Topological Density Research Articles

Rational Design of Isolated Tetrahedrally Coordinated Ti(IV) Sites in Zeolite Frameworks for Methyl Oleate Epoxidation.

The rational design of isolated metals containing zeolites is crucial for the catalytic conversion of biomass-derived compounds. Herein, we explored the insertion behavior of the isomorphic substitution of Ti(IV) in different zeolite frameworks, including ZSM-35 (FER), ZSM-5, and BEA. The different aluminium topological densities of each zeolite framework lead to the creation of different degrees of vacant sites for hosting the tetrahedrally coordinated Ti(IV) active sites. These observations show the precise control of the degree of four-coordinated Ti(IV) sites in a zeolite framework, especially in BEA topology, by tuning the degree of unoccupied sites in the host zeolite structure via dealumination. Interestingly, the more vacancies in the host zeolite structure, the more isolated tetrahedrally coordinated Ti(IV) can be increased, eventually enhancing the catalytic performance in methyl oleate (MO) epoxidation for producing methyl-9,10-epoxystearate (EP). The engineered Ti-β exhibits outstanding performances in bulky MO epoxidation with the amount of produced EP per number of Ti sites up to 17.1±1.8 mol mol-1. This observation discloses an alternative strategy for optimizing catalyst efficiency in the rational design of the Ti-embedding zeolite catalyst, endeavoring to reach highly efficient catalytic performance.

Structural, vibrational, and electrical study of the topological insulator PbBi2Te4 at high pressure

We report a joint experimental and theoretical study of the structural, vibrational, and electric properties of the topological insulator PbBi2Te4 under compression through X-ray diffraction, Raman scattering, and electrical measurements at high pressure, which are complemented with theoretical calculations that include the analysis of the topological electron density. The internal polyhedral compressibility of the rhombohedral phase, the behavior of its Raman-active modes, the electrical behavior, and the nature of its different bonds under compression are discussed and compared with their parent binary compounds and with related ternary materials. Interestingly, PbBi2Te4 retains its topological insulating properties as far as the rhombohedral tetradymite-like phase is retained under compression, unlike other tetradymite-like compounds. In addition, PbBi2Te4 undergoes an unconventional reversible pressure-induced decomposition into the high-pressure phases of its parent binary compounds (PbTe and Bi2Te3) above 8 GPa. Finally, we discuss that the intralayer bonds in the tetradymite-like structure of PbBi2Te4 are electron-deficient multicenter bonds; i.e. bonds of the same kind as those present in its parent binary compounds, in related chalcogenides, such as SnSb2Te4, and in general in chalcogenide-based phase change materials. These unconventional bonds are intermediate between covalent and metallic bonds and provide exceptional properties to the materials.

Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets.

The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral magnets, can each be considered as forms of density waves but with distinct topologies. The SkX exhibits gyrodynamics analogous to electrons under a magnetic field, while the HL state resembles topological trivial spin density waves. However, unlike the charge density waves, the theoretical analysis of the sliding motion of SkX and HL remains unclear, especially regarding the similarities and differences in sliding dynamics between these two spin density waves. In this Letter, we systematically explore the sliding dynamics of SkX and HL in chiral magnets in the limit of large current density. We demonstrate that the sliding dynamics of both SkX and HL can be unified within the same theoretical framework as density waves, despite their distinct microscopic orders. Furthermore, we highlight the significant role of gyrotropic sliding induced by impurity effects in the SkX state, underscoring the impact of nontrivial topology on the sliding motion of density waves. Our theoretical analysis shows that the effect of impurity pinning is much stronger in HL compared with SkX, i.e., χ^{SkX}/χ^{HL}∼α^{2} (χ^{SkX}, χ^{HL}: susceptibility to the impurity potential, α (≪1) is the Gilbert damping). Moreover, the velocity correction is mostly in the transverse direction to the current in SkX. These results are further substantiated by realistic Landau-Lifshitz-Gilbert simulations.

Topology Optimization Driven Bone-Remodeling Simulation for Lumbar Interbody Fusion.

