Edge Stability Research Articles

Finite presentability of twisted Brin–Thompson groups

Given a group G acting faithfully on a set S, we characterize precisely when the twisted Brin–Thompson group SVG is finitely presented. The answer is that SVG is finitely presented if and only if we have the following: G is finitely presented, the action of G on S has finitely many orbits of two-element subsets of S, and the stabilizer in G of any element of S is finitely generated. Since twisted Brin–Thompson groups are simple, a consequence is that any subgroup of a group admitting an action as above satisfies the Boone–Higman conjecture. In the course of proving this, we also establish a sufficient condition for a group acting cocompactly on a simply connected complex to be finitely presented, even if certain edge stabilizers are not finitely generated, which may be of independent interest.

Advanced network design for 6G: Leveraging graph theory and slicing for edge stability

The advent of 6 G networks will emphasize AR/VR-based tactile internet and touch-enabled services, requiring solutions to address latency and reliability issues in tactile data perception, particularly in edge networking. This article highlights the critical role of graph theory in improving network design for both symmetric and randomly deployed networks, and it emphasizes the importance of network slicing in managing densely connected edge networks. These networks typically consist of numerous edge devices that enable data transfer to higher layers, enhancing connectivity and ensuring network stability within a confined range. The paper compares the accuracy of conventional networks before and after implementing network slicing, with the goal of increasing reliability by dividing the edge network into segments, thereby reducing computation time. The study proposes a method for optimal node segregation and path determination in edge networks using both uniform and random network slicing. Network performance is assessed using metrics such as computation time and node failure rate. The paper concludes that network slicing is the most effective design approach for touch technology interfaces within 6 G and IoT frameworks.

Enhanced Durability of Wood Cutting Tools through Thermal Cycling.

This study investigates the impact of multi-step austenitization heat treatment on the in-service life of modified AISI A8 cold work tool steel knives used in wood cutting. The knives were subjected to two treatment methods: single quenching and double tempering (SQDT) and double quenching and double tempering (DQDT). Both treatments were followed by physical vapor deposition (PVD) coating to enhance surface properties. The DQDT treatment resulted in a finer microstructure and more uniform carbide distribution. Field tests on 24 knives over 124 h demonstrated up to 130% improvement in wear resistance for DQDT knives, along with superior edge stability and better PVD coating preservation. DQDT knives exhibited ductile fractures characterized by dimples, contrasting with the brittle fracture and cleavage facets in SQDT knives. Residual stress measurements showed higher compressive stresses in DQDT knives (-280 MPa) compared to SQDT knives (-30 MPa), which increased further after field testing. The enhanced performance of DQDT knives is attributed to their refined microstructure, improved carbide distribution, and higher compressive residual stresses, offering significant potential for improving wood cutting tool efficiency and durability.

Stability impact on wind turbine blades trailing edge from bonding zone modelling methods

Abstract The trailing edge of wind turbine blade will undergo a large deformation under the action of load, resulting in a higher risk of damage and failure. The finite element analysis modeling method directly affects the simulation result, furthermore impacts the result of blade structure design. Therefore, it is necessary to find out a modeling method, which is capable to reflect the stability of bonding regions more accurately. This paper aims to discuss the influences of different finite element modeling methods on the buckling stability of blade trailing edge. The influences of shell element, tetrahedron element and hexahedron element on the blade stiffness are considered. The bonding region were simulated separately by combining shell element with bonding web, shell element with tetrahedron element and shell element with hexahedron. The influences of different bonding region modeling methods on the trailing edge buckling factor were analyzed by using the eigenvalue buckling analysis method of finite element. The simulation results provided data support for the future validation of the blade trailing edge bonding area modeling method. The results show that, the tetrahedral mesh provides a higher stiffness, followed by the hexahedral mesh, and the adhesive web form has the smallest stiffness. In order to simulate the more realistic stiffness of the adhesive area at the trailing edge of the blade, adhesive web plates can be built in the flange area of the blade root and the core material area of the trial adhesive mold; The direct bonding area can be simulated employing the hexahedron mesh; The tetrahedral mesh has high stiffness and is not suitable for modeling the adhesive area at the trailing edge. Blade simulation modeling can flexibly use different adhesive forms according to actual situations, ensuring the reliability of the simulation model.

The isomorphism problem for small-rose generalized Baumslag-Solitar groups

A generalized Baumslag-Solitar group is a finitely generated group that acts on a tree with infinite-cyclic vertex and edge stabilizers. In this paper, we show that the isomorphism problem is solvable for small-rose non-ascending generalized Baumslag-Solitar groups.

