Homotopy Research Articles

LANDSLIDE DETECTION AND MONITORING TECHNIQUES: A BIBLIOMETRIC ANALYSIS AND FUTURE DIRECTIONS

The devastating consequences of landslides demand rigorous assessment and effective management strategies to minimise risks. In this context, landslide detection and monitoring are crucial in identifying potential hazards and implementing proactive mitigation measures. This study uses the Scopus database to present a bibliometric analysis of 1,112 peer-reviewed journal articles on landslide detection and monitoring techniques published between 2002 and 2022. The analysis reveals a remarkable surge in publications, from 4 in 2002 to 180 in 2022, with the last five years (2018-2022) accounting for over 60% of the total publications. Over 3,259 unique researchers from 75 countries contributed to this field, with a significant portion originating from Asia, Europe, and North America. China and Italy emerged as the leading countries, producing over half of the articles. Nicola Casagli, from Italy, authored the most publications and garnered the highest number of citations. Remote Sensing emerged as the most preferred journal for authors, while Landslides garnered the highest total citations, and Geomorphology has the most normalised citations per article. The Chinese Academy of Sciences, China University of Geosciences, and the University of Florence in Italy were the most productive research institutions. The Natural Science Foundation of China (NSFC) emerged as the top funding agency. “Landslide”, “landslide monitoring”, and “early warning systems” were the top three most frequently used keywords. Keyword analysis identified landslide detection and monitoring advancements in remote sensing, analytical methods, and in-situ techniques. Co-occurrence analysis of trending research terms highlighted three distinct thematic clusters: remotely sensed data with machine learning and image analysis for landslide detection, field instrumentation for continuous deformation monitoring, and development of early warning systems for landslide hazard assessment and mitigation.

Origami multifunctional metagrating for a mechanically controlled electromagnetic wavefront

Metasurface or artificial electromagnetic (EM) structures offer viable options for manipulating EM waves with compact periodic structures. Tunable metasurfaces are ideal for many engineering and scientific applications because they can manipulate EM wavefronts. However, it is challenging to implement tunable metasurfaces that can achieve multiple functions for integration. In addition, integrated multifunctional metasurfaces are often structurally complicated and bulky. This paper proposes a simple spatial modulation mechanism that uses Miura origami reconfigurable one-dimensional metagrating to achieve multiple control of EM wavefront. Theoretical predictions, numerical simulations, and experiments confirm and validate the basic concepts. In particular, the continuous geometric deformation of the Miura-ori lattice is a promising method for compensating the dispersion of characters in gradient metasurfaces. Considering origami structures’ outstanding mechanical properties and strong deformation abilities, this discovery opens up another avenue for lightweight and deployable meta-devices.

Image‐based backbone reconstruction for non‐slender soft robots

AbstractOne advantage of soft robots to conventional robots is their continuous deformation, which makes them highly adaptable to their surroundings. To describe the kinematics of soft robots it is not sufficient to only know the position of the end‐effector. Instead, the steady state of a soft robot can be described by its backbone curvature. An image‐based backbone reconstruction method is used and adopted for a non‐slender soft robot to reconstruct the backbone curve using polynomials to describe an arc length‐dependent curvature. A constant curvature and cubic curvature polynomial have been tested to reconstruct the backbone curve. In the case of a pressurized soft robot without externally applied loads, the constant curvature polynomial can be used to reconstruct the backbone of the soft robot using an image‐based approach, yielding good agreement with the captured images. However, some care has to be put into the consideration of the soft robot geometry in this method, to guide the optimization procedure. From our findings, we can conclude that it is not necessary to apply markers to the soft robot to reconstruct the backbone, nor is it necessary to have a detailed geometric model of the soft robot to be used in a differential rendering process. An image‐based iterative‐closest‐point optimization method, with some carefully placed estimate points, to integrate the volumetric structure of the soft robot can yield good results for the reconstructed backbones.

