Topological Classification Research Articles

Exploring mesophase formation: Structural characterization approaches in a soft sphere model

This study employs Molecular Dynamics simulations to enhance the structural characterization of sphere mixture systems, focusing on local order parameters to identify order-disorder transitions within lamellar and hexagonal mesophases. The structural characterization included the use of neural networks and the search for clusters with topological order. We have identified the order-disorder transition at a characteristic temperature TOD, effectively captured by the structural parameters analyzed. Below TOD, the system organizes into an ordered mesophase, while above this temperature, it transitions into an isotropic liquid state. Moreover, within the isotropic region, we observe that the liquid begins to form clusters. This clustering phenomenon becomes evident below a specific temperature, denoted as T⁎. At T⁎, there are noticeable changes in the volume versus temperature curves, indicating a process of micellization or clustering in the system. The structural parameters used in our study also register this behavioral change at T⁎, further supporting the occurrence of this phenomenon. Additionally, our analysis of the overlap in detecting ordered particles between the two structural parameters using the Sørensen-Dice similarity coefficient reveals a significant spatial correlation in the isotropic phase, with a correlation higher than what would be expected in a random case. This indicates that both neural networks and topological cluster classification detect statistically similar ordered regions in the isotropic phase, highlighting the clustering. Our findings reveal that the structural parameters effectively capture both the order-disorder transition at TOD and the clustering process at T⁎. These results provide valuable insights into the self-assembly mechanisms and phase behavior in this soft-sphere model, advancing our understanding of self-assembly processes in material science, particularly in exploring phase behavior in mesogenic nanoparticle systems.

Gauge-invariant optical selection rules for excitons

Presently, the optical selection rules for excitons under circularly-polarized light are manifestly gauge-dependent. Recently, Fernando et al. introduced a gauge-invariant, quantized interband index. This index may improve the topological classification of material excited states because it is intrinsically an inter-level quantity. In this work, we expand on this index to introduce its chiral formulation, and use it to make the selection rules gauge-invariant. We anticipate this development to strengthen the theory of quantum materials, especially two-dimensional semiconductor photophysics.

Thermodynamic topology of phantom AdS black holes in massive gravity

In this work, we explore the thermodynamic topology of phantom AdS black holes in the context of massive gravity. To this end, we evaluate these black holes in two distinct ensembles: the canonical and grand canonical ensembles (GCE). We begin by examining the topological charge linked to the critical point and confirming the existence of a conventional critical point (CP1) in the canonical ensemble (CE), this critical point has a topological charge of −1 and acts as a point of phase annihilation, this situation can only be considered within the context of the classical Einstein–Maxwell (CEM) theory (η=1), while no critical point is identified in the GCE. Furthermore, we consider black holes as a topological defect within the thermodynamic space. To gain an understanding of the local and global topological configuration of this defect, we will analyze its winding numbers, and observe that the total topological charge in the CE consistently remains at 1. When the system experiences a pressure below the critical threshold, it gives rise to the occurrence of annihilation and generation points. The value of electric potential determines whether the total topological charge in the GCE is zero or one. As a result, we detect a point of generation point or absence of generation/annihilation point. Based on our analysis, it can be inferred that ensembles significantly impact the topological class of phantom AdS black holes in massive gravity.

Engineering Topological States in 1D Pi-Conjugated Polymers

The emergence of topological states is at the vanguard of modern condensed matter physics. In this talk, I will revise our recent findings regarding the expression of topological SSH edge states on 1D acene and periacene pi-conjugated polymers. Importantly, thanks to the resolution capabilities provided by scanning probe microscopies, complemented by theory, I will provide the relation between the dominant resonant form and the topological quantum class of the distinct materials.

