Boundary Components Research Articles

Friction-induced vibration and noise characteristics, and interface tribological behavior during high-speed train braking: The effect of the residual height of the brake pad friction block

A tribology test was carried out on a test device to simulate the braking performance of a high-speed train and investigate the effect of the friction block's residual height on friction-induced vibration and noise (FIVN) characteristics and interface tribology behavior. A finite element model (FEM) of the test device was established using the real boundary conditions and component material parameters. A wear simulation of the friction block was performed, and the Archard wear equation was used to obtain the surface wear of the friction block after stable friction had occurred. Complex eigenvalue analysis (CEA) and implicit dynamic analysis (IDA) were carried out. The effect of the friction block's height on the surface wear level, the complex mode and dynamic response, and the interface contact behavior are discussed. The results show that the friction block wears at an angle due to the friction force at the braking interface. Thus, the contact stress occurs predominantly at the leading edge of the friction block, leading to significant wear, high temperatures, and eccentric wear of the friction block. The taller the friction block, the larger the inclination angle is, and the more significant the eccentric wear degree is. Excessive wear at the leading edge causes debris to enter the brake interface. As a result, the wear surface of friction block is significantly damaged, including large contact plateaus and extensive exfoliation and ploughing. This damage increases the complexity of the braking interface's tribological behavior and causes high-intensity FIVN. However, the inclination angle decreases as the friction block's height decreases, resulting in better wear behavior of the friction interface and lower FIVN intensity. Although the friction block height significantly affects the intensity and evolution of FIVN, it does not change the system's inherent frequency.

Linking number and folded ribbon unknots

We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The folded ribbonlength is the length to width ratio of such a folded ribbon knot. The folded ribbon knot is also a framed knot, and the ribbon linking number is the linking number of the knot and one boundary component of the ribbon. We find the minimum folded ribbonlength for [Formula: see text]-stick unknots with ribbon linking numbers [Formula: see text] and [Formula: see text], and we prove that the minimum folded ribbonlength for [Formula: see text]-gons with obtuse interior angles is achieved when the [Formula: see text]-gon is regular. Among other results, we prove that the minimum folded ribbonlength of any folded ribbon unknot which is a topological annulus with ribbon linking number [Formula: see text] is bounded from above by [Formula: see text].

Alternative versions of the Johnson homomorphisms and the LMO functor

Let $\Sigma$ be a compact connected oriented surface with one boundary component and let $\mathcal{M}$ denote the mapping class group of $\Sigma$. By considering the action of $\mathcal{M}$ on the fundamental group of $\Sigma$ it is possible to define different filtrations of $\mathcal{M}$ together with some homomorphisms on each term of the filtration. The aim of this paper is twofold. Firstly we study a filtration of $\mathcal{M}$ introduced recently by Habiro and Massuyeau, whose definition involves a handlebody bounded by $\Sigma$. We shall call it the "alternative Johnson filtration", and the corresponding homomorphisms are referred to as "alternative Johnson homomorphisms". We provide a comparison between the alternative Johnson filtration and two previously known filtrations: the original Johnson filtration and the Johnson-Levine filtration. Secondly, we study the relationship between the alternative Johnson homomorphisms and the functorial extension of the Le-Murakami-Ohtsuki invariant of $3$-manifolds. We prove that these homomorphisms can be read in the tree reduction of the LMO functor. In particular, this provides a new reading grid for the tree reduction of the LMO functor.

Reeb flows without simple global surfaces of section

We construct, for any given positive integer $n$, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than $n$ boundary components. We use a connected sum operation for open books to construct such systems. We prove that this property is stable with respect to $C^{4+\epsilon}$-small perturbations of the Hamiltonian given on the symplectization.

A model for random three-manifolds

We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the number of tetrahedra tends to infinity, these manifolds are connected and have a single boundary component.We prove a lawof large numbers for the genus of this boundary component, we show that the Heegaard genus of these manifolds is linear in the number of tetrahedra and we bound their first Betti number. We also show that, asymptotically almost surely as the number of tetrahedra tends to infinity, our manifolds admit a unique hyperbolic metric with totally geodesic boundary.We prove a law of large numbers for the volume of this metric, prove that the associated Laplacian has a uniform spectral gap and show that the diameter of our manifolds is logarithmic as a function of their volume. Finally, we determine the Benjamini–Schramm limit of our sequence of random manifolds.

MOVES ON CURVES ON NONORIENTABLE SURFACES

Let Ng,n denote a nonorientable surface of genus g with n punctures and one boundary component. We give an algorithm to calculate the geometric intersection number of an arbitrary multicurve ℒ with so-called relaxed curves in Ng,n making use of measured π1-train tracks. The algorithm proceeds by the repeated application of three moves which take as input the measures of ℒ and produces as output a multicurve ℒ′ which is minimal with respect to each of the relaxed curves. The last step of the algorithm calculates the number of intersections between ℒ′ and the relaxed curves.

