Planar Topology Research Articles

Method of Designing a Planar Scan Angle Enhancing Metalens Featuring Lossless Wide Scanning at mmWave

For the first time, a method to design a planar scan angle enhancing lens with minimum beam distortion for automotive radar at millimeter-wave is presented. The proposed lens is not only advantageous regarding its planar topology but also offers a solution to the chronic problem surrounding planar phased array antenna and planar lenses: scan loss. In this article, ray optics and ray transfer matrix are applied to Galilean lens configuration from which the concept of scan enhancement and compensating parameters are conceived. The basic idea of compensating lies in re-focusing the portion of the beams and suppressing transmission at extreme angles. Visual analysis of the wave refraction and designing of the lens system is conducted using 2-D ray-tracing code. Full-wave simulation validates the effectiveness of the proposed idea by extending the limited scan range of the phased array antenna from 45° to 58° with gain fluctuation below 1.1 dB at E-band. The radiation efficiency is calculated to be 0.86 at 76.5 GHz. Furthermore, the proposed lens system is fabricated using low-temperature co-fired ceramic (LTCC) technology and experimentally verified. Series-fed array antennas integrated with scan angle enhancing meta lens (SAEMLs) confirmed the shift of the gain peak from 46° to 58°, proving that SAEML can effectively extend the scanning range of phased arrays with small gain variation.

Sparse Billboard and T-Shaped Arrays for Two-Dimensional Direction of Arrival Estimation

In two-dimensional direction of arrival (2D-DOA) estimation, planar arrays can estimate the elevation and azimuth angles simultaneously. However, many planar array topologies such as billboard, L-shaped, T-shaped, and 2D nested arrays suffer from mutual coupling that results from the small separation between the physical sensors (antennas), which limits the estimation capability of the sensor array. In an attempt to reduce mutual coupling between sensors, this article proposes sparse billboard and T-shaped arrays in which the number of closely separated sensors is significantly reduced. In addition to extending the CRB for fourth order coarray, this article also derives closed-form expressions for the sensor locations and the number of consecutive lags or the uniform degrees of freedom (uDOF), in the fourth-order difference coarray (FODC). Simulation results demonstrate the robustness of the proposed sparse arrays against mutual coupling.

Quest for the Most Aromatic Pathway in Charged Expanded Porphyrins.

Despite the central role of aromaticity in the chemistry of expanded porphyrins, the evaluation of aromaticity remains difficult for these extended macrocycles. The presence of multiple conjugation pathways and different planar and nonplanar π-conjugation topologies makes the quantification of global and local aromaticity even more challenging. In neutral expanded porphyrins, the predominance of the aromatic conjugation pathway passing through the imine-type nitrogens and circumventing the amino NH groups is established. However, for charged macrocycles, the question about the main conjugation circuit remains open. Accordingly, different conjugation pathways in a set of neutral, anionic, and cationic expanded porphyrins were investigated by means of several aromaticity indices rooted in the structural, magnetic, and electronic criteria. Overall, our results reveal the predominance of the conjugation pathway that passes through all nitrogen atoms to describe the aromaticity of deprotonated expanded porphyrins, while the outer pathway through the perimeter carbon atoms becomes the most aromatic in protonated macrocycles. In nonplanar and charged macrocycles, a discrepancy between electronic and magnetic descriptors is observed. Nevertheless, our work demonstrates AVmin remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Synthesis of Square Planar Cu4 Clusters.

Template-assisted synthesis of well-defined polynuclear clusters remains a challenge for [M4 ] square planar topologies. Herein, we present a tetraamine scaffold R L(NH2 )4 , where L is a rigidified resorcin[4]arene, to direct the formation of C4 -symmetric R L(NH)4 Cu4 clusters with Cu-Cu distances around 2.7 Å, suggesting metal-metal direct interactions are operative since the sum of copper's van der Waals radii is 2.8 Å. DFT calculations display HOMO to HOMO-3 residing all within a 0.1 eV gap. These four orbitals display significant electron density contribution from the Cu centers suggesting a delocalized electronic structure. The one-electron oxidized [Cu4 ]+ species was probed by variable temperature X-band continuous wave-electron paramagnetic resonance (CW-EPR), which displays a multiline spectrum at room temperature. This work presents a novel synthetic strategy for [M4 ] clusters and a new platform to investigate activation of small molecules.