Davies-type phase transitions in 4D Dyonic AdS black holes from topological perspective

In this work, we discussed the Davies-type phase transitions in two distinct categories of dyonic AdS black holes (BHs). The first one is dyonic AdS BHs within four-dimensional spacetime framework. The second one is the dyonic BHs with quasitopological electromagnetism (QE) in Einstein-Gauss-Bonnet gravity (EGBG). First, we analyze the increasing and decreasing behavior of divergency depending upon different parameters which provides useful information about the region that are physical and stable. We also discuss the critical behavior of BHs in three different statistical ensembles: the canonical, mixed and grand canonical. It is noted that BHs can be classified into distinct topological classes based on their topological charge (Q) which assumes discrete values of 0,+1,−1. This topological charge plays a pivotal role in determining the phase structure and stability of the BHs within each ensemble. A topological charge of 0 corresponds to a neutral topological state that could be indicative of a more complex underlying structure, while charges of +1 or −1 indicate the presence of additional structures such as magnetic monopoles or dyons, which significantly influence the thermodynamic properties and phase transitions of the system.

Theory of Refraction, Ray–Wave Tilt, Hidden Momentum, and Apparent Topological Phases in Isotropy-Broken Materials Based on Electromagnetism of Moving Media

The mysterious nature of electromagnetic momentum in materials is considered one of the most significant challenges in physics, surpassing even Hilbert’s mathematical problems. In this paper, we demonstrate that the difference between the Minkowski and Abraham momenta, which consists of Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We show that individual electromagnetic waves with non-unit indices of refraction (n) appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames, these high-k waves are Fresnel–Fizeau dragged from rest to their phase velocities, acquiring longitudinal hidden momentum and related refractive properties. On a material level, all electromagnetic waves belong to Fresnel wave surfaces, which are topologically classified according to hyperbolic phases by Durach and determined by the electromagnetic material parameters. For moving observers, material parameters appear modified, leading to alterations in Fresnel wave surfaces and even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of electromagnetic momentum tilt, defined as the non-zero angle between Abraham and Minkowski momenta or, equivalently, between the rays and the wavefront propagation direction. This momentum tilt is only possible in isotropy-broken media, where the E and H fields can be longitudinally polarized in the presence of electric and magnetic bound charge waves. The momentum tilt can be understood as a differential aberration of rays and waves when observed in the material rest frame.

Dimension Reduction of Multidimensional Structured and Unstructured Datasets through Ensemble Learning of Neural Embeddings

Dimension reduction aims to project a high‐dimensional dataset into a low‐dimensional space. It tries to preserve the topological relationships among the original data points and/or induce clusters. NetDRm, an online dimensionality reduction method based on neural ensemble learning that integrates different dimension reduction methods in a synergistic way, is introduced. NetDRm is designed for datasets of multidimensional points that can be either structured (e.g., images) or unstructured (e.g., point clouds, tabular data). It starts by training a collection of deep residual encoders that learn the embeddings induced by multiple dimension reduction methods applied to the input dataset. Subsequently, a dense neural network integrates the generated encoders by emphasizing topological preservation or cluster induction. Experiments conducted on widely used multidimensional datasets (point‐cloud manifolds, image datasets, tabular record datasets) show that the proposed method yields better results in terms of topological preservation ( curves), cluster induction (V measure), and classification accuracy than the most relevant dimension reduction methods.

Thermodynamic topology of D = 4,5 Horava Lifshitz black hole in two ensembles

In this paper, we investigate the thermodynamic topology of four and five-dimensional Hořava-Lifshitz (HL) black holes within Hořava gravity. To analyze their thermodynamic topology, we treat these HL black holes as topological defects in their thermodynamic spaces and compute the winding numbers at these defects. Our study is conducted in two different ensembles: the fixed ϵ ensemble and the fixed ζ ensemble, where ϵ is a parameter of the HL black holes, and ζ is its conjugate parameter. In the fixed ϵ ensemble, we consider three different horizon types: spherical (k=+1), flat (k=0), and hyperbolic (k=−1), while in the fixed ζ ensemble, we examine two horizon types: spherical (k=+1) and hyperbolic (k=−1). For all the aforementioned cases, we study the local and global topology of these black holes and classify them into topological classes based on their topological charges. We calculate the topological number for each case. This process uncovers some novel phase diagrams that reveal a number of multiple defect curve phenomenon. Additionally, we explore how the topological charge of these black holes depends on the values of the thermodynamic parameters. Our findings indicate that the thermodynamic topology of Hořava-Lifshitz black holes in D=4,5 is significantly influenced by the type of horizon, the choice of ensemble, the values of pressure, and the parameters ϵ or ζ.