The Flux Homomorphism on a Surface with Boundary and Central Extensions of Diffeomorphism Groups

Let Σg,11 be a genus g compact oriented surface with one boundary component and one marked point x. Let G be the identity component of the group of symplectomorphisms that preserve the marked point x. By using the flux homomorphism and the short exact sequence 1→Grel→G→Diff+(S1)→1, we construct a central ℝ-extension of Diff+(S1). We also show that the second cohomology class corresponding to the central ℝ-extension is equal to the Euler class of Diff+(S1) up to non-zero constant multiple.

Sensitivity analysis of structural-acoustic fully-coupled system using isogeometric boundary element method

In many engineering challenges, the whole interaction between the structural domain and the acoustic domain must be taken into account, particularly for the acoustic analysis of thin structures submerged in water. The fast multipole boundary element approach is used in this work to simulate the external acoustic domain and the finite element method is used to describe the structural components. To improve coupling analysis accuracy, discontinuous higher-order boundary components are created for the acoustic domain. The isogeometric boundary element method (IGABEM) discretizes unknown physical fields by using CAD spline functions as basis functions. IGABEM is inherently compatible with CAD and can perform numerical analysis on CAD models without having to go through the time-consuming meshing process required by traditional FEM/BEM and volume parameterization in isogeometric finite element methods. IGABEM’s power in tackling infinite domain issues and combining CAD and numerical analysis is fully used when it is applied to structural form optimization of three-dimensional external acoustic problems. The structural-acoustic design and optimization procedures benefit from the use of structural-acoustic design sensitivity analysis because it may provide information on how design factors affect radiated acoustic performance. This paper provides adjoint operator-based equations for sound power sensitivity on structural surfaces and direct differentiation-based equations for sound power sensitivity on arbitrary closed surfaces surrounding the radiator. Numerical illustrations are provided to show the precision and viability of the suggested approach.

BMO and Dirichlet Problem for Degenerate Beltrami Equation

Following Bojarski and Vekua, we have studied the Dirichlet problem \( \underset{z\to \zeta }{\lim}\operatorname{Re}\ f(z)=\varphi \left(\zeta \right) \) as z → ζ, z ∈ D, ζ ∈ ∂D, with continuous boundary data φ(ζ) in bounded domains D of the complex plane ℂ, where f satisfies the degenerate Beltrami equation \( {f}_{\overline{z}}=\mu (z){f}_z,\left|\mu (z)\right|<1 \), a.e. in D. Assuming that D is an arbitrary simply connected domain, we have established, in terms of μ, the BMO and FMO criteria, as well as a number of other integral criteria, on the existence and representation of regular discrete open solutions to the stated above problem. We have also proven similar theorems on the existence of multivalued solutions to the problem with single-valued real parts in an arbitrary bounded domain D with no boundary component degenerated to a single point. Finally, we have given a similar solvability and representation results concerning the Dirichlet problem in such domains for the degenerate A-harmonic equation associated with the Beltrami equation.

Flexibility of Steklov eigenvalues via boundary homogenisation

Recently, D. Bucur and M. Nahon used boundary homogenisation to show the remarkable flexibility of Steklov eigenvalues of planar domains. In the present paper we extend their result to higher dimensions and to arbitrary manifolds with boundary, even though in those cases the boundary does not generally exhibit any periodic structure. Our arguments use a framework of variational eigenvalues and provide a different proof of the original results. Furthermore, we present an application of this flexibility to the optimisation of Steklov eigenvalues under perimeter constraint. It is proved that the best upper bound for normalised Steklov eigenvalues of surfaces of genus zero and any fixed number of boundary components can always be saturated by planar domains. This is the case even though any actual maximisers (except for simply connected surfaces) are always far from being planar themselves. In particular, it yields sharp upper bound for the first Steklov eigenvalue of doubly connected planar domains.

Prescribing Gaussian curvature on surfaces with conical singularities and geodesic boundary

We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argument, we derive a general existence result for surfaces with at least two boundary components. This seems to be the first result in this setting. Moreover, we allow to have conical singularities with both positive and negative orders, that is cone angles both less and greater than 2pi.

A necessary and sufficient condition for a Heegaard splitting to be keen weakly reducible

In this work, we first present a necessary and sufficient condition to closed orientable 3-manifold admitting keen weakly reducible Heegaard splitting. By an example, we show that condition is not suitable for compact orientable manifold with non-sphere boundary component. At last, we give a necessary and sufficient condition for compact orientable 3-manifold to have a keen weakly reducible Heegaard splitting.

2-handle additions producing toroidal and reducible manifolds

Let M be a simple 3-manifold and F a boundary component of genus at least two and suppose α,β are two separating slopes on F. It is shown that if both 2-handle attaching M[α] and M[β] are toroidal then Δ(α,β)≤10 or Δ(α,β)=12 or Δ(α,β)=18. Furthermore, in the cases Δ(α,β)=12 or 18, M[α] and M[β] each contains an essential torus which intersects the 2-handle once and F has genus at least 4 or 8, respectively. As a corollary, if g(F)=3 then Δ(α,β)≤10 and if g(F)=2 then Δ(α,β)≤8. Moreover, if F has genus at least two and M[α] is toroidal and M[β] reducible then Δ(α,β)≤4.

