Topological Behavior Research Articles

A renormalized slip-tube anisotropy model for sliding cross-links in soft gel towards ultrahigh toughness

Abstract Adaptive cross-links in polymer networks enable slide-ring and highly entangled gels with excellent mechanical toughness including high extensibility and strong fracture resistance. However, few studies have been conducted to explore the connection between adaptive cross-linking networks and topological structures, and also their deformation mechanism in network structures has not been fully understood. In this study, a renormalized slip-tube anisotropy model is developed to describe the topological polymer networks and understand working principles of adaptive cross-links in topological networks in the sliding gels. Initially, Langevin chain statistics is employed to characterize the stored segment redistribution and large deformation behavior of polymer chains with using an adaptive factor. Moreover, a renormalized slip-tube free energy equation has been formulated by introducing the tube constraint free energy to describing the topological mechanics and thermodynamics for the adaptive cross-linking networks. Furthermore, an anisotropic model is extended to describe the topological networks and mechanical toughening behaviors in sliding gels. Finally, the proposed model has been verified using the experimental results reported in literature, providing a fundamental approach to formulate the topological toughening principle in sliding gels undergoing mechanically adaptive cross-linking.

Coupling characteristics of optical skyrmions based on localized spoof plasmons (LSP)

In this work, we theoretically investigate the coupling characteristics of optical skyrmions based on localized spoof plasmons (LSPs). First, the single LSP optical skyrmion is realized and resonance modes attributed to different topological features are analyzed. Second, the coupling effect is observed through decreasing the distance between the adjacent LSP optical skyrmions. The coupling LSP optical skyrmions can preserve the topological behaviors, and particularly, three coupling modes (mode-a, mode-b, and mode-c) can be observed. Mode-a presents uniform magnetic field distributions, while mode-b and mode-c can be observed with asymmetric magnetic field distributions. Finally, the ten-coupling LSP optical skyrmions supported by space-coiling cylinders and square structures are realized and the robust topological features are discussed. The results may contribute to the future investigation on designing optical skyrmion crystals and advanced optical devices.

Gapless topological behaviors in a long-range quantum spin chain

Topology is a fascinating phenomena in condensed-matter physics typically associated with a bulk gap. However, recent research shifts focus to quantum critical points or phases that exhibit nontrivial topological properties. Here we explore a cluster-Ising chain with long-range antiferromagnetic interactions that decay as a power law with distance. Using large-scale density matrix renormalization group simulations, we demonstrate that the nontrivial topology at the critical point remains stable against long-range interactions, resulting in a topologically nontrivial critical line. Moreover, even within the gapped region, the interplay between topology and long-range interaction can give rise to a topological phase featuring algebraically decaying correlations and edge modes, similar to gapless topological phases. We refer to this phase as the algebraic topological phase, which exhibits nontrivial gapless topological behaviors and arises solely from long-range interactions without short-range counterparts. The findings pave the way for more studies on topological states in long-range systems.

Evolutionary topology optimization with stress control for composite laminates using Tsai-Wu criterion

In this study, a topology optimization technique with stress control is proposed for the composite laminates. The bi-directional evolutionary structural optimization (BESO) method is selected to avoid the stress singularity. The technique expresses the failure index based on the Tsai-Wu criterion, thereby ensuring a comprehensive consideration of the anisotropy. To address the local nature of stress and multi-layer structure of laminates, a nested p-norm is employed, providing a global approximation of the local maximum failure index. To mitigate the highly non-linear stress behaviors, filter schemes are applied to both sensitivity numbers and design variables. Sensitivity numbers are derived via adjoint sensitivity analysis and Lagrange multipliers to address stress-based and stress-constrained problems. The proposed framework is validated through systematic numerical studies across various examples and conditions, offering insights into the topological behaviors of composite laminates. This study underscores the importance of considering distinct tensile and compressive strength in composite materials, which represents a key innovation. Additionally, the relationships among stiffness-based, stress-constrained, and stress-based designs are explored in depth.