Synthesis of Square Planar Cu4 Clusters

AbstractTemplate‐assisted synthesis of well‐defined polynuclear clusters remains a challenge for [M4] square planar topologies. Herein, we present a tetraamine scaffold RL(NH2)4, where L is a rigidified resorcin[4]arene, to direct the formation of C4‐symmetric RL(NH)4Cu4 clusters with Cu−Cu distances around 2.7 Å, suggesting metal‐metal direct interactions are operative since the sum of copper's van der Waals radii is 2.8 Å. DFT calculations display HOMO to HOMO‐3 residing all within a 0.1 eV gap. These four orbitals display significant electron density contribution from the Cu centers suggesting a delocalized electronic structure. The one‐electron oxidized [Cu4]+ species was probed by variable temperature X‐band continuous wave‐electron paramagnetic resonance (CW‐EPR), which displays a multiline spectrum at room temperature. This work presents a novel synthetic strategy for [M4] clusters and a new platform to investigate activation of small molecules.

Hyperbolic Graphene Framework with Optimum Efficiency for Conductive Composites.

Constructing conductive filler networks with high efficiency is essential to fabricating functional polymer composites. Although two-dimensional (2D) sheets have prevailed in nanocomposites, their efficiency in enhancing conductive functions seems to reach a limit, as if merely addressing the dispersion homogeneity. Here, we exploit the unrecognized geometric curvature of 2D sheets to break the efficiency limit of filler systems. We introduce the hyperbolic curvature concept to mediate the incompatibility between 2D planar topology and 3D filler space and hold the efficient conductive path through face-to-face contact. The hyperbolic graphene framework exhibits a record efficiency in enhancing electrically and thermally conductive functions of nanocomposites. At a volume loading of only 1.6%, the thermal and electrical conductivities reach 31.6 W/(mK) and 13 911 S/m, respectively. We demonstrate that the conductive nanocomposites with a hyperbolic graphene aerogel framework are useful for thermal management, sensing, and electromagnetic shielding. Our work provides a solution to reconcile the incompatibility between the 2D planar structure of sheets and the highly expected 3D conductive path, presenting a geometrically optimal filler system to break the efficiency limit of multifunctional nanocomposites and broaden the structural design space of 2D sheets by curvature modulation to meet more applications.

Navigating planar topologies in near-optimal space and time

We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of m edges within 4m bits, which is close to the information-theoretic lower bound of about 3.58m. With 4m+o(m) bits of space, we show how to answer a number of topological queries relating nodes, edges, and faces, most of them in any time in ω(1). Indeed, 3.58m+o(m) bits suffice if the graph has no self-loops and no nodes of degree one. Further, we show that with O(m) bits of space we can solve all those operations in O(1) time.

Connectivity-aware Graph: A planar topology for 3D building surface reconstruction

Multi-view Stereo (MVS) meshes suffer from occlusions or missing data, making most surface reconstruction methods invalid. Due to data imperfections, existing methods, just like PolyFit, have made a trade-off between reconstruction accuracy and time consumption. We propose a novel approach that automatically reconstructs a building surface model from raw triangular mesh with data incompleteness. Unlike existing methods that extract high-quality primitives, our method focuses on assemblies of primitives to control the level of geometric detail in the reconstructed models. We design a topological relationship of the primitives to form a plane connection graph. To be precise, we first combine the scalability of shapes with plane primitives. Then strong and soft connections between primitives are constructed by calculating the confidence of the plane intersection in space. Furthermore, the topological relations of all primitives are encoded into an undirected graph. Finally, a watertight and manifold model is extracted from the faces of a candidate set by energy minimization. Experiments on the Helsinki 3D dataset demonstrate the superiority of our method in time consumption and reconstruction error, as measured by Hausdorff distance. Our method outperforms other primitive-based algorithms in handling non-planar structures. Even when dealing with imperfect data, a watertight model is still obtained.

