trivial word or structure becomes a term in its own right. (e.g. P. Guiraud, R. Barthes, Iu. Cristeva, Tz. Todorov, etc.). Nonetheless, Dantzig has managed to create a unique meta-language which requires a novel vision as to define and subject it to the lexicographic activity.

Hybrid optimization algorithm for optimal designing of microstrip patch antenna

AbstractMicrostrip Patch Antennas (MPAs) are generally renowned for their adaptability regarding feasible geometries, which makes them appropriate for numerous diverse conditions. The suitability to integrate and the trivial structure with microwave incorporated circuits was said to be the major advantage among several advantages. MPA poses constricted bandwidth; thus it has a complication while tuning. In addition, MPAs are renowned for their reduced gain. As a result, there is a necessity to raise the gain and bandwidth of MPA. This work intends to put forward a novel approach that gets a non‐linear objective for assisting the modeling of solution spaces for antenna constraints. Thus, “Salp Swarm based Shark Smell Optimization (SS‐SSO) that hybrids the concepts of Salp Swarm Algorithm (SSA) and Shark Smell Optimization (SSO)” is developed that tuned the constraints of MPA. The implication of the developed approach is to boost the antenna gain by optimal electing of dielectric value, patch length, substrate width, and thickness of MPA.

Adjoint functor theorems for homotopically enriched categories

We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category V admitting certain limits. When V is equipped with the trivial model structure this recaptures the enriched version of Freyd's adjoint functor theorem. For non-trivial model structures, we obtain new adjoint functor theorems of a homotopical flavour — in particular, when V is the category of simplicial sets we obtain a homotopical adjoint functor theorem appropriate to the ∞-cosmoi of Riehl and Verity. We also investigate accessibility in the enriched setting, in particular obtaining homotopical cocompleteness results for accessible ∞-cosmoi.

Coexistence of photonic and phononic corner states in a second-order topological phoxonic crystal

Recently, higher-order topological insulators (HOTIs) have been extended from the electronic system to classical wave systems. Beyond the conventional bulk-boundary correspondence, HOTIs can host zero-dimensional topologically protected corner states, which show the strong field localization and robustness against fabrication flaws. Here, we propose a second-order topological phoxonic crystal (PXC) based on a two-dimensional (2D) square lattice, of which different unit cell choices can show either a topologically trivial or non-trivial band structure characterized by the 2D Zak phase. The proposed PXC supports the coexistence of photonic and phononic topological corner states, and their robustness to disorders and defects is numerically demonstrated. Our work opens a venue for achieving simultaneous confinement of photons and phonons, which is potentially useful for exploring the interaction of photonic and phononic second-order topological states and for designing novel topological optomechanical devices.

Observation of Anderson phase in a topological photonic circuit

Disordered systems play a central role in condensed matter physics, quantum transport, and topological photonics. It is commonly believed that a topological nontrivial phase would turn into a trivial phase where the transport vanishes under the effect of Anderson localization. Recent studies predict a counterintuitive result, that adding disorder to the trivial band structure triggers the emergence of protected edge states, the so-called topological Anderson phase. Here, we experimentally observe such a topological Anderson phase in a CMOS-compatible nanophotonic circuit, which implements the Su-Schrieffer-Heeger (SSH) model with incommensurate disorder in the intercell coupling amplitudes. The existence of the Anderson phase is verified by the spectral method, based on the continuous detection of the nanoscale light dynamics at the edge. Our results demonstrate the inverse transition between distinct topological phases in the presence of disorder, as well as offering a single-shot measurement technique to study the light dynamics in nanophotonic systems.

Tailoring quadrupole topological insulators with periodic driving and disorder

The quadrupole topological insulator (QTI) has attracted intense studies as a prototype of symmetry-protected higher-order topological phases of matter with a quantized quadrupole moment. The realization of QTIs has been reported in various static settings with periodic structures. Here, we theoretically investigate topological phase transitions and establish the QTI phase in a periodically driven system with disorder. In the clean limit, the Floquet QTI phase emerges from a topologically trivial band structure driven by elliptically polarized irradiation. More strikingly, starting from a pure and static system with trivial topology, we unveil an intriguing QTI phase which necessitates the simultaneous presence of disorder and periodic driving. Furthermore, we reveal that particle-hole symmetry is sufficient to protect the QTI. Our work not only establishes a new strategy to design QTIs but also enriches the symmetry-protected mechanism of higher-order topology.