Fast and Compact Partial Differential Equation (PDE)-Based Dynamic Reconstruction of Extended Position-Based Dynamics (XPBD) Deformation Simulation

Dynamic simulation is widely applied in the real-time and realistic physical simulation field. How to achieve natural dynamic simulation results in real-time with small data sizes is an important and long-standing topic. In this paper, we propose a dynamic reconstruction and interpolation method grounded in physical principles for simulating dynamic deformations. This method replaces the deformation forces of the widely used eXtended Position-Based Dynamics (XPBD), which are traditionally derived from the gradient of the energy potential defined by the constraint function, with the elastic beam bending forces to more accurately represent the underlying deformation physics. By doing so, it establishes a mathematical model based on dynamic partial differential equations (PDE) for reconstruction, which are the differential equations involving both the parametric variable u and the time variable t. This model also considers the inertia forces caused by acceleration. The analytical solution to this model is then integrated with the XPBD framework, built upon Newton’s equations of motion. This integration reduces the number of design variables and data sizes, enhances simulation efficiency, achieves good reconstruction accuracy, and makes deformation simulation more capable. The experiment carried out in this paper demonstrates that deformed shapes at about half of the keyframes simulated by XPBD can be reconstructed by the proposed PDE-based dynamic reconstruction algorithm quickly and accurately with a compact and analytical representation, which outperforms static B-spline-based representation and interpolation, greatly shortens the XPBD simulation time, and represents deformed shapes with much smaller data sizes while maintaining good accuracy. Furthermore, the proposed PDE-based dynamic reconstruction algorithm can generate continuous deformation shapes, which cannot be generated by XPBD, to raise the capacity of deformation simulation.

Deformation Heat in Tension of Steel Elements

The purpose of the work is an approximate computational and experimental assessment of the specific energy intensity and heat generation at various stages of the material’s operation when the sample is stretched. The paper discusses an approximate method for estimating the specific energy intensity and heat generation at four stages of tensile deformation of a steel sample. Finite element modeling of the work of the manufactured sample under elastic-plastic tension was performed in the ANSYS multifunctional software package. The load in the digital model of the sample was applied according to the full-scale test program. The experiment used flat samples in accordance with GOST 1497, a WAW-1000 testing machine with a 100T microcomputer, and a testo 875i thermal imager with a temperature sensitivity of 0.05 °C at 30 °C. We compared the obtained values on graphs of full-scale tests and a digital model of the samples, identifying critical points and deviation values. Phased loading revealed that the development of destruction occurs on the descending branches and is accompanied by the gradual development of local instability of plastic deformation in the form of a “neck”. It is shown that the heating temperature of the tensile metal can be calculated using the formulas proposed in the paper or by calculation using the ANSYS software package. The test results showed that the surface temperatures of the samples at each stage differ significantly. Four main areas were identified on the graph of changes in the sample surface temperature at a point. An analysis of the existing database of measuring instruments and the ability to obtain and process data was carried out. Experimental values of surface temperatures during continuous quasi-static deformation exceed their calculated values (up to 5 times). The kinetics of changes in the temperature field of the sample surface was carried out using thermographic instruments.

Microstructure and strength of cold-drawn large strain Fe35Ni35Cr20Mn10 high-entropy alloy

