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Magnetic skyrmion bags are composite topological spin textures with arbitrary topological charges. Here, we computationally study the transient rotational motion of skyrmion bags, which is characterized by a global rotation of inner skyrmions around the central point. Distinct from conventional rotational modes found in skyrmions, the observed rotation is a forced motion associated with the breathing mode induced solely by vertical microwave fields. The driving force behind this rotation originates from the interactions between outer and inner skyrmions, with the angular velocity determined by the phase difference resulting from their asynchronous breathing behaviors. It is also found that skyrmion bags with larger skyrmion numbers are more conducive to the occurrence of the rotation. Our results are useful for understanding the cluster dynamics of complex topological spin textures driven by dynamic fields. [ABSTRACT FROM AUTHOR]

A central paradigm of nonequilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which nonequilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous nonequilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single-shot X-ray photon correlation spectroscopy to resolve the nonequilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition in a (PbTiO3)16/(SrTiO3)16 superlattice. Such ferroelectric superlattice systems are a useful platform to study phase transitions and topological dynamics due to their high degree of tunability. This provides an approach for capturing the nucleation of the light-induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. We identify a nonequilibrium correlation response spanning >10 orders of magnitude in timescales, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We further show how the observed time-dependent long-time correlations can be understood in terms of stochastic and non-Markovian dynamics of domain walls, encoded in waiting-time distributions with power-law tails. This work defines possibilities for probing the nonequilibrium and correlated dynamics of disordered and heterogeneous media. [ABSTRACT FROM AUTHOR]

We consider the homology theory of étale groupoids introduced by Crainic and Moerdijk [A homology theory for étale groupoids. J. Reine Angew. Math. 521 (2000), 25–46], with particular interest to groupoids arising from topological dynamical systems. We prove a Künneth formula for products of groupoids and a Poincaré-duality type result for principal groupoids whose orbits are copies of an Euclidean space. We conclude with a few example computations for systems associated to nilpotent groups such as self-similar actions, and we generalize previous homological calculations by Burke and Putnam for systems which are analogues of solenoids arising from algebraic numbers. For the latter systems, we prove the HK conjecture, even when the resulting groupoid is not ample. [ABSTRACT FROM AUTHOR]

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of p -periodic points admits a natural free action of ℤ / p ℤ for each prime number p. We are interested in the growth of its index and coindex as p → ∞. Our main result shows that there exists a fixed-point free dynamical system having the divergent coindex sequence. This solves a problem posed by M. Tsukamoto, M. Tsutaya and M. Yoshinaga, G -index, topological dynamics and marker property, preprint (2020), arXiv:2012.15372. [ABSTRACT FROM AUTHOR]

In topological band theory, phonon boundary modes consequence of a topologically non-trivial band structure feature desirable properties for atomically-precise technologies, such as robustness against defects, waveguiding, and one-way transport. These topological phonon boundary modes remain to be studied both theoretically and experimentally in synthetic materials, such as polymers and supramolecular assemblies at the atomistic level under thermal fluctuations. Here we show by means of molecular simulations, that surface-confined Su-Schrieffer-Heeger (SSH) phonon analogue models express robust topological phonon boundary modes at heavy boundaries and under thermal fluctuations. The resulting bulk-heavy boundary correspondence enables patterning of boundary modes in polymer chains and weakly-interacting supramolecular lattices. Moreover, we show that upon excitation of a single molecule, propagation along heavy-boundary modes differs from free boundary modes. Our work is an entry to topological vibrations in supramolecular systems, and may find applications in the patterning of phonon circuits and realization of Hall effect phonon analogues at the molecular scale. Topological phonon boundary modes (TBM) hold promises for advanced phononic applications. Here, the authors introduce the bulk-heavy boundary correspondence to pattern TBM in polymers and supramolecular assemblies under thermal fluctuations. [ABSTRACT FROM AUTHOR]

Transcriptional induction coincides with the formation of various chromatin topologies. Strong evidence supports that gene activation is accompanied by a general increase in promoter-enhancer interactions. However, it remains unclear how these topological changes are coordinated across time and space during transcriptional activation. Here, we combine chromatin conformation capture with transcription and chromatin profiling during an embryonic stem cell (ESC) differentiation time course to determine how 3D genome restructuring is related to transcriptional transitions. This approach allows us to identify distinct topological alterations that are associated with the magnitude of transcriptional induction. We detect transiently formed interactions and demonstrate by genetic deletions that associated distal regulatory elements (DREs), as well as appropriate formation and disruption of these interactions, can contribute to the transcriptional induction of linked genes. Together, our study links topological dynamics to the magnitude of transcriptional induction and detects an uncharacterized type of transcriptionally important DREs. [Display omitted] • Temporal analysis reveals several chromatin topology types • Topological dynamics is linked with the magnitude of gene activation • Lost and transient mostly precede, while de novo contacts also follow transcription • Transient interactions can modulate transcriptional induction Mahara et al. show that genome folding dynamics and the magnitude of transcriptional induction are linked during ESC differentiation. Thereby, pervasive transient interactions can contribute to full activation of connected genes, irrespective of their chromatin signature. This activity can involve temporal facilitation of promoter interactions with strong enhancers. [ABSTRACT FROM AUTHOR]