This study proposes a numerical approach for simulating bone remodeling in lumbar interbody fusion (LIF). It employs a topology optimization method to drive the remodeling process and uses a pixel function to describe the structural topology and bone density distribution. Unlike traditional approaches based on strain energy density or compliance, this study adopts von Mises stress to guide the remodeling of LIF. A novel pixel interpolation scheme associated with stress criteria is applied to the physical properties of the bone, directly addressing the stress shielding effect caused by the implanted cage, which significantly influences the bone remodeling outcome in LIF. Additionally, a boundary inverse approach is utilized to reconstruct a simplified analysis model. To reduce computational cost while maintaining high structural resolution and accuracy, the Scaled Boundary Finite Element Method (SBFEM) is introduced. The proposed numerical approach successfully generates results that closely resemble human lumbar interbody fusion.

Precursor‐Mediated Direct Growth of Defect‐Rich Hierarchical Nanocarbons for Electrocatalytic Hydrogen Peroxide Production†

Comprehensive SummaryCarbon‐based nanomaterials show great potential in selective electrochemical oxygen reduction reaction (ORR) through two‐electron (2e−) pathway for H2O2 production, which provides an eco‐friendly alternative to industrial energy‐intensive anthraquinone process. However, it still remains challenging to directly construct topological defects, which makes it difficult to study the working mechanism on 2e– ORR. Herein, we propose a precursor‐mediated chemical vapor deposition (CVD) approach for direct growth of topological defect‐rich hierarchical nanocarbons. Boric acid (H3BO3) is introduced into the precursor for disturbing the nucleation and growth through decomposing B‐containing species, which can in situ induce the formation of pentagon defects. The topological defect is found to be capable of introducing lattice strain, which can modify the electronic structure of nanocarbons and promote the key intermediate (*OOH) formation, thus greatly enhancing the 2e– ORR performance. Experimentally, the 2e– ORR selectivity shows a positive correlation to the topological defect density, where the average H2O2 selectivity reaches above 90% over a wide potential range with optimized concentration of H3BO3 as mediator. Moreover, in a flow cell, the hierarchical nanocarbons achieve a high H2O2 production rate of 998 mmol·gcatalyst−1·h−1 over 20 h of continuous electrocatalysis with stable current density (>100 mA·cm–2) and Faradaic efficiency (> 90%). This work provides a straightforward method for the synthesis of active metal‐free carbon‐based catalyst for sustainable H2O2 production.

Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics

Chiral magnetohydrodynamics is devoted to understanding the late-time and long-distance behavior of a system with an Adler-Bell-Jackiw anomaly at finite temperatures. The non-conservation of the axial charge is determined by the topological density \vec{E} \cdot \vec{B}E→⋅B→; in a classical hydrodynamic description this decay rate can be suppressed by tuning the background magnetic field to zero. However it is in principle possible for thermal fluctuations of \vec{E} \cdot \vec{B}E→⋅B→ to result in a non-conservation of the charge even at vanishing BB-field; this would invalidate the classical hydrodynamic effective theory. We investigate this by computing the real-time susceptibility of the topological density at one-loop level in magnetohydrodynamic fluctuations, relating its low-frequency limit to the decay rate of the axial charge. We find that the frequency-dependence of this susceptibility is sufficiently soft as to leave the axial decay rate unaffected, validating the classical hydrodynamic description. We show that the susceptibility contains non-analytic frequency-dependence which is universally determined by hydrodynamic data. We comment briefly on possible connections to the recent formulation of the ABJ anomaly in terms of non-invertible symmetry.

Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity

This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schrödinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the topological density. The Klein-Gordon solution leads to the Wheeler-de Witt Hamiltonian and quasinormal modes, and we demonstrate the connection between the potential and the black hole temperature within the Schwarzschild limit. Additionally, we discuss different solutions of the Schrödinger equation, with one solution highlighting the influence of the Airy solution on the wave function's evolution over time.

Phase- and temperature-driven chiral topological superfluids on a honeycomb lattice

The correlated spinful Haldane model exhibits rich topological phases consisting of chiral topological superfluids (TSFs) and topological spin density waves. However, most of previous studies mainly focus on the case with the fixed hopping phase or at zero temperature. In this paper, we study the attractive spinful Haldane model with arbitrary phase at finite temperature. The chiral TSFs with Chern number C = 2 and 4 emerge driven by the phase and temperature. In particular, the temperature can drive a C = 2 topological superfluid from a trivial normal insulator phase at an appropriate interaction. The bulk topology of all TSFs is uncovered by the Wilson loop method, and confirmed by the responses of edge dislocations.