The Fe35Ni35Cr20Mn10 high-entropy alloy wires can achieve a large strain of 8.73 and a section reduction ratio of 99.98 %,and possess a high strength of 1868 MPa via traditional wire drawing. The microstructure evolution and mechanical properties of cold-drawn Fe35Ni35Cr20Mn10 high-entropy alloy are characterized by microstructure observation and tensile test. The results showed that The Fe35Ni35Cr20Mn10 HEA has excellent plastic forming capacity and excellent phase stability during plastic deformation. The Fe35Ni35Cr20Mn10 HEA has excellent continuous drawing ability, the main deformation mechanism is the plane slip and cross slip of the dislocation and the dynamic recovery of the sublamellar layer make the lamellar structure maintain a dynamic equilibrium state, and the lamellar thickness is basically unchanged to support the continuous plastic deformation under high strain conditions. The dynamic balance of coarsening and refining of lamellar structure in the process of plastic deformation is mainly due to the merging of HEA lamellar caused by the movement of trigeminal node induced by strain. Texture evolution showed that the <111> and <100> fiber textures were the stable texture component and the texture component content remained unchanged even under further increased strain. The Fe35Ni35Cr20Mn10 high-entropy alloy wire with high strain of 8.73 possesses excellent strength, and its tensile strength is 1868 MPa at room temperature, which has the largest strain. The dislocations proliferation, lamellar structure refinement and texture strengthening lead to high strength of the Fe35Ni35Cr20Mn10 high-entropy alloy wire.

Dynamic bifurcation of nonautonomous evolution equations under Landesman–Lazer condition with cohomology methods

In this article we study the dynamic bifurcation of nonautonomous evolution equations by using cohomology methods. First, we construct a homotopy equivalence relation between the nonautonomous system and a product flow. Then, we slightly extend some continuation theorems on bifurcations for autonomous equations, and prove some new cohomology consequences on the reduced singular groups. Based on this homotopy equivalence relation and these conclusions, we establish some typical results on the dynamic bifurcation from infinity of the abstract nonautonomous evolution equation. Finally, we consider the parabolic equation ut−Δu=λu+f(x,u)+g(x,t) associated with the Dirichlet boundary condition, where f(x,u) satisfies the appropriate Landesman–Lazer type condition. Some new results on the dynamical behaviors of this equation near resonance of the equation are derived.

Stability of L2-Invariants on Stratified Spaces

Abstract Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_{\Gamma }$ be a Galois $\Gamma $-covering. Under additional assumptions on $\overline{M}$, satisfied for example by Witt pseudo-manifolds, we show that the $L^{2}$-Betti numbers and the Novikov–Shubin invariants are well defined. We then establish their invariance under a smoothly stratified codimension-preserving homotopy equivalence, thus extending results of Dodziuk, Gromov, and Shubin to these pseudo-manifolds.

The Borsuk–Ulam property for homotopy classes on bundles, parametrized braids groups and applications for surfaces bundles

Let M and N be fiber bundles over the same base B, where M is endowed with a free involution τ over B. A homotopy class δ∈[M,N]B (over B) is said to have the Borsuk–Ulam property with respect to τ if for every fiber-preserving map f:M→N over B which represents δ there exists a point x∈M such that f(τ(x))=f(x). In the cases that B is a K(π,1)-space and the fibers of the projections M→B and N→B are K(π,1) closed surfaces SM and SN, respectively, we show that the problem of decide if a homotopy class of a fiber-preserving map f:M→N over B has the Borsuk-Ulam property is equivalent of an algebraic problem involving the fundamental groups of M, the orbit space of M by τ and a type of generalized braid groups of N that we call parametrized braid groups. As an application, we determine the homotopy classes of fiber-preserving self maps over S1 that satisfy the Borsuk-Ulam property, with respect to all involutions τ over S1, for the torus bundles over S1 with M=N=MA and A=[1n01].

Nielsen fixed point theory for split n-valued maps on the Klein bottle

In this work we begin the study of n-valued maps on the Klein bottle, denoted by K, where we focus on the split ones. We provide an explicit description of Pn(K) (the n-th pure braid group of K) as an iterated semi-direct product of the form Fn⋊θn−1(⋯⋊(F2⋊θ1π1(K))), where the Fi′s are free groups on i letters. Given a split n-valued map Φ={f1,…,fn} its pointed homotopy class is determined by a pair of braids in Pn(K). We also provide a formula for N(Φ), the Nielsen number of Φ, which is completely determined by two braids, which in turn also determine the homotopy classes of the functions fi′s. If Φ={f1,f2} is a 2-valued map with N(Φ)=0, we show that there exists at least one 2-valued map Φ′={f1′,f2′}, such that Φ′ is fixed point free and for i=1,2 it holds that [fi]=[fi′], where [] denotes a pointed homotopy class of maps. Finally, we display an infinite family of pointed homotopy classes in [K,F2(K)], such that N(ϕ)=0, for any ϕ in the family. Furthermore, the map from [K,F2(K)] to [K,K×K], induced by the inclusion F2(K)→K×K, takes this family to one single element in [K,K×K]. We do not know if these 2-valued maps of the family can be deformed to fixed point free maps.