Coherent interaction of a quantum emitter and the edge states in two-dimensional optical topological insulators

The two-dimensional optical topological insulators have exhibited a series of novel optical behaviors, especially the topologically protected edge states. We theoretically locate an initial excited quantum emitter (QE) in the two-dimensional ring resonator array and analyze the evolution of the QE in three kinds structures, i.e., topologically nontrivial, trivial, and graphene structure. We found that the dynamic evolution in the nontrivial topological structure is much different from that in the trivial and the graphene structures. When the QE excites edge states in nontrivial structures, the excited edge states can detour along the boundary and re-interact coherently with the QE, resulting in the recovery of the QE population. However, this repeated energy exchange is incomplete, depending on the coupling $g$ between the QE and the resonator. More importantly, we check the influence of the QE's position and the coupling $g$ (between the QE and the resonator) on dynamic evolution of the whole system. For the nontrivial structure, the effective excitation of edge states by the QE requires that: (1) the QE is located in the resonator in boundary and (2) $g$ is much less than coupling coefficient $J$ (between neighbor resonators). When $g$ is much larger than $J$, the QE cannot excite edge states anymore. We give the critical value ${g}_{\mathrm{c}}$ and find that it relates to band gap and size. Our paper is conducive to an in-depth understanding of the interaction between light and matter in optical topological insulators and provides a useful reference for quantum communication and quantum computing mediated by topological photonics.

Topology dependence of skyrmion Seebeck and skyrmion Nernst effect

We explore the dynamics of skyrmions with various topological charges induced by a temperature gradient in an ultra-thin insulating magnetic film. Combining atomistic spin simulations and analytical calculations we find a topology-dependent skyrmion Seebeck effect: while skyrmions and antiskyrmions move to the hot regime, a topologically trivial localized spin structure moves to the cold regime. We further reveal the emergence of a skyrmion Nernst effect, i.e. finite, topology-dependent velocities transverse to the direction of the temperature gradient. These findings are in agreement with accompanying simulations of skyrmionic motion induced by monochromatic magnon currents, allowing us to demonstrate that the magnonic spin Seebeck effect is responsible for both, skyrmion Seebeck and Nernst effect. Furthermore we employ scattering theory together with Thiele’s equation to identify linear momentum transfer from the magnons to the skyrmion as the dominant contribution and to demonstrate that the direction of motion depends on the topological magnon Hall effect and the topological charge of the skyrmion.

Superconducting Triplet Rim Currents in a Spin-Textured Ferromagnetic Disk.

Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin–orbit coupling, which results in spin accumulation at the bilayer–vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both 0 and π channels can be realized in the same device.

Giant Enhancement of Nonlinear Harmonic Generation in a Silicon Topological Photonic Crystal Nanocavity Chain

AbstractStrongly enhanced third‐harmonic generation (THG) by the topological localization of an edge mode in a Su‐Schrieffer‐Heeger (SSH) chain of silicon photonic crystal nanocavities is demonstrated. The edge mode of the nanocavity chain not only naturally inherits resonant properties of the single nanocavity, but also exhibits the topological feature with mode robustness extending well beyond individual nanocavity. By engineering the SSH nanocavities with alternating strong and weak coupling strengths on a silicon slab, the edge mode formation that entails a strong THG signal similar to that obtained from a single nanocavity is observed, which both show three orders of magnitude enhancement compared with that in a trivial SSH structure. The results indicate that the photonic crystal nanocavity chain can provide a promising on‐chip platform for topology‐driven nonlinear photonics.

Gap-com: general model selection criterion for sparse undirected gene networks with nontrivial community structure

We introduce a new model selection criterion for sparse complex gene network modeling where gene co-expression relationships are estimated from data. This is a novel formulation of the gap statistic and it can be used for the optimal choice of a regularization parameter in graphical models. Our criterion favors gene network structure which differs from a trivial gene interaction structure obtained totally at random. We call the criterion the gap-com statistic (gap community statistic). The idea of the gap-com statistic is to examine the difference between the observed and the expected counts of communities (clusters) where the expected counts are evaluated using either data permutations or reference graph (the Erdős-Rényi graph) resampling. The latter represents a trivial gene network structure determined by chance. We put emphasis on complex network inference because the structure of gene networks is usually nontrivial. For example, some of the genes can be clustered together or some genes can be hub genes. We evaluate the performance of the gap-com statistic in graphical model selection and compare its performance to some existing methods using simulated and real biological data examples.

Realization of Second-Order Photonic Square-Root Topological Insulators

Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root HOTIs typically manifest two paired nonzero energy corner states. In this work, we experimentally demonstrate the second-order square-root HOTIs in photonics for the first time to our knowledge, thereby unveiling such distinct corner states. The specific platform is a laser-written decorated honeycomb lattice (HCL), for which the squared Hamiltonian represents a direct sum of the underlying HCL and breathing Kagome lattice. The localized corner states residing in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with the coexistence of spin-1/2 and spin-1 Dirac-Weyl Fermions and may bring about new possibilities in topology-driven photonic devices.