In this paper we develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics when the acting group is second countable and locally compact. As an application, we show extensions of Schwartzman's theorem in this context. Also, we get new results when the acting group is {\mathbb Z}^d: any half-space of \mathbb {R}^d contains a vector defining a (oriented) nonexpansive direction in the sense of Boyle and Lind. Finally, we deduce rigidity properties of distal Cantor systems. [ABSTRACT FROM AUTHOR]

We consider open dynamical systems defined on compact metric spaces with multiple shrinking holes. We study the points which are indecisive, i.e. change infinitely many times the escape hole as the holes shrink. We prove that, for transitive homeomorphisms, complete indecisiveness is generic. We provide examples of applications of the results. [ABSTRACT FROM AUTHOR]

Understanding how polymers deform in response to local stresses and strains, and how strains propagate from a local disturbance, are grand challenges in wide-ranging fields from materials manufacturing to cell mechanics. These dynamics are particularly complex for blends of polymers of distinct topologies, for which several different species-dependent mechanisms may contribute. Here, we use OpTiDDM (Optical Tweezers integrating Differential Dynamic Microscopy) to elucidate deformation fields and propagation dynamics of binary blends of linear, ring and supercoiled DNA of varying sizes. We reveal robust non-monotonic dependence of strain alignment and superdiffusive transport with strain rate. However, peak alignment and superdiffusivity are surprisingly decoupled, occurring at different strain rates resonant with the distinct relaxation rates of the different topologies. Despite this universal resonance, we find that strain propagation of ring-linear blends is dictated by entanglements while supercoiled-ring blends are governed by Rouse dynamics. Our results capture critical subtleties in propagation and deformation dynamics of topological blends, shedding new light on the governing physics and offering a route towards decoupled tuning of response features. We anticipate our approach to be broadly generalizable to mapping the deformation dynamics of polymer blends, with an eye towards bottom-up bespoke materials design. In biology and in manufacturing, biomaterials are often subject to localized and spatially nonuniform strains and stresses. Yet, understanding the extent to which strains are absorbed, distributed, or propagated across different spatiotemporal scales remains a grand challenge. Here, we combine optical tweezers with differential dynamic microscopy to elucidate deformation fields and propagation dynamics of blends of linear, ring and supercoiled DNA, revealing robust non-monotonic trends and decoupling of strain alignment and superdiffusivity, and capturing critical subtleties in propagation and deformation dynamics. Our results, shedding important new physical insight to guide decoupled tuning of response features, may be leveraged to map the deformation dynamics of wide-ranging systems of biopolymers and other macromolecules, with an eye towards bottom-up bespoke biomaterials design. [Display omitted] [ABSTRACT FROM AUTHOR]

ABSTRACT In modern cities, vehicle ad hoc networks (VANETs) hold great promise for improving safety on the roads, traffic control, and communicating. The constantly changing and intricate nature of VANETs hampers adequate routing due to a variety of factors. The work examines the use of a multitiered metaheuristic algorithm that combines Bellman–Ford routing with the Fire Hawk, Gannet Optimization, and Mayfly Optimization algorithms to find optimal routing solutions for VANETs. The suggested work addresses network topological dynamics, actual time limitations, flexibility, connectivity problems, and security issues, in addition to the different quality of service (QoS) requirements in VANETs. Bellman–Ford serves as the foundational routing layer and maintains communication, whereas Fire Hawk, Gannet Optimization, and Mayfly Optimization improve and optimize routing patterns at subsequent levels. The multitier approach aims to strike a balance between the rational and probabilistic aspects of routing so as to satisfy the minimal latency needs of applications that are safety‐critical and respond quickly to the rapid changes in VANETs. The suggested work is evaluated with a traffic density ranging from 500 to 5000 with a step size of 500, and it has been observed that for the highest traffic density of 5000, the proposed work obtains a latency of 3.88 ms, data delivery rate of 0.944, a throughput of 2.94 Mbps, and energy efficiency of 97.14%. The proposed work remains robust compared to integrating state‐of‐the‐art metaheuristic algorithms such as ECRA, HOPRP, and CM. Overall, the proposed routing techniques increase routing efficiency in VANETs and make it possible to create vehicle communication networks that are more trustworthy and safe. [ABSTRACT FROM AUTHOR]

Target skyrmions (TSks) are topological spin textures where the out-of-plane component of the magnetization twists an integer number of k- π rotations. Based on a magnetic multilayer stack in the form of n × [CoFeB/MgO/Ta], engineered to host topological spin textures via dipole and DMI energies, we have stabilized 1 π , 2 π , and 3 π target skyrmions by tuning material properties and thermal-excitations close to room temperature. The nucleated textures, imaged via Kerr and Magnetic Force Microscopies, are stable at zero magnetic field and robust within a range of temperatures (tens of Kelvin) close to room temperature (RT = 292 K) and over long time scales (months). Under applied field (mT), the TSks collapse into the central skyrmion core, which resists against higher magnetic fields (≈ 2 × TSk annihilation field), as the core is topologically protected. Micromagnetic simulations support our experimental findings, showing no TSk nucleation at 0 K, but a ≈ 30 % probability at 300 K for the experimental sample parameters. Our work provides a simple method to tailor spin textures in continuous films, enabling free movement in 2D space and creating a platform transferable to technological applications where the dynamics of the topological textures can be exploited beyond geometrical confinements. [ABSTRACT FROM AUTHOR]