A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction–diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration.Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.

Realizing regular representations of finite groups

Given a regular representation of a finite group G and a positive integer number n, we construct a (finite) topological space X such that its group of homotopy classes of self-homotopy equivalences E(X) and its group of homeomorphisms Aut(X) are isomorphic to G, and the action of G on the n-th homology group Hn(X) is the regular representation. We also discuss other representations.

On minimal fixed points set of fiber preserving maps of S1-bundles over S1

In this work, we describe the minimal fixed points set of fiberwise maps of S1-bundles over S1, up to fiberwise homotopies. There are two fibrations under these conditions, one orientable, the torus, and the other non-orientable, the Klein bottle. For fiberwise maps the minimal fixed points set can be empty, otherwise it is described as the finite union of disjoint circles. We present models for which the fixed points set are minimal, where minimal means that no proper subset can be realized as the fixed points set in the same fiberwise homotopy class.

Homotopy classification of knotted defects in ordered media

We give a homotopy classification of the global defects in ordered media and explain it via the example of biaxial nematic liquid crystals, that is, systems where the order parameter space is the quotient of the three-sphere S 3 by the quaternion group Q . As our mathematical model, we consider continuous maps from complements of spatial graphs to the space S 3 / Q modulo a certain equivalence relation and find that the equivalence classes are enumerated by the six subgroups of Q . Through monodromy around meridional loops, the edges of our spatial graphs are marked by conjugacy classes of Q ; once we pass to planar diagrams, these labels can be refined to elements of Q associated with each arc. The same classification scheme applies not only in the case of Q but also to arbitrary groups.

Fuzzy Relative Homotopy and Fuzzy Weak Equivalence with Some Results

In this paper, first introduce my concept fuzzy homotopic and fuzzy homotopic relative and weproved that the relation fuzzy homotopic relative is a fuzzy equivalence relation. Secondly , weintroduce the concepts fuzzy homotopy equivalence, fuzzy fundamental group and fuzzy weak homotopy equivalence. We have proven some important theorems.

Proximity Relative Homotopy and Proximity Weak Equivalence

In this paper, we introduce and study proximity path covering property (PPCP), we define the concept of naw proximity relative homotopy (PRH), and Mixed proximity relative homotopy (MPRH), and study proximity weak equivalence (PWE), some theories and properties

Fault diagnosis of the harmonic reducer based on dual-path convolutional network with multi-channel hybrid attention mechanism

Abstract Harmonic reducers are prone to tooth breakage and other failures due to continuous deformation of the flexure wheel during operation. To identify the fault types of harmonic reducers under different working conditions, a fault diagnosis method (MADCNN-BiGRU) based on Dual-path Convolution Neural Network (DCNN) with Multi-channel Hybrid Attention Mechanism (MCHAM) and Bidirectional Gated Recurrent Unit (BiGRU) was proposed. Firstly, a novel MCHAM focuses on the critical information part of the vibration signal and can effectively suppress the noise and redundant information. Secondly, a new soft threshold function is constructed to regulate the attention weights dynamically. Thirdly, BiGRU obtains feature information for different time series locations to identify the faults correctly. Fourthly, the harmonic reducer test rig is established to collect vibration signals of harmonic reducers with different faults under different working conditions. The comparative experimental results show that MADCNN-BiGRU has excellent capacity for generalization and robustness, and can effectively diagnose under various complicated situations.