Thermodynamics and electronic structure of edges in monolayer MoSi2N4

MoSi2N4 is a two-dimensional ternary nitride semiconductor that has attracted attention for its excellent mechanical and thermal properties. Theoretical studies predict that zigzag edges of this material can host magnetic edge states and Dirac fermions, but the stability of such edges has not been examined. Here, we present a density functional theory study of the electronic and thermodynamic properties of MoSi2N4 edges. We develop a (partial) ternary phase diagram that identifies a region of chemical potentials within which MoSi2N4 is stable over competing elemental or binary phases. Based on this phase diagram, we determine the thermodynamic stability of several armchair and zigzag edges and elucidate their electronic structures. Bare zigzag edges, predicted to host exotic electronic states, are found to be substantially higher in energy than armchair edges and, thus, unlikely to occur in practice. However, with hydrogen passivation, these zigzag edges can be stabilized relative to their armchair counterparts while retaining metallicity and magnetic order. Our analysis provides a solid thermodynamic basis for further exploration of MoSi2N4 in nanoscale electronics and spintronics.

Effect of symmetry-breaking on the MHD edge stability limit of tokamak plasmas

We demonstrate for the first time that symmetry-breaking in tokamak plasmas reduces the window of stable edge operational space, leading to a lower achievable edge pressure gradient. Predictive simulations with the linear magnetohydrodynamic stability code CASTOR3D show a reduction of the critical pressure gradient by up to 30%, in agreement with experimental observations. The analysis has been extended to experimental plasmas considering, for the first time, ion diamagnetic drift effects in realistic non-axisymmetric (3D) tokamak geometry. The 3D geometry in plasmas with edge localised modes (ELMs) increases the growth rate of edge instabilities compared to the axisymmetric case. Further reducing the edge pressure gradient eliminates the instabilities corresponding to an experiment with suppressed ELMs, reproducing the empirically observed threshold for ELM suppression. Our findings highlight the importance of predictions of the ELM occurrence in full 3D geometry for future tokamak devices with intentionally and unintentionally broken axisymmetry.

Heuristic predictions of RMP configurations for ELM suppression in ITER burning plasmas and their impact on divertor performance

A subspace of resonant magnetic perturbation (RMP) configurations for edge localized mode (ELM) suppression is predicted for H-mode burning plasmas at 15 MA current and 5.3 T magnetic field in ITER. Perturbations to the core plasma can be reduced by a factor of 2 for equivalent edge stability proxies, while the perturbed plasma boundary geometry remains mostly resilient. The striated domain of perturbed field lines connecting from the main plasma (normalized poloidal flux <1 ) to the divertor targets is found to be significantly larger than the expected heat load width in the absence of RMPs. This facilitates heat load spreading with peak values at an acceptable level below 10MWm−2 on the outer target already at moderate gas fueling and low Ne seeding for additional radiative dissipation of the 100MW of power into the scrape-off layer (SOL). On the inner target, however, re-attachment is predicted away from the equilibrium strike point due to increased upstream heat flux, higher downstream temperature and less efficient impurity radiation.

Principal Component Analysis–Based Feature Recognition Technology for Marine Plankton Images in IoT Systems

Abstract To improve the accuracy of traditional plankton image feature recognition techniques, a principal component analysis (PCA)–based method for plankton image feature recognition in Internet of Things (IoT) systems was designed and proposed. According to the characteristics of a microscopic image of marine living plankton with much noise, a noise suppression method based on wavelet is established to meet the needs of edge information retention and stability in image processing. At the same time, the adaptive threshold gray segmentation, mathematical morphology operation, and canny edge detection operator are combined to complete the marine plankton image segmentation. Based on the global feature and texture information of contours, the feature set is composed. At the same time, PCA is used to reduce the dimensionality of the feature space and complete the feature recognition of plankton images in the IoT system. The test results show that this method has higher accuracy, shorter recognition time, lower cost, and certain applicability.

Separation and relative quasiconvexity criteria for relatively geometric actions

Bowditch characterized relative hyperbolicity in terms of group actions on fine hyperbolic graphs with finitely many edge orbits and finite edge stabilizers. In this paper, we define generalized fine actions on hyperbolic graphs, in which the peripheral subgroups are allowed to stabilize finite subgraphs rather than stabilizing a point. Generalized fine actions are useful for studying groups that act relatively geometrically on a CAT(0) cube complex, which were recently defined by the first two authors. Specifically, we show that any group acting relatively geometrically on a CAT(0) cube complex admits a generalized fine action on the one-skeleton of the cube complex. For generalized fine actions, we prove a criterion for relative quasiconvexity of subgroups that cocompactly stabilize quasiconvex subgraphs, generalizing a result of Martínez-Pedroza and Wise in the setting of fine hyperbolic graphs. As an application, we obtain a characterization of boundary separation in generalized fine graphs and use it to prove that Bowditch boundary points in relatively geometric actions are always separated by a hyperplane stabilizer.