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system's occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework's application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell's equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework. [ABSTRACT FROM AUTHOR]

Topologically ordered phases of matter elude Landau's symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors. Recently, there have been proposals to extend the concept of time crystals to topological order. Here the authors observe a prethermal topologically ordered time crystal on a superconducting quantum processor, where discrete time-translation symmetry breaking manifests for nonlocal rather than local observables. [ABSTRACT FROM AUTHOR]

ABSTRACT The lattice loop formed by adjacent coupling of tunnel diode LC oscillators has been shown to generate topological defects due to broken mirror symmetry, which rotate in the opposite direction to the rotating pulse. Leveraging the injection locking of the rotational dynamics of these topological defects can lead to a subharmonic injection locking scheme with a large division ratio. This paper aims to enhance the design by elucidating the relationship between loop size, the number of topological defects, and the division ratio. Furthermore, we perform bifurcation analysis of the injection locking system, demonstrating that when the external signal strength reaches a certain threshold, defect pinning by the external signal occurs, leading to an extension of the lock range. The dynamics of topological defects are well suited to the so‐called progressive multiphase injection locking. In this paper, we clarify the degree of lock range extension achieved by introducing this technique. [ABSTRACT FROM AUTHOR]

We investigate the influence of vortices remote from the boundary on the near-wall flow dynamics in wall-bounded flows. A vortex ring with precisely controlled local twist is introduced into the outer layer of a channel flow at a moderate Reynolds number. We find that the minimum vorticity flux for triggering the transition to turbulence is significantly reduced from the initial disturbance of an untwisted vortex ring to that of a twisted ring. In particular, the latter disturbance can cause vortex bursting in the early transitional stage. The impact of vortex bursting on the transition process is characterised by the near-wall, wall-normal velocity with the rapid distortion theory. The wall-normal velocity grows during vortex bursting, and leads to streak formation and then the transition to turbulence. The notable wall-normal velocity is induced by the large di-vorticity generated in vortex bursting. We model the growing radial component of the di-vorticity in terms of the local twist, and demonstrate that its surge is due to the generation of highly twisted vortex lines in vortex bursting. Then, we derive that the generation of the di-vorticity in the outer layer enhances the wall-normal velocity in the inner layer via the Poisson equation with the image method and the multipole expansion. Thus, we elucidate that the vortex bursting can have an effect on the transition process. [ABSTRACT FROM AUTHOR]

Følner density is a very natural notion of density which is defined on any semigroup satisfying the Strong Følner Condition (SFC). (These include all commutative semigroups and all left cancellative left amenable semigroups.) Piecewise syndetic and thick are notions of largeness arising from topological dynamics. It has been known that if S satisfies SFC and is either left cancellative or satisfies a weak right cancellation requirement, then every thick subset has density 1. We show here that in any semigroup S satisfying SFC a subset of S is thick if and only if it has density 1. As a consequence, every piecewise syndetic set has positive density. [ABSTRACT FROM AUTHOR]

Graphene-based nanomaterials have demonstrated significant potential in environmental applications and more particularly in water treatment, especially with the extensive use of emerging pollutants (EP). These pollutants originate either from wastewater treatment plants or agricultural activities. This study focused on the antibiotic amoxycillin which is most commonly administered to humans, livestock, and aquaculture to fight a multitude of infectious diseases. In order to understand the use of graphene oxide as an adsorbent in the removal of amoxycillin and to clarify the interfacial interaction at the molecular level, a Density Function Theory study at the B3PW91/cc-pVDZ level of theory, molecular dynamics simulation, and independent gradient model were performed to determine the structural and energetic properties, and to analyse the different interactions involved in the approach. The obtained results shows that AMX exhibits a nucleophilic behaviour whereas GO acts as an electrophile, and that the adsorption process occurs spontaneously via a parallel mode indicating strong interactions. It was established that the stability of the formed complexes is mainly due to the existence of both hydrogen bonds and Van der Waals type interactions. [ABSTRACT FROM AUTHOR]

We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number k of real continuous functions $f_1,\ldots , f_k$ such that the functions $f_i\circ T^n$ , $n\in {\mathbb {Z}}$ , $1\leq i\leq k,$ span a dense linear vector space in the space of real continuous functions on X endowed with the supremum norm. We study some properties of topological systems with finite multiplicity. After giving some examples, we investigate the multiplicity of subshifts with linear growth complexity. [ABSTRACT FROM AUTHOR]