Interrogating an along-strike variation in the evolution and rheology of a large continental strike-slip fault zone

Along-strike variations in lithology, temperature, fluid activity, etc. can induce rheological changes in strike-slip faults that may be recorded by different fault rocks and fabrics. This article interrogates localized formation of granite-derived mylonite in a large strike-slip fault zone in which ultramylonite is the principle granite-derived fault rock to better understand this rock record of faulting. Microtextures show that rate-limiting deformation mechanisms in mylonite were dislocation creep in quartz and diffusion creep in very-fine-grained feldspar aggregates. Microtextures also show that mylonite formation is fully compatible with continuous viscous deformation whereas coeval ultramylonite along strike formed after whole-rock cataclasis at the brittle-viscous transition. Differential stresses determined from quartz aggregates in ultramylonites are 40–150% greater than stresses in mylonites. Hence, mylonites represent a local weak sector within this otherwise relatively strong fault zone. Mylonite formation is correlated with syndeformational chemical alteration as well as quartz microstructures and mineral assemblages indicating elevated deformation temperatures. Not all mylonite samples record significant chemical alteration. Therefore, mylonite formation likely records locally elevated temperatures. These results illustrate how a local shift in deformation conditions can affect the evolution and rheology of a large strike-slip fault zone, and how fault rocks record these processes.

Dynamic Characteristics of the Long Runout Rock‐ice Avalanche at High Altitude—A Case from the Zelongnong Basin, Eastern Himalayan Syntaxis, China

AbstractRock‐ice avalanches have frequently occurred in the Eastern Himalayan Syntaxis region due to climate change and active tectonic movements. These events commonly trigger catastrophic geohazard chains, including debris flows, river blockages, and floods. This study focuses on the Zelongnong Basin, analyzing the geomorphic and dynamic characteristics of high‐altitude disasters. The basin exhibits typical vertical zonation, with disaster sources initiating at elevations exceeding 4000 m and runout distances reaching up to 10 km. The disaster chain movement involves complex dynamic effects, including impact disintegration, soil‐rock mixture arching, dynamic erosion, and debris deposition, enhancing understanding of the flow behavior and dynamic characteristics of rock‐ice avalanches. The presence of ice significantly increases mobility due to lubrication and frictional melting. In the disaster event of September 10, 2020, the maximum flow velocity and thickness reached 40 m/s and 43 m, respectively. Furthermore, continuous deformation of the Zelongnong glacier moraine was observed, with maximum cumulative deformations of 44.68 m in the distance direction and 25.96 m in the azimuth direction from March 25, 2022, to August 25, 2022. In the future, the risk of rock‐ice avalanches in the Eastern Himalayan Syntaxis region will remain extremely high, necessitating a focus on early warning and risk mitigation strategies for such basin disasters.

Flexible Tactile Sensors with Gradient Conformal Dome Structures.

The trade-off between high sensitivity and wide detection range remains a challenge for flexible capacitive pressure sensors. Gradient structure can provide continuous deformation and lead to a wide sensing range. However, it simultaneously augments the distance between two electrodes, which diminishes the variation in the relative distance and results in a decreased sensitivity. Herein, a conformal design is introduced into the gradient structure to construct a flexible capacitive pressure sensor. The gradient conformal dome structure is fabricated by a simple reverse dome adsorption process. Taking advantage of the progressive deformation behavior of the gradient dielectric, and the significant improvement of relative distance variation between two electrodes from the conformal design, the sensor achieves a sensitivity of 0.214 kPa-1 in an ultrabroad linear range up to 200 kPa. It maintains high-pressure resolution under the preload of 10 and 100 kPa. Benefiting from the rapid response and excellent repeatability, the sensor can be used for physiological monitor and human motion detection, including arterial pulse, joint bending, and motion state. The gradient conformal design strategy may pave a promising avenue to develop pressure sensors with high sensitivity and wide linear range.