Dual tri-isolated DC H-6 inverter with minimal power components design

Multilevel inverters have been forecasted in recent years for industrial and renewable energy applications due to its inherent characteristics of shaping the output voltage nearer to sinusoidal shape through concatenating several two/three level inverters using isolated DC sources or DC-link capacitors. However, the classical topologies used for synthesizing stepped voltage have several outwards like more number of DC sources or DC-link capacitors and switching devices used. In this paper, an effort has been sighted to bring a new topology for generating stepped voltage to overcome the above mentioned demerits. In addition to this, a new digital pulse width modulation (PWM) strategy is developed in-line with a new topology to eliminate the use of carrier and reference signals. The performance of the proposed topology and developed control strategy are evaluated in MATLAB/ Simulink platform and an laboratory prototype is constructed for experimental investigations to accord the simulation results.

Thermodynamic Topology of Topological Black Hole in F(R)-ModMax Gravity’s Rainbow

Abstract In order to include the effect of high energy and topological parameters on black holes in $\mathrm{ F}(R)$ gravity, we consider two corrections to this gravity: energy-dependent spacetime with different topological constants, and a nonlinear electrodynamics field. In other words, we combine $\mathrm{ F}(R)$ gravity’s rainbow with ModMax nonlinear electrodynamics theory to see the effects of high energy and topological parameters on the physics of black holes. For this purpose, we first extract topological black hole solutions in $\mathrm{ F}(R)$-ModMax gravity’s rainbow. Then, by considering black holes as thermodynamic systems, we obtain thermodynamic quantities and check the first law of thermodynamics. The effect of the topological parameter on the Hawking temperature and the total mass of black holes is obvious. We also discuss the thermodynamic topology of topological black holes in $\mathrm{ F}(R)$-ModMax gravity’s rainbow using the off-shell free energy method. In this formalism, black holes are assumed to be equivalent to defects in their thermodynamic spaces. For our analysis, we consider two different types of thermodynamic ensembles. These are: fixed q ensemble and fixed $\phi$ ensemble. We take into account all the different types of curvature hypersurfaces that can be constructed in these black holes. The local and global topology of these black holes are studied by computing the topological charges at the defects in their thermodynamic spaces. Finally, in accordance with their topological charges, we classify the black holes into three topological classes with total winding numbers corresponding to $-1, 0$, and 1. We observe that the topological classes of these black holes are dependent on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles.

Topological classes of thermodynamics of the rotating charged AdS black holes in gauged supergravities

In this paper, we investigate the topological numbers of rotating charged AdS black holes in both four- and five-dimensional gauged supergravity theories. Our analysis is conducted within the framework of the thermodynamical topological approach to black holes, utilizing the generalized off-shell Helmholtz free energy. We demonstrate that the number of rotation parameters plays a significant role in determining the topological numbers of five-dimensional rotating AdS black holes. Moreover, our findings indicate that the topological numbers of both four- and five-dimensional rotating AdS black holes are not influenced by the number of electric charge parameters. This highlights a distinct difference in how rotation and electric charge parameters impact the thermodynamic topological properties of these black holes.

Lower density soft operators and density soft topologies

The classical density topology is derived from the Lebesgue density points of Lebesgue measurable sets. Wilczynski proposed a more general scheme for defining density points. It turns out that his scheme works in the category sense in addition to the measure-theoretic one. The sets of density points necessitate some properties of the operator of density points. Such an operator is named the lower density operator. In this theme, we introduce lower density soft operators on (abstract) chargeable soft spaces along with their basic properties. Among others, we show that each lower density soft operator defines a system of parametric lower density operators. Then, we study density soft topologies, the soft topologies generated by lower density soft operators. The main attributes and topological properties of density soft topologies are analyzed. We finalize this work by demonstrating several characterizations of (simple) soft density topologies. In particular, we prove that in density soft topologies, the Borel soft σ-algebra coincides with the soft σ-algebra of soft sets with the Baire property.