En Face Endocardial Cushion Preparation for Planar Morphogenesis Analysis in Mouse Embryos.

The study of the cellular and molecular mechanisms underlying the development of the mammalian heart is essential to address human congenital heart disease. The development of the primitive cardiac valves involves the epithelial-to-mesenchymal transition (EMT) of endocardial cells from the atrioventricular canal (AVC) and outflow tract (OFT) regions of the heart in response to local inductive myocardial and endocardial signals. Once the cells delaminate and invade the extracellular matrix (cardiac jelly) located between the endocardium and the myocardium, the primitive endocardial cushions (EC) are formed. This process implies that the endocardium has to fill the gaps left by the delaminated cells and has to reorganize itself to converge (narrow) or extend (lengthen) along an axis. Current research has implicated the planar cell polarity (PCP) pathway in regulating the subcellular localization of the factors involved in this process. Classically, the initial phases of cardiac valve development have been studied in cross-sections of embryonic hearts or in ex vivo AVC or OFT explants cultured on collagen gels. These approaches allow the analysis of apico-basal polarity but do not allow the analysis of cell behavior within the plane of the epithelium or of the morphological changes of migrating cells. Here, we show an experimental approach that allows the visualization of the endocardium at valvulogenic regions as a planar field of cells. This experimental approach provides the opportunity to study PCP, planar topology, and intercellular communication within the endocardium of the OFT and AVC during valve development. Deciphering new cellular mechanisms involved in cardiac valve morphogenesis may contribute to understanding congenital heart disease associated with endocardial cushion defects.

A planar micro rotary actuator for endoscopic optical scanning

Optical endoscopy is an essential technique for diagnosing disease in modern medicine. Side-viewing endoscopic probes with an embedded distal actuator that circumferentially scans an imaging light within an organ’s lumen are expected to significantly enhance the imaging ability of the probes. To this end, this work develops and experimentally analyzes an electromagnetic micro rotary actuator with a planar and hollow architecture. The actuator uses a liquid-phase bearing based on ferrofluid that is self-sustained on the magnetic rotor to eliminate complex bearing structures and enable low-friction actuation. Compared to preceding tubular designs, the planar topology allows for 83% downsizing in the actuator’s axial size, which helps preserve probe flexibility. Furthermore, the hollow design provides an unobstructed optical path through the actuator body, which removes imaging blind spots. A proof-of-concept scanner device is prototyped using flex-circuit microfabrication and 3D printing techniques for its electromechanical characterization. The prototype is successfully driven to revolve the rotor with 45° steps on a ring-shaped planar stator, which are then cycled at high frequencies to continuously spin the rotor up to a maximum rate of 2000 rpm with a device temperature below 45 °C, a safety threshold for tissue damage. The demonstrated stepwise and high-speed modes of laser scanning suggests the feasibility of the scanner design for multimodal imaging application toward advancing optical endoscope technology.

Topology and Morphology Design of Spherically Reconfigurable Homogeneous Modular Soft Robots.