Toroidal electromagnetic pulses have been recently reported as nontransverse, space-time nonseparable topological excitations of free space. However, their propagation dynamics and topological configurations have not been comprehensively experimentally characterized. In addition, the existing generators were limited in optical and terahertz domains; however, the feasibility and significance of generating such pulses at microwave frequencies have been overlooked. Here, we report that microwave toroidal pulses can be launched by a transient finite-aperture broadband horn antenna emitter, as an electromagnetic counterpart of "air vortex cannon." Applying this effective generator, we experimentally map the toroidal pulses' topological skyrmionic textures in free space and demonstrate their resilient propagation dynamics, i.e., how that, during propagation, the pulses evolve toward stronger space-time nonseparability and closer proximity to the canonical Hellwarth–Nouchi toroidal pulses. Our work offers a practical opportunity for using topologically robust toroidal pulses as information carriers in high-capacity telecom, cell phone technology, remote sensing, and global positioning, especially where microwave frequencies are predominant. [ABSTRACT FROM AUTHOR]

Current-driven dynamics of topological spin textures, such as skyrmions and antiskyrmions, have garnered considerable attention in condensed matter physics and spintronics. As compared with skyrmions, the current-driven dynamics of their antiparticles – antiskyrmions − remain less explored due to the increased complexity of antiskyrmions. Here, we design and employ fabricated microdevices of a prototypical antiskyrmion host, (Fe0.63Ni0.3Pd0.07)3P, to allow in situ current application with Lorentz transmission electron microscopy observations. The experimental results and related micromagnetic simulations demonstrate current-driven antiskyrmion dynamics confined within stripe domains. Under nanosecond-long current pulses, antiskyrmions exhibit directional motion along the stripe regardless of the current direction, while the antiskyrmion velocity is linearly proportional to the current density. Significantly, the antiskyrmion mobility could be enhanced when the current flow is perpendicular to the stripe direction. Our findings provide novel and reliable insights on dynamical antiskyrmions and their potential implications on spintronics. Antiskyrmions, like skyrmions, are a form of topological spin texture, with a topological charge of opposite sign to the equivalent skyrmion with the same polarity. While antiskyrmions have been less explored, they offer some potential advantages for applications, and here, Guang et al demonstrate antiskyrmion motion within stripe domains. [ABSTRACT FROM AUTHOR]

Symbolic dynamics is effective for the classification of orbital types and their complexity in one-dimensional maps. In this paper, techniques of symbolic dynamics are used to analyze the chaotic dynamical properties of a two-parameter family of piecewise smooth unimodal maps with one break point. Boundary crisis and interior crisis are described via the kneading sequences, while for the period-3 window, a subshift of finite type is constructed. In addition, based on the symbolic model, the topological entropy of the map is computed, and the existence of chaotic sets of Smale horseshoe type is also proved. [ABSTRACT FROM AUTHOR]

Matter entanglement is a common chaotic structure found in both quantum and classical systems. For classical turbulence, viscous vortices are like sinews in fluid flows, storing and dissipating energy and accommodating strain and stress throughout a complex vortex network. However, to explain how the statistical properties of turbulence arise from elemental vortical structures remains challenging. Here, we use the quantum vortex tangle as a skeleton to generate an instantaneous classical turbulent field with intertwined vortex tubes. Combining the quantum skeleton and tunable vortex thickness makes the synthetic turbulence satisfy key statistical laws, offering valuable insights for elucidating energy cascade and extreme events. By manipulating the elemental structures, we customize turbulence with desired statistical features. This bottom-up approach of designing turbulence provides a testbed for analyzing and modeling turbulence. [ABSTRACT FROM AUTHOR]

Consider a minimal-free topological dynamical system $(X, \mathbb Z^d)$. It is shown that the radius of comparison of the crossed product C*-algebra $\mathrm {C}(X) \rtimes \mathbb Z^d$ is at most half the mean topological dimension of $(X, \mathbb Z^d)$. As a consequence, the C*-algebra $\mathrm {C}(X) \rtimes \mathbb Z^d$ is classified by the Elliott invariant if the mean dimension of $(X, \mathbb Z^d)$ is zero. [ABSTRACT FROM AUTHOR]

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the behaviour of the system itself. An adequate description of these systems is offered by temporal hypergraphs, that integrate these features within the same framework. However, tools for their temporal and topological characterization are still scarce. Here we develop a series of methods specifically designed to analyse the structural properties of temporal hypergraphs at multiple scales. Leveraging the hyper-core decomposition of hypergraphs, we follow the evolution of the hyper-cores through time, characterizing the hypergraph structure and its temporal dynamics at different topological scales, and quantifying the multi-scale structural stability of the system. We also define two static hypercoreness centrality measures that provide an overall description of the nodes aggregated structural behaviour. We apply the characterization methods to several data sets, establishing connections between structural properties and specific activities within the systems. Finally, we show how the proposed method can be used as a model-validation tool for synthetic temporal hypergraphs, distinguishing the higher-order structures and dynamics generated by different models from the empirical ones, and thus identifying the essential model mechanisms to reproduce the empirical hypergraph structure and evolution. Our work opens several research directions, from the understanding of dynamic processes on temporal higher-order networks to the design of new models of time-varying hypergraphs. [ABSTRACT FROM AUTHOR]