Twisting Between Topological Phases in 1D Conjugated Polymers via a Multiradical Transition State

AbstractIn recent years, it has become possible via on‐surface bottom‐up synthesis to engineer the topological character of carbon nanostructures. Graphene nanoribbons and 1D conjugated polymers (1DCPs) have thus tailored so as to host either topologically trivial or non‐trivial phases. Molecular design is the primary means to set the topological class of these nanomaterials. However, external control over topology is also demonstrated via electric fields or top‐down hydrogenation. Inspired by the connection between topology and π‐conjugation, here it is demonstrated via first‐principles calculations that aryl ring twist angles also serve as topological knobs. Focusing on rationally designed 1DCPs composed of triarylmethyl (TAM) units, it is shown that rotation of certain aryl rings enables a transition from the trivial to the topologically non‐trivial phase. Accordingly, fixing a particular twist angle configuration (e.g., via chemical functionalization) is equivalent to robustly setting a targeted topological phase. It is also found that in considered 1DCPs, the quantum phase transition occurs without the electronic band gap closing, due to a multiradical antiferromagnetic phase emerging at the transition point. All in all, this study highlights the potential of aryl ring twisting for engineering topological properties in carbon nanomaterials and establishes TAM 1DCPs as exotic topological 1D systems.

Achievement splitting for topological states with pseudospin in phase modulation by using gyromagnetic photonic crystals

As we know, valley-Hall kink states or pseudospin helical edge states are excited by polarized-momentum-locking [left-handed circular polarization (LCP) and right-handed circular polarization (RCP)] because the valley-Hall kink modes or pseudospin polarized modes have intrinsic and local chirality, which is difficult for these states to achieve phase modulation. Here we theoretically design and study a compatible topological photonic system with coexistence of photonic quantum Hall phase and pseudospin Hall phase, which is composed of gyromagnetic photonic crystals with a deformed honeycomb lattice containing six cylinders. A typical kind of hybrid topological waveguide states with pseudospin-characteristic, magnetic field-dependent, and strong robustness against backscattering and perfect electric conductor (PEC) is realized in the present system. Furthermore, we re-design a structure with intersection-liked, achieve splitting for one-way pseudospin quantum Hall edge states by using phase modulation. Robustness of the one-way pseudospin-quantum Hall edge states in splitting has been demonstrated as well. Additionally, PEC inserted in transport channel brings optical path difference in waveguide transmission, which would influence splitting for hybrid topological waveguide states in phase difference modulation. This work not only provides a new way for manipulation (i.e., phase modulation) of hybrid topological waveguide states in compatible topological photonic system from distinct topological classes but also has potential in various applications, such as sensing, signal processing, and on-chip communications.

THE WAR AS A SOCIO-CULTURAL PHENOMENON IN A CONTEMPORARY UKRAINIAN PHILOSOPHICAL DISCOURSE

An armed conflict between Ukraine and Russian Federation lasts for the past 10 years on and on February 24, 2022 it turned into full-scale war with all arsenal of conventional arm available used, nuclear excluded.The war turned into a new social and political reality that defined socio-political and socio-cultural vectors of development of Ukrainians and their state – focused on oppression to occupant’s conquer – for many years ahead.The war, as a socio-cultural phenomenon and the new stage of Ukrainian nation became a topic of research of the domestic academic environment. It defined in home philosophical research circles new polemic that aims at thinking through an ontological nature of the conflict, its social, cultural, and historical causes, to reveal its specific character in the past and in the present, to find out where the balance was lost in the structural order of the security, its lawful preventive mechanisms failure.Many analytical attempts to describe topological classification of that conflict (in the context of the growth of the contemporary philosophical discourse) were conducted. It were given some answers on the question on the roots of the conflict, on its continuity. It was pointed out its destructive impact on the condition of the Ukrainians, its social and cultural evolution from the point of view of different philosophical views and research programmes or contemporary historical narratives, modern principles of the native and Western-European philosophy.An evolution of the points of view on ontological and historical reasons of the war and philosophical reflections of the native scholars were considered in this article. Some problematic issues, determined by the different phases of the conflict were researched.