Imagine a swarm of terrestrial robots that can explore an environment, and, on completion of this task, reconfigure into a spherical ball and roll out. This dimensional change alters the dynamics of locomotion and can assist them in maneuvering variable terrains. The sphere-plane reconfiguration is equivalent to projecting a spherical shell onto a plane, an operation that is not possible without distortions. Fortunately, soft materials have the potential to adapt to this disparity of the Gaussian curvatures. Modular Soft Robots (MSoRos) have promise of achieving dimensional change by exploiting their continuum and deformable nature. However, the design of such soft robots has remained unexplored thus far. Here, for the first time, we present the topology and morphology design of MSoRos that are capable of reconfiguring between spherical and planar configurations. Our approach is based in geometry, where a platonic solid determines the number of modules required for plane-to-sphere reconfiguration and the radius of the resulting sphere, for example, four "tetrahedron-based" or six "cube-based" MSoRos are required for spherical reconfiguration. The methodology involves: (1) inverse orthographic projection of a "module-topology curve" onto the circumscribing sphere to generate the spherical topology; (2) azimuthal projection of the spherical topology onto a tangent plane at the center of the module resulting in the planar topology; and (3) adjusting the limb stiffness and curling ability by manipulating the geometry of cavities to realize a physical finite-width, Motor-Tendon Actuated MSoRo that can actuate between the sphere-plane configurations. The topology design is shown to be scale invariant, that is, the scaling of base platonic solid is reflected linearly in spherical and planar topologies. The module-topology curve is optimized for the reconfiguration and locomotion ability using an intramodular distortion metric that quantifies sphere-to-plane distortion. The geometry of the cavity optimizes for the limb stiffness and curling ability without compromising the actuator's structural integrity.

Conformal IRS-Empowered MIMO-OFDM: Channel Estimation and Environment Mapping

We consider the channel estimation and environment mapping problems in multiple-input multiple-output orthogonal frequency division multiplexing systems empowered by intelligent reconfigurable surfaces (IRSs). In order to acquire more in-depth environmental information, as well as, to flexibly take into account existing real-life infrastructure, we propose a novel three-dimensional conformal IRS architecture consisting of reflective unit cells distributed on curved surfaces. We model the training signal as a third-order canonical polyadic tensor and construct a tensor factorization problem. Given specific conditions on the allocated temporal-frequency training resources, we develop four channel estimation approaches, i.e., least squares, direct, wideband direct and wideband subspace methods, by leveraging tensor techniques and nonlinear system solvers. By fully exploiting the characteristics of conformal IRSs, we propose two decoupling modes to precisely recover the multipath parameters without ambiguities, which cannot be supported by the traditional IRS planar topologies. We implement scatterer mapping and user positioning tasks based on precise parameter estimates. Simulation results indicate that the proposed conformal IRS structure and estimation schemes can recover the channel state information with remarkable accuracy, thereby offering a centimeter-level resolution of environment mapping.

Planar π-extended cycloparaphenylenes featuring an all-armchair edge topology.

The [n]cycloparaphenylenes ([n]CPPs)-n para-linked phenylenes that form a closed-loop-have attracted substantial attention due to their unique cyclic structure and highly effective para-conjugation leading to a myriad of fascinating electronic and optoelectronic properties. However, their strained topology prevents the π-extension of CPPs to convert them either into armchair nanobelts or planarized CPP macrocycles. Here we successfully tackle this long-standing challenge and present the bottom-up synthesis and characterization of atomically precise in-plane π-extended [12]CPP on Au(111) by low-temperature scanning probe microscopy and spectroscopy combined with density functional theory. The planar π-extended CPP is a nanographene with an all-armchair edge topology. The exclusive para-conjugation at the periphery yields delocalized electronic states and the planarization maximizes the overlap of p orbitals, which both reduce the bandgap compared to conventional CPPs. Calculations predict ring currents and global aromaticity in the doubly charged system. The intriguing planar ring topology and unique electronic properties make planar π-extended CPPs promising quantum materials.

Variation Range of Different Inductor Topologies with Shields for RF and Inductive Sensing Applications.