Complex systems are characterized by emergent patterns created by the nontrivial interplay between dynamical processes and the networks of interactions on which these processes unfold. Topological or dynamical descriptors alone are not enough to fully embrace this interplay in all its complexity, and many times one has to resort to dynamics-specific approaches that limit a comprehension of general principles. To address this challenge, we employ a metric--that we name Jacobian distance--which captures the spatiotemporal spreading of perturbations, enabling us to uncover the latent geometry inherent in network-driven processes. We compute the Jacobian distance for a broad set of nonlinear dynamical models on synthetic and real-world networks of high interest for applications from biological to ecological and social contexts. We show, analytically and computationally, that the process-driven latent geometry of a complex network is sensitive to both the specific features of the dynamics and the topological properties of the network. This translates into potential mismatches between the functional and the topological mesoscale organization, which we explain by means of the spectrum of the Jacobian matrix. Finally, we demonstrate that the Jacobian distance offers a clear advantage with respect to traditional methods when studying human brain networks. In particular, we show that it outperforms classical network communication models in explaining functional communities from structural data, therefore highlighting its potential in linking structure and function in the brain. [ABSTRACT FROM AUTHOR]

Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term. Previous quantum simulations of higher-order topological phases have utilized synthetic dimensions. Here the authors simulate high-order topological phases on lattices with spatial dimension up to four on a superconducting quantum computer using a mapping to a many-body Hamiltonian in a reduced dimension. [ABSTRACT FROM AUTHOR]

Given a partial action α of a groupoid G on a ring R, we study the associated partial skew groupoid ring R ⋊ α G , which carries a natural G-grading. We show that there is a one-to-one correspondence between the G-invariant ideals of R and the graded ideals of the G-graded ring R ⋊ α G . We provide sufficient conditions for primeness, and necessary and sufficient conditions for simplicity of R ⋊ α G . We show that every ideal of R ⋊ α G is graded if and only if α has the residual intersection property. Furthermore, if α is induced by a topological partial action θ, then we prove that minimality of θ is equivalent to G-simplicity of R, topological transitivity of θ is equivalent to G-primeness of R, and topological freeness of θ on every closed invariant subset of the underlying topological space is equivalent to α having the residual intersection property. As an application, we characterize condition (K) for an ultragraph in terms of topological properties of the associated partial action and in terms of algebraic properties of the associated ultragraph algebra. [ABSTRACT FROM AUTHOR]

In this paper, we present a model describing the collective motion of birds. The model introduces spontaneous changes in direction which are initialized by few agents, here referred to as leaders, whose influence acts on their nearest neighbors, in the following referred to as followers. Starting at the microscopic level, we develop a kinetic model that characterizes the behavior of large flocks with transient leadership. One significant challenge lies in managing topological interactions, as identifying nearest neighbors in extensive systems can be computationally expensive. To address this, we propose a novel stochastic particle method to simulate the mesoscopic dynamics and reduce the computational cost of identifying closer agents from quadratic to logarithmic complexity using a k-nearest neighbors search algorithm with a binary tree. Finally, we conduct various numerical experiments for different scenarios to validate the algorithm's effectiveness and investigate collective dynamics in both two and three dimensions. [ABSTRACT FROM AUTHOR]

This article is about the periodic points characterization of automorphisms of some solenoids, whose duals are subgroups of algebraic number fields. Here, we use the theory of adeles for describing a solenoid and the periodic points of its automorphisms. This is in line with the earlier characterizations which considered other classes of solenoids. [ABSTRACT FROM AUTHOR]

We investigate the ultrafast spin dynamics of the prototypical topological insulator Bi2Se3 using time-resolved Kerr rotation (polarization-change) measurements across near-infrared wavelengths. The Kerr rotation angle Δ θ K of Bi2Se3 was found to significantly depend on the photon energy around a resonance transition (∼ 1.0 eV) of bulk states, as well as the ellipticity of the pump light, in the presence of spin excitation. The observed photon-energy dependence of Δ θ K can be well simulated by assuming spin-dependent refractive-index changes in the presence of bandgap renormalization and state-filling effect upon photoexcitation. Our study delivers comprehensive insights into the opto-spintronic properties of bulk Bi2Se3 and the fundamental physical processes underlying polarization changes. These findings are expected to be crucial in developing ultrafast magneto-optical memory devices, which can perform read-and-write operations in the terahertz regime. [ABSTRACT FROM AUTHOR]

Let $ f: S^2 \to S^2 $ be a continuous map of degree $ d $, $ |d|>1 $, and let $ N_nf $ denote the number of fixed points of $ f^n $. We show that if $ f $ is a Thurston map with non-hyperbolic orbifold, then either the growth rate inequality $ \limsup \frac{1}{n} \log N_nf\geq \log |d| $ holds for $ f $, or $ f $ has exactly two critical points which are fixed and totally invariant. [ABSTRACT FROM AUTHOR]