Stable Heuristic Miner 2: Evaluating the Statistical Stability in Event Logs to Discover Business Processes

Automated process discovery as one of the paradigms of process mining has attracted both industries and academic researchers. These methods offer visibility and comprehension out of complex and unstructured event logs. Over the past decade, the classic heuristic miner and applied heuristic-based process discovery algorithms showed promising results in revealing the hidden process patterns in information systems. One of the challenges related to such algorithms is the arbitrary selection of recorded behaviors in an event log. The offered filtering thresholds are manually adjustable, which could lead to the extraction of a non-optimal process model. This is also visible in commercial process mining solutions. Recently, the first version of the stable heuristic miner algorithm targeted this issue by evaluating the statistical stability of an event log. However, the previous version was limited to evaluating only activities’ behaviors. In this article, we’ll be evaluating the statistical stability of both activities and edges of a graph, which could be discovered from an event log. As a contribution, the stable heuristic miner 2 is introduced. Consequently, the definition of the descriptive reference process model has improved. The novel algorithm is evaluated by using two real-world event logs. These event logs are the familiar Sepsis data set and the urology department patients’ pathways event log, which is recorded by monitoring the interpreted location data of patients on hospital premises and is shared with the scientific community in this article.

Impact of triangularity on edge peeling–ballooning modes in H-mode plasmas

Triangularity is an important shaping parameter in tokamak plasmas that affects the edge plasma state. In this work, we utilize the BOUT++ code to study the effect of positive and negative triangularity on the peeling–ballooning modes with H-mode profiles. The model equilibria with a JET-like geometry are self-consistently generated by the CORSICA equilibrium code, with a fixed pressure profile when varying triangularity. The linear simulations reveal that increasing positive triangularity results in the increase in magnetic shear and decrease in radial electric field (Er) curvature, leading to the stabilization of the peeling–ballooning modes. On the contrary, the increase in negative triangularity results in a destabilizing effect due to the decrease in magnetic shear and increase in Er curvature. It is found that the modification of Er shear due to triangularity variation cannot impact edge stability significantly. The nonlinear simulations further demonstrate that more positive triangularity results in reduced nonlinear energy loss fraction or pedestal collapse, while more negative triangularity results in increased nonlinear energy loss fraction or pedestal collapse. These results provide qualitative insights into experimental observations of the high pedestal pressure profiles with positive triangularity configuration and restricted low pedestal pressure profiles with negative triangularity configuration.

Profinite genus of free products with finite amalgamation

A finitely generated residually finite group G is an OEˆ-group if any action of its profinite completion Gˆ on a profinite tree with finite edge stabilizers admits a global fixed point. In this paper, we study the profinite genus of free products G1⁎HG2 of OEˆ-groups G1,G2 with finite amalgamation H. Given such G1,G2,H we give precise formulas for the number of isomorphism classes of G1⁎HG2 and of its profinite completion. We compute the genus of G1⁎HG2 and list various situations when the formula for the genus simplifies.

Tight bounds on the chromatic edge stability index of graphs

The chromatic edge stability index esχ′(G) of a graph G is the minimum number of edges whose removal results in a graph with smaller chromatic index. We give best-possible upper bounds on esχ′(G) in terms of the number of vertices of degree Δ(G) (if G is Class 2), and the numbers of vertices of degree Δ(G) and Δ(G)−1 (if G is Class 1). If G is bipartite we give an exact expression for esχ′(G) involving the maximum size of a matching in the subgraph induced by the vertices of degree Δ(G). Finally, we consider whether a minimum mitigating set, that is a set of size esχ′(G) whose removal reduces the chromatic index, has the property that every edge meets a vertex of degree at least Δ(G)−1; we prove that this is true for some minimum mitigating set of G, but not necessarily for every minimum mitigating set of G.