In this study, different planar inductor topologies were studied to evaluate their characteristic parameters’ variation range upon approaching Fe- and Cu-based shield plates. The use of such materials can differently alter the electrical properties of planar inductors such as the inductance, resonant frequency, resistance, and quality factor, which could be useful in multiple devices, particularly in inductive sensing and radio-frequency (or RF) applications. To reach an optimal design, five different square topologies, including spiral, tapered, non-spiral, meander, and fractal, were built on a printed circuit board (PCB) and assessed experimentally. At the working frequency of 1 MHz, the results showed a decrease in the inductance value when approaching a Cu-based plate and an increase with Fe-based plates. The higher variation range was noticeable for double-layer topologies, which was about 60% with the Cu-based plate. Beyond an intrinsic deflection frequency, the inductance value began to decrease when approaching the ferromagnetic plate because of the ferromagnetic resonance (FMR). It has been shown that the FMR frequency depends on the inductor topology and is larger for the double-layer spiral one. The Q-factor was decreasing for all topologies but was much faster when using ferromagnetic plates because of the FMR, which intensely increases the track resistance. The resonant frequency was increasing for all double-layer topologies and decreasing for single-layer ones, which was mainly due to the percentage change in the stray capacitance compared to the inductance variation. The concept of varying inductors by metal shielding plates has great potential in a wide range of nondestructive sensing and RF applications.

Miniaturized Dual-Band Dual-Mode TM-Mode Dielectric Filter in Planar Configuration

This paper reports a new class of compact inline dual-band bandpass filters using TM-mode dielectric resonators in planar configuration. Thanks to the employment of the dielectric-loaded TM-mode waveguide configuration and the dual-mode TM₁₂₀ and TM₂₁₀ resonances, substantial size miniaturization and volume saving (>70%) can be obtained in comparison with conventional waveguide technology. Additionally, the planar topology of the presented concept offers highly desirable advantages for industry and mass production including the ease of manufacturing, assembly, and tuning. Furthermore, the resonating doublets and the nonresonating TM₁₁₀ mode are effectively utilized to introduce and control both inter-band and outer-band transmission zeros, advantageously increasing the isolation between the two passbands and enhancing the outer-band rejection regions. The general design procedure of the proposed filter is discussed in detail. A three-pole C-band dual-band dual-mode TM-mode dielectric filter is designed, implemented, and measured to validate the proposed configuration.

Joint search of optimal topology and trajectory for planar linkages

We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex periodic motion, which is an important component when building low-cost, modular robots, mechanical toys, and foldable structures in our daily lives (chairs, bikes, and shelves). The design of such structures requires trial and error even for experienced engineers. Our research provides semi-automatic methods for exploring novel designs given high-level specifications and constraints. We formulate this problem as a non-smooth numerical optimization with quadratic objective functions and non-convex quadratic constraints involving mixed-integer decision variables (MIQCQP). We propose and compare three approximate algorithms to solve this problem: mixed-integer conic-programming (MICP), mixed-integer nonlinear programming (MINLP), and simulated annealing (SA). We evaluated these algorithms searching for planar linkages involving 10 − 14 rigid links. Our results show that the best performance can be achieved by combining MICP and MINLP, leading to a hybrid algorithm capable of finding the planar linkages within a couple of hours on a desktop machine, which significantly outperforms the SA baseline in terms of optimality. We highlight the effectiveness of our optimized planar linkages by using them as legs of a walking robot.

In Situ Visualization of Local Distortions in the High-Tc Molecule-Intercalated Lix(C5H5N)yFe2-zSe2 Superconductor.