Stiffness, strength, anisotropy, and buckling of lattices derived from TPMS and Platonic and Archimedean solids

Lattice metamaterials have gained considerable attention due to their distinctive topological structures and multifunctional properties. In this work, the effect of topology, loading conditions, and relative density on the effective mechanical properties of various novel lattice architectures is investigated numerically and experimentally. Thirteen strut-based lattices derived from triply periodic minimal surfaces (five lattices) as well as Platonic (three lattices) and Archimedean (five lattices) solids are considered for the first time, and their anisotropic mechanical properties, including uniaxial, shear, and bulk moduli and strengths as well as their total stiffness, buckling strengths, Poisson’s ratio, and anisotropy are investigated as a function of a wide range of relative densities (0.1% to 37%). Finite element analysis is employed to capture the full effective behavior of these lattices using periodic boundary conditions. Bifurcation analysis is performed to predict the threshold relative density governing their buckling vs yielding deformation behavior. Selected lattice structures of various relative densities are 3D printed using polymer selective laser sintering additive manufacturing technique and tested under quasi-static uniaxial compression where the experimental and numerical results are compared. The numerical results indicate that the deformation behavior can be altered between stretching and bending dominated mode of deformation as function of loading. Archimedean lattices are shown to outperform a wide range of strut-based lattices. This work opens the doors for more investigations of the multifunctional properties of these novel types of lattices and their engineering applications. Furthermore, the generated comprehensive data are useful in optimizing latticed structures using topology optimization techniques.

On thermal fluctuations and quantum regularities of F(R,G) gravity black holes with constant topological Euler density in nonlinear electrodynamics

We discuss the corrected thermodynamics and naked singularity structure of the topological static spherically symmetric solution in F(R,G) - gravity coupled with Born-Infeld—like nonlinear electrodynamics. Solutions admitting black holes with constant topological Euler density is analyzed in view of various thermodynamical variables. The inclusion of logarithmic correction to the entropy is extended to the other thermodynamical variables and the contribution of corrected variables are displayed on various plots. The stability of black hole under the effect of thermal variables is also studied. As a second scope of this study, solutions admitting timelike naked singularity are probed with bosonic and fermionic quantum wave packets to see if the singularity is quantum mechanically regular or not. In this context, the evolution of these probes remains well-defined if the corresponding spatial Hamiltonian operator is essentially self-adjoint. Our calculations reveal that when the singularity is probed with specific wave modes involving spin—0 and spin—1/2 quantum wave packets, the corresponding wave operators turn out to be essentially self-adjoint, which in turn implies unique well-defined time evolution.

Optimization optical and radiation shielding properties via controlling the Hirshfeld topological constraints: A case study of carbonate-based crystals

This work explores the potential of carbonate-based ceramics (CBC) as materials for optical and radiation shielding applications. The results reveal the distinctive behavior of various CBC materials in shielding γ-rays. At an intermediate energy of E = 0.5 MeV, SiO2 has a MAC value of 0.087, whereas the MAC values for the CBCs are as follows: (CMs, MAC (g/cm2)): (CaCO3, 0.088), (MgCO3, 0.087), (SrCO3, 0.086), (BaCO3, 0.096), (ZnCO3, 0.086), (CdCO3, 0.091), and (PbCO3, 0.145). Also, the effective atomic numbers (Zeff) found to range from 11.03 to 78.82. These values surpass those of silicon dioxide (SiO2), highlighting the superior γ-ray attenuation capabilities of CBC. The work also delves also into the optical properties of CBC materials, highlighting the interplay between density (2.61 < ρ < 6.72 g/cm3), band gap energy (2.680<Eg < 5.050 eV), and refractive index (1.99254 < n < 2.48905). Furthermore, the study delves into the impact of charge density within Hirshfeld voids on these properties, revealing that as the interatomic interactions increase: 2.1% < O⋯C<26.8%, 9.3% < O⋯O<26.3%, or 63.3% < O … A2⁺<86.4% (A = Ca, Mg, Sr, Ba, Zn, Cd) due to higher charge density, thus the LAC and n values may tune among the studied CBC. The fine-tuning of topological and charge density distributions within the crystal's voids offers a promising avenue to optimize these materials for enhanced radiation shielding effectiveness or optical properties. This interplay between crystal structure, composition, charge distribution, Hirshfeld topological constraints as key factors in determining their radiation attenuation and optical capabilities was explored.