Skyrmion bags are spin structures with arbitrary topological degrees. They are expected to be promising next-generation information carriers due to their inherent high topological degrees. Here, we report the dynamics of the topological transition process when a skyrmion bag passes through a voltage gate driven by spin current in a synthetic antiferromagnetic racetrack with voltage-controlled magnetic anisotropy. The topological degrees of skyrmion bags controlled by voltage gate and driving current density are investigated. It is found that the different topological degrees of skyrmion bags transformed in this process are related to the interaction between antiskyrmions inside skyrmion bags, and the energy of each inner antiskyrmion after topological transformation is on the order of $10^{{-}19}\;J$. Furthermore, we have realized the successive transition of a skyrmion bag from a high topological degree to a low topological degree on a racetrack with three voltage gates. This work is helpful for designing high-density racetrack memory and logical devices based on skyrmion bags. [ABSTRACT FROM AUTHOR]

Advancements in photonics technologies have significantly enhanced their capability to facilitate experiments involving quantum light, even at room temperature. Nevertheless, fully integrating photonic chips that include quantum light sources, effective manipulation and transport of light minimizing losses, and appropriate detection systems remains an ongoing challenge. Topological photonic systems have emerged as promising platforms to protect quantum light properties during propagation, beyond merely preserving light intensity. In this work, we delve into the dynamics of non-classical light traversing a Su-Schrieffer-Heeger photonic lattice with topological domain walls. Our focus centers on how topology influences the quantum properties of light as it moves across the array. By precisely adjusting the spacing between waveguides, we achieve dynamic repositioning and interaction of domain walls, facilitating effective beam-splitting operations. Our findings demonstrate high-fidelity transport of non-classical light across the lattice, replicating known results that are now safeguarded by the topology of the system. This protection is especially beneficial for quantum communication protocols with continuous variable states. Our study enhances the understanding of light dynamics in topological photonic systems and paves the way for high-fidelity, topology-protected quantum communication. [ABSTRACT FROM AUTHOR]

We investigate the influence of vortices remote from the boundary on the near-wall flow dynamics in wall-bounded flows. A vortex ring with precisely controlled local twist is introduced into the outer layer of a channel flow at a moderate Reynolds number. We find that the minimum vorticity flux for triggering the transition to turbulence is significantly reduced from the initial disturbance of an untwisted vortex ring to that of a twisted ring. In particular, the latter disturbance can cause vortex bursting in the early transitional stage. The impact of vortex bursting on the transition process is characterised by the near-wall, wall-normal velocity with the rapid distortion theory. The wall-normal velocity grows during vortex bursting, and leads to streak formation and then the transition to turbulence. The notable wall-normal velocity is induced by the large di-vorticity generated in vortex bursting. We model the growing radial component of the di-vorticity in terms of the local twist, and demonstrate that its surge is due to the generation of highly twisted vortex lines in vortex bursting. Then, we derive that the generation of the di-vorticity in the outer layer enhances the wall-normal velocity in the inner layer via the Poisson equation with the image method and the multipole expansion. Thus, we elucidate that the vortex bursting can have an effect on the transition process. [ABSTRACT FROM AUTHOR]

Eddies of various sizes are visible to the naked eye in turbulent flow. Each eddy scale corresponds to a fraction of the total energy released by the turbulence cascade. Understanding the dynamic mechanism of the energy cascade is crucial to the study of turbulent mixing. In this paper, an energy cascade multi-layer network (ECMN) based on the complex network algorithm is proposed to investigate the spatio-temporal evolution of the energy cascade, covering both the inertial and dispersive ranges. The dynamic process of energy cascade is transformed into a topological structure based on the node definition and edge determination. The topological structure allows for the exploration of eddies interaction and chaotic energy transfer across scales. The model results show the intermittent and non-uniform nature of the energy cascade. Meanwhile, the scale gap found in the model verifies the fractal property of the energy evolution. We also found that scales of the generated eddies in energy cascade process are stochastic, and a synchronous energy cascade pattern is demonstrated according to the constructed framework. Furthermore, it provides a topological way to evaluate the contribution of large and small scale eddies. In addition, a network structure coefficient κ is proposed to evaluate the energy transfer strength. It agrees very well with the fluctuation of dissipation rates. All of this shows that the network model can effectively reveal the inhomogeneous properties of the energy cascade and quantify the turbulent mixing intensity based on the intermittent scale interaction. This also provides new insights into the study of fractal scales of nonlinear complex systems and the bridging of chaotic dynamics with topological frameworks. [ABSTRACT FROM AUTHOR]

We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines, instead of the velocity. The spin Euler equation enables a feasible Lagrangian study of fluid dynamics, as the isosurface of a spin-vector component is a vortex surface and material surface in ideal flows. We establish a non-blowup criterion for the spin Euler equation, suggesting that the Laplacian of the spin vector must diverge if the solution forms a singularity at some finite time. The direct numerical simulations (DNS) of three ideal flows – the vortex knot, the vortex link and the modified Taylor–Green flow – are conducted by solving the spin Euler equation. The evolution of the Lagrangian vortex surface illustrates that the regions with large vorticity are rapidly stretched into spiral sheets. The DNS result exhibits a pronounced double-exponential growth of the maximum norm of Laplacian of the spin vector, showing no evidence of the finite-time singularity formation if the double-exponential growth holds at later times. Moreover, the present criterion with Lagrangian nature appears to be more sensitive than the Beale–Kato–Majda criterion in detecting the flows that are incapable of producing finite-time singularities. [ABSTRACT FROM AUTHOR]