Characteristics of electrolyte-supported SOFC single cells using hexagonal perovskite Ba3MoNbO8.5 and Ba7Nb4MoO20 ceramics

The characteristics of two solid oxide fuel cells (SOFCs) were compared using Ba3MoNbO8.5 and Ba7Nb4MoO20 sintered at 1100 and 1300 °C, respectively, as electrolytes. The electrolyte-supported SOFC single cells, Pt ǀ Sm0.2Ce0.8O1.9 ǀ electrolyte ǀ Sm0.2Ce0.8O1.9 ǀ Pt, with an electrolyte thickness of 1.0 mm were prepared. The resistivity of the bulk + grain boundary components of Ba3MoNbO8.5 and Ba7Nb4MoO20 were 2.25k and 212 Ω cm, respectively, at 600 °C, and their apparent activation energies for ion conduction were 122.3 and 72.8 kJ mol−1, respectively at 450–600 °C. When the I–V curves were evaluated at 450–600 °C with the introduction of 3% H2 (N2 balance) and air to the anode and cathode, respectively, the open circuit voltages and maximum power outputs at 600 °C were 0.95 V and 1.3 mW cm−2 for Ba3MoNbO8.5 and 0.97 V and 9.3 mW cm−2 for Ba7Nb4MoO20, respectively.

Band width estimates via the Dirac operator

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the distance between the boundary components of $V$ is at most $C_n/\sqrt{\sigma}$, where $C_n = \sqrt{(n-1)/{n}} \cdot C$ with $C < 8(1+\sqrt{2})$ being a universal constant. This verifies a conjecture of Gromov for such manifolds. In particular, our result applies to all high-dimensional closed simply connected manifolds $M$ which do not admit a metric of positive scalar curvature. We also establish a quadratic decay estimate for the scalar curvature of complete metrics on manifolds, such as $M \times \mathbb{R}^2$, which contain $M$ as a codimension two submanifold in a suitable way. Furthermore, we introduce the "$\mathcal{KO}$-width" of a closed manifold and deduce that infinite $\mathcal{KO}$-width is an obstruction to positive scalar curvature.

Mapping Class Group Representations Derived from Stated Skein Algebras

We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.

Exceptional surgeries in 3-manifolds

Myers shows that every compact, connected, orientable 3 3 -manifold with no 2 2 -sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 3 3 -manifold subject to the above conditions contains a hyperbolic knot which admits a non-trivial non-hyperbolic surgery, a toroidal surgery in particular. We conclude with a question and a conjecture about reducible surgeries.

Some consequences of the distributional stress equilibrium condition

We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First, we obtain the local equilibrium conditions in the bulk and at the interface, the latter inclusive of interfacial stress and stress dipole fields. Second, we obtain the necessary and the sufficient conditions on the divergence-free non-smooth stress field for there to exist a stress function field such that the stress equilibrium is trivially satisfied. In doing so, we allow the domain to be non-contractible with mutually disjoint connected boundary components. Both derivations illustrate the utility of the theory of distributions in dealing with singular stress fields.

An imaginary refined count for some real rational curves

In 2015, Mikhalkin introduced a refined count for the real rational curves in a toric surface which pass through a set consisting of real points and pairs of complex conjugated points chosen generically on the toric boundary of the surface. He then proved that the result of this refined count depends only on the number of pairs of complex conjugated points on each toric divisor. Using the tropical geometry approach and the correspondence theorem, we address the computation of the refined count when the pairs of complex conjugated points are chosen purely imaginary and belonging to the same component of the toric boundary. Despite the non-genericity, we relate this refined count for purely imaginary values to the refined invariant of Mikhalkin for generic values. That allows us to extend the relation between these classical refined invariants and the tropical refined invariants from Block–Göttsche.

Stated skein algebras of surfaces

We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group $\mathcal{O}{{q^2}}(\operatorname{SL}(2))$ thus providing a topological interpretation for its structure morphisms. We also show that its stated skein algebra lifts in a suitable sense the Reshetikhin–Turaev functor, and in particular, we recover the dual $R$-matrix for $\mathcal{O}{{q^2}}(\operatorname{SL}(2)$ in a topological way. We deduce that the skein algebra of a surface with $n$ boundary components is a comodule algebra over $\mathcal{O}{{q^2}}(\operatorname{SL}(2))^{\otimes n}$ and prove that cutting along an ideal arc corresponds to Hochshild cohomology of bicomodules. We give a topological interpretation of braided tensor product of stated skein algebras of surfaces as “gluing on a triangle”; then we recover topologically some bialgebras in the category of $\mathcal{O}{{q^2}}(\operatorname{SL}(2))$-comodules, among which the “transmutation” of $\mathcal{O}\_{{q^2}}(\operatorname{SL}(2))$. We also provide an operadic interpretation of stated skein algebras as an example of a “geometric non-symmetric modular operad”. In the last part of the paper, we define a reduced version of stated skein algebras and prove that it allows to recover Bonahon–Wong's quantum trace map and interpret skein algebras in the classical limit when $q\to 1$ as regular functions over a suitable version of moduli spaces of twisted bundles.