Emergent topological quasiparticle kinetics in constricted nanomagnets

The ubiquitous domain wall kinetics under magnetic field or current application describes the dynamic properties in nanostructured magnets. However, when the geometrical size of a nanomagnetic system is constricted to the limiting domain wall length scale, the competing energetics between anisotropy, exchange, and dipolar interactions can cause emergent kinetics due to quasiparticle relaxation, similar to bulk magnets of atomic origin. This paper presents a joint experimental and theoretical study to support this argument: constricted nanomagnets, made of antiferromagnetic and paramagnetic neodymium thin film with honeycomb motif, reveal fast kinetic events at picosecond timescales due to the relaxation of topological quasiparticles that persist to low temperature in the absence of any external stimuli. This discovery is especially important considering the fact that paramagnets or antiferromagnets have no net magnetization. Yet, the kinetics in neodymium nanostructures is quantitatively similar to that found in ferromagnetic counterparts and only varies with the thickness of the specimen. This suggests that a universal, topological quasiparticle-mediated dynamical behavior can be prevalent in nanoscopic magnets, irrespective of the nature of the underlying magnetic material. Published by the American Physical Society 2024

On the Non-Linearity of S-Type Variable Exponent Absolutely Summable New Difference Sequence Space

This article presents the domain of general quantum difference in Nakano sequence space. Some topological and geometric behavior, the multiplication mappings defined on it, and the spectrum of mapping ideals constructed by this space and s−numbers have been introduced. Existing results are constructed by controlling the general quantum difference and power of this new space, which is a major strength.

TopoTxR: A topology-guided deep convolutional network for breast parenchyma learning on DCE-MRIs

Characterization of breast parenchyma in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a challenging task owing to the complexity of underlying tissue structures. Existing quantitative approaches, like radiomics and deep learning models, lack explicit quantification of intricate and subtle parenchymal structures, including fibroglandular tissue. To address this, we propose a novel topological approach that explicitly extracts multi-scale topological structures to better approximate breast parenchymal structures, and then incorporates these structures into a deep-learning-based prediction model via an attention mechanism. Our topology-informed deep learning model, TopoTxR, leverages topology to provide enhanced insights into tissues critical for disease pathophysiology and treatment response. We empirically validate TopoTxR using the VICTRE phantom breast dataset, showing that the topological structures extracted by our model effectively approximate the breast parenchymal structures. We further demonstrate TopoTxR’s efficacy in predicting response to neoadjuvant chemotherapy. Our qualitative and quantitative analyses suggest differential topological behavior of breast tissue in treatment-naïve imaging, in patients who respond favorably to therapy as achieving pathological complete response (pCR) versus those who do not. In a comparative analysis with several baselines on the publicly available I-SPY 1 dataset (N = 161, including 47 patients with pCR and 114 without) and the Rutgers proprietary dataset (N = 120, with 69 patients achieving pCR and 51 not), TopoTxR demonstrates a notable improvement, achieving a 2.6% increase in accuracy and a 4.6% enhancement in AUC compared to the state-of-the-art method.

Quantum analogous spin states of ultrasonic guided waves

In quantum mechanics, spin is a physical property that dominates the topological behaviors. While manifesting the spin states they reveal complex interaction of physical parameters in a topological media. The guided waves’ inherent spin states are made of real physical spin angular momentum from the superposition of elastic waves. Thus, here the elastic spin state that naturally manifests by the ultrasonic guided waves in an elastic wave guide is explained through quantum analogous perspective. Guided wave modes are the superposition of two longitudinally polarized and two transverse polarized elastic wave potentials propagating in diverging and converging pattern. Spin nature of transverse waves is well known. Spin nature of longitudinal waves is also recently being explored. However, due to the unique modal superposition of guided Rayleigh-Lamb wave modes the physical understanding of spin state is incomplete for the guided waves in a bounded media. Unlike only one hybrid spin states described in earlier works, guided waves may manifest total six with four well defined hybrid spin states explicitly derived and explained in this article. These six spin states play crucial role in the physics of spin-momentum locking of guided waves. Two spin states originated from the interaction of similar potentials and four hybris spin states originated from the interaction of potentials with different directions of wave vector and polarization vector, as emerged in guided waves. Understanding from fundamentals and exploiting the phenomena of spin-momentum locking in guided waves may have several applications in nondestructive evaluation.

Optical skyrmion and its "zipper-like" topological behavior in an energy flux field.

The optical skyrmion and its topological behavior are analyzed in an energy flux field constructed by an X-type vortex in a high numerical aperture system. The conditions for the formation of a skyrmion structure in this field are discussed, showing that the vortex pattern of the transverse energy flow and the inverse energy flow are crucial for the skyrmions and also are controlled by the phase gradient of the X-type vortex. Notably, the "zipper-like" topological reaction, which is the first, to our knowledge, found in ferromagnetic materials, is observed, and the physical mechanism is also explained by the relation of orbital angular momentum density and Poynting vectors. The results will reach the topological theory and may have applications in optical traps and data storage.