The abundant topological magnetic textures in three-dimensional systems provide opportunities to investigate the fundamental spin dynamics and realize spintronic applications. The dynamics of such magnetic textures have however rarely been studied, especially for those driven by spin waves, which allow applications with ultralow energy consumption and ease of implementation even in insulating systems. Here, we report our micromagnetic simulations on the spin-wave-driven dynamics of a skyrmion tube (SkT) and chiral bobber (ChB) in a thick magnetic film. We predict tornado-like dynamics in both SkT and ChB, where the topological centers present a lateral rotation with the rotation centers forming a distorted profile in the thickness direction. While the velocity of SkT scales with the driving power, the ChB motion presents a threshold in the driving field, which is found to depend linearly on its penetration length. This distinct behavior could be useful to differentiate ChB from SkT and estimate its penetration length experimentally. The magnetic dynamics driven by spin waves can be useful for low-consumption devices, which is however still largely unexplored in three-dimensional system. Here, the authors find, using micromagnetic simulations, spin-wave-driven tornado-like dynamics of skyrmion tube and chiral bobber in thick magnetic films. [ABSTRACT FROM AUTHOR]

The mini-workshop New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem discussed recent advances in the study of dynamical properties of continuous linear operators, and in the related study of universal properties of holomorphic functions. Ideas from topological dynamics, ergodic theory, and very recent advances on the invariant subspace problem were also considered. [ABSTRACT FROM AUTHOR]

Over the last decade, substantial progress has been made in understanding the topology of quasi-two-dimensional (2-D) non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of three-dimensional (3-D) active fluid flows still poses interesting open questions. Here, we study the topology of a spherically confined active flow using 3-D direct numerical simulations of generalized Navier-Stokes (GNS) equations at the scale of typical microfluidic experiments. Consistent with earlier results for unbounded periodic domains, our simulations confirm the formation of Beltrami-like bulk flows with spontaneously broken chiral symmetry in this model. Furthermore, by leveraging fast methods to compute linking numbers, we explicitly connect this chiral symmetry breaking to the entanglement statistics of vortex lines. We observe that the mean of linking number distribution converges to the global helicity, consistent with the asymptotic result by Arnold [In Vladimir I. Arnold - Collected Works (ed. A.B. Givental, B.A. Khesin, A.N. Varchenko, V.A. Vassiliev & O.Y. Viro), pp. 357-375. Springer]. Additionally, we characterize the rate of convergence of this measure with respect to the number and length of observed vortex lines, and examine higher moments of the distribution. We find that the full distribution is well described by a k-Gamma distribution, in agreement with an entropic argument. Beyond active suspensions, the tools for the topological characterization of 3-D vector fields developed here are applicable to any solenoidal field whose curl is tangent to or cancels at the boundaries of a simply connected domain. [ABSTRACT FROM AUTHOR]

Any affine map on the (n + 1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. We explore the dynamical aspects of these maps by investigating about their distality and expansivity. [ABSTRACT FROM AUTHOR]

The second multiplicative Zagreb eccentricity index E*2 (G) of a simple connected graph G is expressed as the product of the weights ε(a)εG(b) over all edges ab of G, where ε(a) stands for the eccentricity of the vertex a in G. In this paper, some extremal problems on the E*2 index over some special graph classes including trees, unicyclic graphs and bicyclic graphs are examined, and the corresponding extremal graphs are characterized. Besides, the relationships between this vertex-eccentricity-based graph invariant and some well-known parameters of graphs and existing graph invariants such as the number of vertices, number of edges, minimum vertex degree, maximum vertex degree, eccentric connectivity index, connective eccentricity index, first multiplicative Zagreb eccentricity index and second multiplicative Zagreb index are investigated. [ABSTRACT FROM AUTHOR]

The purpose of this study is to analyze the topological structure dynamics of the complex network of stocks before and after the outbreak of the COVID-19, so as to provide a basis for preventing financial risks. We calculate Pearson correlation coefficient between enterprises according to logarithmic rate of return and trading volume ratio of enterprises' stocks, and then constructed a complex network of stock market price and volume before and after the outbreak of the COVID-19. First, through thresholding and heat map imaging of the correlation matrix, the change characteristics of the correlation between various industries in 2019 and 2020 are studied. Second, the node degree, average weighted degree, graph density, clustering coefficient, and average clustering coefficient are used to study the topological structure change of the complex network of stock correlation. Third, the principle of node betweenness centrality is used to analyze the characteristics of a complex network after removing the core nodes. The research shows that, first, under the influence of the COVID-19 pandemic, the correlation among industries has the characteristics of industrial clusters, that is, the correlation in a industry is strengthened. In addition to banking, the correlation between industries has weakened, and the correlation between the banking industry and other industries has strengthened. Second, the node difference in betweenness centrality of core nodes in 2020 is higher than that in 2019, indicating that the network stability in 2019 is higher than that in 2020. These two points indicate that under the influence of the COVID-19 epidemic, the complex network topology of China's entire stock market has changed, and companies need to undertake countermeasures in the face of the crisis to effectively prevent and control systemic risks. [ABSTRACT FROM AUTHOR]