Controlling chaos and codimension-two bifurcation in a discrete fractional-order Brusselator model

This paper explores the qualitative behavior of a discrete fractional–order Brusselator model. We analyze the local dynamics of the model around its fixed point and determine its topological classification. We perform the bifurcation analysis for both codimension-one and codimension-two cases to examine the system behavior near critical parameter values. Using normal form theory and center manifold theorem (CMT), we prove that the model exhibits period-doubling bifurcation around its interior fixed point. We also study the existence and direction of Neimark–Sacker bifurcation using normal form theory. For codimension-two bifurcation, we show that the model undergoes 1:2, 1:3, and 1:4 resonances by applying normal form theory and suitable affine transformations. The system displays a rich variety of bifurcations, including quasi–periodicity, periodic orbits, chaotic behavior, and resonance bifurcation. Furthermore, the existence of chaos is discussed in the sense of Marotto, and a novel chaos control method is proposed for discrete Brusselator model using an extended pole–placement approach. This modified approach is more suitable for codimension-two bifurcation situations. Numerical simulations are used to illustrate the theoretical discussion.

Topology classification in bi-anisotropic topological photonic crystals via the Wilson loop approach [Invited

Topological photonic crystals have attracted tremendous attention due to their promise of robust optical properties and great potential for applications in on-chip devices. Numerous successful experimental demonstrations have shown or proved their topological properties, however, many of them turn out to have a nature of fragile topological phases. Here, using theoretical methods of fragile topology, we analyze two cases of topological photonic crystals with preserved time reversal symmetry, which utilize (1), the intrinsic duality and bi-anisotropy, and (2), accidental duality and structural bi-anisotropy respectively to induce their topological order. Our results show that the former case belongs to a Wannier-obstructed type of topological phase, indicating strong topological protection in their edge states. However, the latter meta-waveguide designs with structural bi-anisotropy widely implemented in experiments are Wannierizable, implying the fragile properties of their topology and gapped edge spectra. Our results provide new insights into the topological properties of photonic crystals as well as other bosonic systems with time-reversal symmetry.

Thermodynamic topology of Kerr-Sen black holes via Rényi statistics

In the present study, we investigate the topological properties of black holes in terms of Rényi statistics as an extension of the Gibbs-Boltzmann (GB) statistics, aiming to characterize the non-Boltzmannian thermodynamic topology of Kerr-Sen and dyonic Kerr-Sen black holes. Through this research, we discover that the topological number derived via Rényi statistics differs from that obtained through GB statistics. Interestingly, although the nonextensive parameter λ changes the topological number, the topological classification of the Kerr-Sen and dyonic Kerr-Sen black holes remains consistent under both GB and Rényi statistics. In addition, the topological numbers associated with these two types of black holes without cosmological constant using Rényi entropy processes are the same as the AdS cases of them by considering the GB entropy, as further evidenced by such a study found here. This indicates the cosmological constant has some potential connections with the nonextensive parameter from the perspective of thermodynamic topology.

Non-probabilistic reliability-based multi-scale topology optimization of thermo-mechanical continuum structures with stress constraints

A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β=3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method.

The dynamics about asteroid (162173) Ryugu

The dynamical environment around the asteroid (162173) Ryugu is analyzed in detail using a constant-density polyhedron model based on the measurements from the Hayabusa2 mission. Six exterior equilibrium points (EPs) are identified along the ridge line of Ryugu, and their topological classifications fall into two distinctive categories. The initial periodic orbit (PO) families are computed and analyzed, including distant retrograde/prograde orbit (DRO/DPO) families and fifteen PO families emanating from the exterior EPs. The fifteen PO families are further divided into three categories: seven converge to an EP, seven reach Ryugu’s surface, and one exhibits cyclic behavior during its progression. The existence of initial PO families converging to an EP is analyzed using the bifurcation of a degenerate EP. Connection between these families and similar ones in the circular restricted three-body problem (CRTBP) is also examined. Bifurcated PO families are identified and computed from the initial PO families, including ten families from the DROs, fifteen from the DPOs, and twenty-five associated with the EPs. The bifurcated families are separately analyzed and categorized in terms of their corresponding initial families. Connections established by the same bifurcation points between different bifurcated families are identified. A comparison is made for the dynamical environments of Ryugu and Bennu to evaluate the similarities and differences in the evolution of EPs and the progression of PO families in top-shaped asteroids.