Crystal growth, structural, vibrational assignments, electronic, topological behavior and Hirshfeld surfaces of 1H-imidazole-1-methanol (HIM) single crystal

Crystal growth, structural, vibrational assignments, electronic, topological behavior and Hirshfeld surfaces of 1H-imidazole-1-methanol (HIM) single crystal

Geodesic planes in a geometrically finite end and the halo of a measured lamination

Recent works [22,23,3,33] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifold M of infinite volume. In this paper, we focus on the remaining case of geodesic planes outside the convex core of M, giving a complete classification of their closures in M.In particular, we show that the behavior is different depending on whether exotic roofs exist or not. Here an exotic roof is a geodesic plane contained in an end E of M, which limits on the convex core boundary ∂E, but cannot be separated from the core by a support plane of ∂E.A necessary condition for the existence of exotic roofs is the existence of exotic rays for the bending lamination. Here an exotic ray is a geodesic ray that has a finite intersection number with a measured lamination L but is not asymptotic to any leaf nor eventually disjoint from L. We establish that exotic rays exist if and only if L is not a multicurve. The proof is constructive, and the ideas involved are important in the construction of exotic roofs.We also show that the existence of geodesic rays satisfying a stronger condition than being exotic, phrased only in terms of the hyperbolic surface ∂E and the bending lamination, is sufficient for the existence of exotic roofs. As a result, we show that geometrically finite ends with exotic roofs exist in every genus. Moreover, in genus 1, when the end is homotopic to a punctured torus, a generic one (in the sense of Baire category) contains uncountably many exotic roofs.

Bohr chaoticity of number-conserving shifts

Let X be a compact metric space and T:X→X be a continuous transformation. A dynamical system (X,T) is called Bohr chaotic if for each weight sequence (wn)∈ℓ∞(N,R) there are f∈C(X) and x∈X such that (wn) is orthogonal to {f∘Tn(x)}. In this paper, we demonstrate that a number-conserving shift X is either finite or Bohr chaotic, uncovering the relationship between the topological behavior and the coefficients of X. Furthermore, a number-conserving shift is consisting of periodic points whenever it is finite.

Dirac crossings and band inversion in hexagonal superconductors emerging by chemical substitution: SrAlGe, BaAlGe, SrGaGe and BaGaGe

In this work, we used DFT calculations to compare the electronic structure of four hexagonal superconducting materials. Two of them are SrAlGe and BaAlGe, and the other two are given by substituting Al for Ga, resulting in SrGaGe and BaGaGe. The band structure, the density of states, and the Fermi surface were obtained for each compound with and without the spin–orbit coupling effect. For the SrGaGe and BaGaGe compounds, a band unfolding calculation was performed. We found that BaGaGe exhibits a quasi-flat-band localized in a specific direction of the Brillouin zone. In addition, band inversion can be induced by replacing Al for Ga in these compounds. Furthermore, we found that linear band crossings are gaped after spin–orbit coupling is considered to SrAlGe, BaAlGe, SrGaGe, and BaGaGe. These Dirac-like band crossings point to non-trivial topological behavior.

Topological behavior of spectral singularities in topological Weyl semimetals.

In this study, we examine the topological character of spectral singularities by using transverse magnetic (TM) mode configuration in a Topological Weyl Semimetal (TWSM). TM mode configuration restrains the effect of Kerr/Faraday rotations and therefore does not allow an extra degree of freedom to occur. We find out that surface currents arise due to topological terms on the surface of TWSM slab where no Fermi arcs are localized. We also investigate the contribution of the Θ-term, which is the origin of axions in topological materials, and especially theb-term, to the topological properties. As a result of our study, we clearly reveal the topological character ofb-term for the first time and we demonstrate the Weyl degeneracy situation in an obvious manner. Our system produces circular currents in the plane of propagation, maintaining a cyclotron shape motion. The presence ofb-term causes the induced current to be topologically protected. Our findings verify that topological properties of TWSM containing two opposite chirality Weyl fermions are robust against external influences. With the findings of our study, the appropriate conditions for the construction of a topological laser and the values that the system parameters can take have been demonstrated.

A new 3D Zn(II)‐based coordination polymer with kgd topology as potent photocatalyst for antibiotic degradation

A new coordination polymer (CP) with composition [Zn3(bpyp)2(TCB)2(H2O)2]n (1) has been engendered by performing reaction of Zn(II) with 1,3,5‐tris‐(4‐carboxyphenyl)benzene (H3TCB) and 2,5‐bis(pyrid‐4‐yl)pyridine (bpyp) under solvothermal condition. The single crystal X‐ray diffraction analysis for 1 suggests kgd topological behavior having resemblance with a tessellation composed of diamond shapes arranged in a star pattern and represented by the Schläfli symbol {41}2{42·62·81}. This newly designed CP exhibits optical band gap of 2.92 eV and employed as photocatalyst for photodegradation of antibiotics, namely, nitrofurazone (NFZ), chloramphenicol (CAP), sulfasalazine (SLA), oxytetracycline (OXY), and furazolidone (FZD). Among these antibiotics, 1 displays best photocatalytic activity against the photodegradation of NFZ and under optimized conditions viz. photocatalyst dosage of 15 mg, and initial NFZ concentration of 40 ppm, the CP 1 displays best catalytic performance and photo‐decomposed 93.04% NFZ with pseudo first order rate constant k of 0.04502 min−1 in 1 h. The likely photocatalytic mechanism has been evaluated using theoretical calculations.