In situ surface evolution dynamics of external-electric-field-triggered structural oscillation on Au(111)

Surface nanostructures serve as an essential role in determining intrinsic physical features and device performance in solid materials. Here, this work systematically investigates the surface dynamical evolution at the nanoscale on Au(111) induced by a “tip-to-surface” external electric field through a scanning tunneling microscope (STM). The Au(111) steps exhibit a “compact to fractal” reconstruction under a relatively high electric field, in which the transition is strengthened with increasing the applied electric field. Inversely, a “fractal to compact” morphological transition enables to be self-triggered at Au(111) surface steps upon a normal STM imaging electric field (very low). These two reversible structural changes are attributed to the diffusion-limited aggregation mechanism where the diffusion barriers were quantified as 0.64–0.75 eV varied with the regularity in step edges. In addition, we further simulate a “terrace-edge-kink” model to trace the effect of atomic coordination on structural transition, determining the surface step edge stability. This study presents insight into morphological and structural transformation at surface steps induced by variant external electric fields, establishing a deep understanding in the nature of surface evolution dynamics.

Analytic study of exposure contrast over feature edge in electron-beam lithography

In electron-beam (e-beam) lithography, the location of a feature edge may vary with experiment due to the stochastic nature of the e-beam exposure and resist-development processes. From the viewpoint of consistent reproducibility of a circuit pattern, it is essential to enhance the stability of a feature edge in the e-beam lithographic process. A fundamental metric affecting the stability is the exposure contrast over the feature edge, and therefore, it is important to understand the dependency of exposure contrast on significant parameters. However, the computer simulation for the dependency analysis is time-consuming and needs to be repeated. In this study, a new method has been developed by deriving closed-form mathematical expressions of exposure contrast for the cases of a single feature and a uniform pattern of multiple features. The mathematical expressions enable the fast analysis of exposure contrast without simulation, and therefore, can serve as a useful tool in e-beam lithography.

Investigating and promoting health behaviors reactivity among Hong Kong older adults in the post-COVID-19 Era: An exploratory network analysis.

Physical distance has increased the risk of developing a variety of health problems, especially among older people. During the COVID-19 lockdown period, physical activity decreased, screen time increased, food consumption increased, as well as exposure to unhealthy behaviour, leading to poorer sleep quality and more negative emotions, which ultimately led to poorer physical health, mental health, and subjective vitality among older adults. Although there were numerous research studies on changes in health behaviours during COVID-19, only a few were targeted at older adults, and none were conducted in Asian countries. The current study is aiming to identify the changes in health behaviours, as well as their associations with older adults' mental health as a result of the COVID-19 pandemic among Hong Kong older adults, using exploratory network analysis. In this study, a random tele-survey was conducted among older adults. A total of 664 participants have been involved in the telephone survey, with 213 males and 451 females, of which mean age was 74.37. The explored network showed strong centrality and edge stability, thus enabling to reveal an overview of the associations between health behaviours and mental well-being of older adults. The lavaan model has also demonstrated the casual paths within the explored network, which indicated the significant impact of sleeping quality, eating habits and social networking on resilience. The outcomes of the study were able to identify the lifestyle changes of Hong Kong older adults due to COVID-19. Although the present study is not regarded as novel internationally, it may be representative of the Hong Kong community. In order to facilitate active aging during the pandemic, a user-friendly electronic platform for healthy living should include older adults in the future.

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. The results are important for understanding the X point features, which affect the tokamak edge stability and transport.

Leading edge stabilisation of vertical boundary layer diffusion flames

The leading edge stability of vertical boundary layer diffusion flames established over a 3D-printed porous gas burner is revealed through Planar Laser-Induced Fluorescence imaging of the OH radical (OH-PLIF). Flame stability is studied by premixing methane and ethylene with increasing volume fractions of bromotrifluoromethane (CF3Br/Halon-1301) to increase the characteristic chemical timescale. Blow-off occurs at 15.7% and 37.3% CF3Br addition for methane and ethylene respectively, which are remarkably large limits compared to other flame configurations. As CF3Br is added, the flame stand-off distance increases and the reaction zone broadens, thereby increasing the flame length. This accelerates the buoyancy-induced flow ahead of the leading edge, promoting O2 entrainment into the flame anchor. Consequently, the radical scavenging effects on the flame anchor reactivity are dampened, resulting in the flame re-anchoring slightly downstream along the plate. Towards extinction, the flame shortens dramatically due to efficient catalytic cycling and radiative quenching at the flame tip resulting from the brominated species and excessive soot formation. This reduces the O2 mass flux into the kinetically dampened flame anchor resulting in blow-off extinction. Therefore, blow-off is controlled by both the leading edge reactivity and trailing edge length. Methane is shown to be considerably more sensitive compared to ethylene to CF3Br owing to its larger flame speed. These results demonstrate that fire-induced buoyancy greatly increases blow-off limits when using chemically active or inert agents in vertical wall fire configurations.

A Gallai’s Theorem type result for the edge stability of graphs

A Gallai’s Theorem type result for the edge stability of graphs