A time-resolved synchrotron X-ray total scattering study sheds light on the evolution of the different structural length scales involved during the intercalation of the layered iron-selenide host by organic molecular donors, aiming at the formation of the expanded-lattice Lix(C5H5N)yFe2-zSe2 hybrid superconductor. The intercalates are found to crystallize in the tetragonal ThCr2Si2-type structure at the average level, however, with an enhanced interlayer iron-selenide spacing (d = 16.2 Å) that accommodates the heterocyclic molecular spacers. Quantitative atomic pair distribution function (PDF) analysis at variable times suggests distorted FeSe4 tetrahedral local environments that appear swollen with respect to those in the parent β-FeSe. Simultaneously acquired in situ synchrotron X-ray powder diffraction data disclose that secondary phases (α-Fe and Li2Se) grow significantly when a higher lithium concentration is used in the solvothermal reaction or when the solution is aged. These observations are in line with the strongly reducing character of the intercalation medium's solvated electrons that mediate the defect chemistry of the expanded-lattice superconductor. In the latter, intralayer correlated local distortions indicate electron-donating aspects that reflect in somewhat enlarged Fe-Se bonds. They also reveal a degree of relief of chemical pressure associated with a large distance between Fe and Se sheets ("taller" anion height) and a stretched Fe-Fe square planar topology. The elongation of the latter, derived from the in situ PDF study, speaks for a plausible increase in the Fe-site vacancy concentration. The evolution of the local structural parameters suggests an optimum reaction window where kinetically stabilized phases resemble the distortions of the edge-sharing Fe-Se tetrahedra, required for a high-Tc in expanded-lattice iron-chalcogenides.

Analytic topological hairy dyonic black holes and thermodynamics

We present and discuss a new family of topological hairy dyonic black hole solutions in asymptotically anti--de Sitter space. The coupled Einstein-Maxwell-scalar gravity system, that carries both the electric and magnetic charges is solved, and exact hairy dyonic black hole solutions are obtained analytically. The scalar field profiles that give rise to such black hole solutions are regular everywhere. The hairy solutions are obtained for planar, spherical, and hyperbolic horizon topologies. In addition, analytic expressions of regularized action, stress tensor, conserved charges, and free energies are obtained. We further comment on different prescriptions for computing the black hole mass with hairy backgrounds. We analyze the thermodynamics of these hairy dyonic black holes in canonical and grand canonical ensembles, and we find that both electric and magnetic charges have a constructive effect on the stability of the hairy solution. For the case of planar and hyperbolic horizons, we find thermodynamically stable hairy black holes that are favored at low temperatures compared to the nonhairy counterparts. We further find that, for a spherical hairy dyonic black hole, the thermodynamic phase diagram resembles to that of a Van der Waals fluid not only in canonical but also in the grand canonical ensemble.

Capillary transfer: Numerical study of how topology affects the fluid flow rate into a planar microstructure with pseudopotential multiphase Lattice-Boltzmann method

We investigate how topology impacts capillary action with the hope of aiding future thermal engineering decisions. Heat pipes and their two-dimensional variant, vapor chambers are essential components in electronics cooling. With thin-film evaporation as the driving force for such high-heat-flux movers, studies have been done to optimize the thermal performance of different designs. However, the fundamental problem of liquid transportation needs to be addressed exclusively: evaporation can only work as long as the new liquid is continuously being replaced. The device achieves this by the capillary process (or wicking) through the thermal ground (or wicks): a configuration of microstructures attached to the device's walls. Some planar topologies of the structure allow for consistent but slower mass feeding; others offer higher bandwidth but with local flow hindrance, creating a pulsating tendency; certain conditions would even block the capillary flow. Surveying the capillary performance of different two-dimensional designs of the thermal ground, we encounter a topological factor that correlates with this mass transfer rate. We incorporate in the factor the wick's width, its height, and the gap between one microstructure to another. An energy model is studied to explain the underlying influence of the structure topology, while Lattice-Boltzmann method is used to evaluate the capillary dynamics inside the thermal ground. With ultra-thin applications in mind, the paper looks at the length scales of micrometers with a wick height of 50 μm. Overall, we find that tightly packed structures pull the most liquid in the same amount of time; however, we find that two core constraints need to be met: sufficient clearance between structures and freedom of mobility.

Two-Loop QCD Corrections to Wbb[over ¯] Production at Hadron Colliders.

We present an analytic computation of the two-loop QCD corrections to ud[over ¯]→W^{+}bb[over ¯] for an on-shell W boson using the leading color and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarized squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.