Structural, topological, and rheological characteristics of entangled short-chain branched polymer melts under shear flow in comparison with the linear analog

We present a detailed analysis of the general influence of short branches on the structural, topological, and rheological behaviors of entangled short-chain branched (SCB) polyethylene (PE) melt systems under shear flow via direct comparison with the corresponding linear analogs using extensive atomistic nonequilibrium molecular dynamics (NEMD) simulations, for a wide range of flow strengths. In comparison with the linear melt, the SCB systems generally exhibit more compact chain structures and larger dynamic resistance, in response to an imposed flow field at all flow strengths. These features essentially arise from (i) the increased chain stiffness due to the torsional restriction of backbone atoms around the branch points and (ii) the fast random Brownian motion of short branches via their very short characteristic relaxation time. We analyzed various structural and rheological properties, such as anisotropic chain dimension and orientation and their detailed distributions, topological characteristics of the entanglement network, material functions, chain rotation dynamics, and flow birefringence. Distinctive physical characteristics of the entangled SCB systems exposed by these individual properties can be consistently understood based on the fundamental structural and dynamical roles of short branches. These findings are considered informative in our systematic understanding and prediction for the general rheological behaviors of long entangled SCB polymer systems under flow, and in tuning the material properties of SCB polymers in practical applications.

Bulk-boundary and RPS thermodynamics from topology perspective

In this study, we investigate the bulk-boundary and restricted phase space (RPS) thermodynamics of Rissner-Nordström (R-N) AdS and 6-dimensional charged Gauss-Bonnet AdS black holes. Additionally, we examine the topological characteristics of the considered black holes and compare them with the results of extended thermodynamics. We determine that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics, whereas the RPS thermodynamics exhibits a distinct behavior. Furthermore, we demonstrate that within the RPS formalism, there is only one critical point with a topological charge of +1 . Moreover, in the RPS formalism, the inclusion of higher-derivative curvature terms in the form of Gauss-Bonnet gravity does not alter the topological classification of critical points in charged AdS black holes.

Topological Photonic Alloy.

We present the new concept of photonic alloy as a nonperiodic topological material. By mixing nonmagnetized and magnetized rods in a nonperiodic 2D photonic crystal configuration, we realized photonic alloys in the microwave regime. Our experimental findings reveal that the photonic alloy sustains nonreciprocal chiral edge states even at very low concentration of magnetized rods. The nontrivial topology and the associated edge states of these nonperiodic systems can be characterized by the winding of the reflection phase. Our results indicate that the threshold concentrations for the investigated system within the first nontrivial band gap to exhibit topological behavior approach zero in the thermodynamic limit for substitutional alloys, while the threshold remains nonzero for interstitial alloys. At low concentration, the system exhibits an inhomogeneous structure characterized by isolated patches of nonpercolating magnetic domains that are spaced far apart within a topologically trivial photonic crystal. Surprisingly, the system manifests chiral edge states despite a local breakdown of time-reversal symmetry rather than a global one. Photonic alloys represent a new category of disordered topological materials, offering exciting opportunities for exploring topological materials with adjustable gaps.

Topological wave equation eigenmodes in continuous 2D periodic geometries

In this paper, we address the topological characterization of the wave equation solutions in continuous two-dimensional (2D) periodic geometries with Neumann or Dirichlet boundary conditions. This characterization is relevant in the context of 2D vibrating membranes and our approach allows one to understand the topological behavior recently observed in acoustic three-dimensional artificial lattices. In particular, the dependence of the topological behavior on the experimental positioning of the coupling channels is explained using simple arguments and a simple method of construction of an equivalent effective tight-binding Hamiltonian is presented.

Coexistence of topological and bipolar magnetic semiconducting behavior in 2D metal-organic frameworks with a p-orbital coloring-triangle lattice

Coexistence of topological and bipolar magnetic semiconducting behavior in 2D metal-organic frameworks with a <i>p</i>-orbital coloring-triangle lattice