Chaotic foliations with Ehresmann connection

We consider smooth codimension q foliations on n-dimensional manifolds where 0<q<n. We use Ehresmann connections as a technical tool to introduce the notion of sensitivity to initial conditions for foliations. We extend Devaney's definition of chaos for cascades to foliations with Ehresmann connection. Our main result states that sensitivity to initial conditions of a foliation with Ehresmann connection follows from topological transitivity and density of minimal sets of the foliation. Compactness both minimal sets and the ambient manifold is not assumed. The results are applied to complete Cartan foliations.

The Hirshfeld topological surfaces, volumes, and their voids charge density interplay on radiation shielding properties: A case study of carbide-based ceramics

Transition metal carbides (TMCs) are explored for their potential as radiation shielding materials, with a focus on their γ-ray attenuation properties. These high-density materials, including WC, TaC, HfC, NbC, and VC, are evaluated across an energy range of 0.015–15.0 MeV. Notably, at low incoming photon energy (0.0150 MeV), these TMCs exhibit mass attenuation coefficients (MAC) (TMC, MAC (g/cm2)): (WC, 130.417), (TaC, 125.730), (HfC, 120.873), (NbC, 23.751), and (VC, 32.377) and effective atomic numbers (Zeff) from 22.69 to 73.68. These values surpass those of silicon dioxide (SiO2), highlighting the superior γ-ray attenuation capabilities of TMCs. TMCs exhibit a distinct trend in MAC values, with tungsten carbide (WC) consistently demonstrating the highest MAC values, making it the most efficient γ-ray attenuator. Hafnium carbide (HfC) closely follows, with tantalum carbide (TaC) exhibiting lower MAC values, while niobium carbide (NbC) and vanadium carbide (VC) display the lowest values. These differences can be attributed to variations in material composition and structure. Furthermore, the study delves into the impact of charge density within Hirshfeld voids on LAC values, revealing that as X⁴⁺ … C interactions increase due to higher charge density, LAC values rise. This fine-tuning of topological and charge density distributions within the crystal's voids offers a promising avenue to optimize these materials for enhanced radiation shielding effectiveness. Overall, this research contributes to the understanding of the potential utility of TMCs in radiation shielding applications, showcasing the interplay between crystal structure, composition, and charge distribution as key factors in determining their radiation attenuation capabilities.

Cogging Torque Reduction of Axial-Modular Flux Switching Permanent Magnet Machine by Module Combination Technique

Flux switching permanent magnet machine exhibits high cogging torque due to the doubly salient topology and high air gap flux density. This paper proposes a new axial-modular flux switching permanent magnet (AM-FSPM) machine, which has an improved torque capability and the potential of cogging torque suppression by module combination technique. The cogging torque analytical expression of the machine with axial-modular topology is derived based on a magnetomotive force-permeance model. Then, the AM-FSPM machines are divided into two types by the combinations of stator-slot and rotor-pole, named fundamental harmonic offset naturally and fundamental harmonic offset manually. In addition, four approaches are investigated to reduce cogging torque by changing modular magnetomotive force and changing modular permeance. It can be concluded that the modular rotor tooth combination method has the most attractive torque performances among the four methods. Finally, the effectiveness of the proposed approaches is verified by the 3D finite element analysis and experimental results.

Rate-dependent behaviour of additively manufactured topology optimised lattice structures

Lattice structures offer a wide range of tuneable qualities that cannot be achieved with bulk materials. While lattice structures offer a range of tuneable qualities, including isotropic properties achievable in bulk materials, the advent of additive manufacturing (AM) advances research in this domain. Although several studies have characterized the quasi-static mechanical properties of lattice structures, there is limited experimental data available on their rate-dependent behaviour. Additionally, most lattice structures are anisotropic, making them unsuitable for applications where loading directions are unknown. In this study, a topology-optimised unit cell with nearly perfect isotropic stiffness is investigated for its isotropic specific energy absorption under high strain rates. The dynamic response of the structure is evaluated using 3 different materials: CPTi, AlSi10Mg, and 316LSS, and both experimental and numerical methods are employed. The influence of topology and relative density on the mechanical properties of the structure are explored, and the specific energy absorption isotropy is determined by loading the lattices in various orientations numerically. This research fills the gap in knowledge regarding the rate-dependent behaviour of lattice structures and offers insight into the potential for isotropic lattice structures in engineering applications.