In this paper, we reduce the logarithmic Sarnak conjecture to the $\{0,1\}$ -symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture holds for any topologically dynamical system with sublinear complexity, we provide a variant of the $1$ -Fourier uniformity conjecture, where the frequencies are restricted to any subset of $[0,1]$ with packing dimension less than one. [ABSTRACT FROM AUTHOR]

We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su-Schrieffer-Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wave-packet in the bulk of the lattice, we observe Bloch oscillations, Landau-Zener transitions, and coupling between the isospin (i.e., the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the nontrivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 ± 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of π. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure and shed light on the similarities and the differences between quantum and classical topological effects. [ABSTRACT FROM AUTHOR]

The metasurface platform with time-varying characteristics has emerged as a promising avenue for exploring exotic physics associated with Floquet materials and for designing photonic devices like linear frequency converters. However, the limited availability of materials with ultrafast responses hinders their applications in the terahertz range. Here we present a time-varying metasurface comprising an array of superconductor-metal hybrid meta-molecules. Each meta-molecule consists of two meta-atoms that are "bonded" together by double superconducting microbridges. Through experimental investigations, we demonstrate high-efficiency linear terahertz frequency conversion by rapidly breaking the bond using a coherent ultrashort terahertz pump pulse. The frequency and relative phase of the converted wave exhibit strong dependence on the pump-probe delay, indicating phase controllable wave conversion. The dynamics of the meta-molecules during the frequency conversion process are comprehensively understood using a time-varying coupled mode model. This research not only opens up new possibilities for developing innovative terahertz sources but also provides opportunities for exploring topological dynamics and Floquet physics within metasurfaces. The time-varying metasurfaces show promise for exploring exotic physics and photonic applications. The authors introduce a time-varying metasurface with superconductor-metal hybrid meta-molecules, demonstrating phase-controllable frequency conversion with high efficiency. [ABSTRACT FROM AUTHOR]

Features of the dynamics of topological defects in an electroconvective structure formed in a π/2-twisted nematic liquid crystal have been studied. The electroconvective structure (Williams domains) is a system of rolls similar to the system of convective cells in thermal convection. Hydrodynamic flows in rolls of the twisted nematic liquid crystal are helicoidal because the axial velocity component existing in addition to the tangential component has opposite directions in the neighboring rolls. This feature is responsible for the formation of stable localized extended objects—linear defects—oriented normally to Williams domains. The continuity condition for a helicoidal flow of an anisotropic liquid in twisted nematic liquid crystals prevents the decay of a linear defect into single dislocations. The length of the linear defect and the number of dislocations in it are controlled by an ac voltage applied to a liquid crystal cell. In contrast to the case of planar orientation, where linear defects decay into single dislocations with increasing applied voltage, zigzag oscillations appear in this case, but the structure of domains remains stationary. The boundaries between zig and zag regions in the core of the linear defect are dislocations with the topological charges S = +1 and –1. An "elementary" decay of a dislocation with the topological charge S = +1 (kink) into the dislocation with S = –1 (antikink) and two dislocations the topological charges S = +1 has been found for the first time in the linear defect of a certain length. The decay of the topological defect is possibly due to the appearance of the local instability of the orientational twist mode of the director n in the defect core caused by the critical growth of hydrodynamic fluctuations with increasing applied voltage. It has been shown that the detected decay of the topological soliton is qualitatively well described by the perturbed sine-Gordon eq-uation. [ABSTRACT FROM AUTHOR]

Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diff+ω(S¹) of orientation-preserving real-analytic circle diffeomorphisms, which include all subgroups of Diff+ω(S¹) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by Dippolito [Ann. of Math. (2) 107 (1978), 403-453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work (by a slightly different list of authors). [ABSTRACT FROM AUTHOR]

The recent observations of exotic quantum phenomena in AV3Sb5 (A = K, Rb, Cs) kagome superconductors have attracted significant attention in materials physics. Here, we propose an innovative two-frequencies laser model for ultrafast control of transient structural distortions. Using first-principles density functional theory in conjunction with the perturbative regime of nonlinear phononics, we investigate the nonharmonic potential energy, the crystal lattice dynamics and the topological properties of CsV3Sb5. We find that driving two infrared-active phonons of different frequencies promotes the desired Raman phonon vibrations, in which the displacement of Sb atoms is closely related to superconductivity. We demonstrate that the dimensional crossover and the topological nontrivial to trivial state transition of superconductor CsV3Sb5 can be triggered by ultrafast optical control. This work can be applied to other layered quantum materials and provide guidance for experiments related to photoinduced topology and superconductivity. [ABSTRACT FROM AUTHOR]