Axial Flux Permanent Magnet Motor Topologies Magnetic Performance Comparison

Axial flux permanent magnet motors have attracted increasing attention due to their compact topology and high torque density. Many topological variations have arisen over time; however, limited research has directly compared the differences in magnetic performance of these topologies. This paper carries out a comprehensive investigation, employing both analytical and 3D finite element analyses, to compare the magnetic performance of three topologies: yokeless and segmented armature (YASA), axial flux internal rotor (AFIR), and offset AFIR. The findings reveal that each topology offers specific advantages for different applications. The YASA topology excels in minimizing core losses; the AFIR configuration achieves the highest torque density; and the offset AFIR topology shows the highest efficiency. The offset AFIR topology appears to offer advantages for a wide array of applications due to its higher power factor and lower permanent magnet loss, leading to reduced costs for converter design and cooling system design.

Topological density correlations in a Fermi gas

Topological density correlations in a Fermi gas

Skeleton Extraction for Articulated Objects With the Spherical Unwrapping Profiles.

Embedding unified skeletons into unregistered scans is fundamental to finding correspondences, depicting motions, and capturing underlying structures among the articulated objects in the same category. Some existing approaches rely on laborious registration to adapt a predefined LBS model to each input, while others require the input to be set to a canonical pose, e.g., T-pose or A-pose. However, their effectiveness is always influenced by the water-tightness, face topology, and vertex density of the input mesh. At the core of our approach lies a novel unwrapping method, named SUPPLE (Spherical UnwraPping ProfiLEs), which maps a surface into image planes independent of mesh topologies. Based on this lower-dimensional representation, a learning-based framework is further designed to localize and connect skeletal joints with fully convolutional architectures. Experiments demonstrate that our framework yields reliable skeleton extractions across a broad range of articulated categories, from raw scans to online CADs.

Synergistic boost of catalytic activity in ZrTe topological catalyst via multiple topologically-electronic states

Topological materials feature highly-active topological surface states and high carrier mobility, making them promising catalysts. While ongoing research centers on topological catalysis, most topological semimetal catalysts tend to showcase either a singular topological electronic state or a lone highly catalytic surface, imposing limitations on overall efficiency. Our study highlights ZrTe as a standout catalyst for hydrogen evolution, boasting multiple topological states that excel across various surfaces. ZrTe exhibits a Weyl nodal ring and a triple degenerate nodal point near the Fermi energy, resulting in topological surface states on multiple surfaces. Notably, the (010) and (001) surfaces exhibit remarkable catalytic performance, with Gibbs free energy (ΔGH*) values surpassing that of the Pt metal. Our work establishes a robust and unequivocal link between catalysis and topological properties on the catalytic surfaces, revealing a linear correlation between ΔGH* and topological surface state density. ZrTe emerges as an exceptional topological catalyst, with both of its topological states significantly contributing to the catalytic performance on distinct surfaces. This pioneering discovery offers a valuable platform for advancing catalyst research in the concept of topological catalysts.

Quantifying the heterogeneous impacts of the urban built environment on traffic carbon emissions: New insights from machine learning techniques

The configuration of the urban built environment is critical for promoting sustainability and achieving carbon neutrality. However, existing studies mostly use linear and spatial econometric models to investigate the relationship between urban built environments and traffic carbon dioxide (CO2) emissions, in-depth studies exploring the heterogeneous impacts of related features on traffic CO2 emission by interpretive machine learning models are scarce. Hence, we extract four dimensionless features to depict the size, compactness, irregularity, and isolation of built-up areas, and road network-related features (i.e., average cluster coefficient, road topological density, and road geometric density), respectively. Subsequently, we develop an interpretive machine learning framework based on the extracted features related to the urban built-up areas and road networks. The interpretive results of the proposed framework uncover that urban morphological features, especially population density (POP), GDP per capita (GDPpc), and urban physical compactness (UPC), have a heterogeneous impact on the per capita traffic emission (PCCE) across different cities. GDPpc is more like a linear relationship with PCCE, and UPC has a significant influence on PCCE when its value is between 62% and 78%. Our results also reveal the nonlinear relationships and interactive effects between these features, providing the implications of urban morphological planning and carbon emission reduction.