Performance Of Topology Research Articles

Computational Technique for Crack Propagation Simulation in Viscoelastic Solid Propellant

To further investigate the fracture response in propellant grain, numerical methodology is proposed to cope with crack propagation simulation especially for the mixed mode condition. The numerical discrete scheme of the propellant linear viscoelastic constitutive model is proposed, which provides a key means for the simulation of crack propagation. In order to simulate the cohesive traction distribution on the new crack surface, the extrinsic Park-Paulino-Roesler (PPR) cohesive zone model (CZM) is introduced. To let the crack propagate along any direction determined, element splitting technique and its corresponding topological operations are proposed step by step. Then, computational simulation implementation process is explained in greater detail. Typical fracture problem, single edge-notched tension test (SENT) is solved to demonstrate the efficiency and accuracy of the proposed method. In addition, double edge-notched tension test (DENT) as well as plate tension test with a slant crack is conducted to show the special fracture characters in viscoelastic solid propellant, like time dependence. Computational results reveal that the method proposed can be utilized in further fracture investigation in solid propellant combined with the experimental findings.

HIC: A high‐reliable in‐band control network for perception layer of software‐defined IoT

AbstractWith the rapid development of the Internet of Things (IoT) and the popularity of the software‐defined idea, the software‐defined Internet of Things (SD‐IoT) came into being. However, the transmission conflict between control flow and data flow in the perception layer with poor channel resources has become an important constraint for SD‐IoT. Thus, this paper adopts the idea of isolated forwarding control flow based on an in‐band channel, that is, selecting some sensor nodes to be responsible for forwarding control flow, and proposes high‐reliable in‐band control network (HIC), a high‐reliability in‐band control network. In order to support real‐time tasks in the IoT environment, HIC adopts a divided control area to support parallel responses of multiple partially overlapping tasks. Further, in each control area, the graph theory is used to model the control node selection problem, and an algorithm for efficiently solving the model is designed based on the community detection method. Finally, we developed the HIC experimental platform composed of HIC‐topology and HIC‐simulation and carried out simulation experiments and analysis from topology generation, maintenance, and operation. The experimental results show that HIC could better adapt to the SD‐IoT under multi‐task deployment, and has great advantages in terms of the success rate and time of topology rapid maintenance compared with similar solutions.

Preservation of absolutely continuous spectrum for contractive operators

Contractive operators T T that are trace class perturbations of a unitary operator U U are treated. It is proved that the dimension functions of the absolutely continuous spectrum of T T , T ∗ T^* , and of U U coincide. In particular, if U U has a purely singular spectrum, then the characteristic function θ \theta of T T is a two-sided inner function, i.e., θ ( ξ ) \theta (\xi ) is unitary a.e. on T \mathbb {T} . Some corollaries to this result are related to investigations of the asymptotic stability of the operators T T and T ∗ T^* (the convergence T n → 0 T^n\to 0 and ( T ∗ ) n → 0 (T^*)^n\to 0 , respectively, in the strong operator topology). The proof is based on an explicit computation of the characteristic function.

Fast High-Order Mesh Correction for Metric-Based Cavity Remeshing and a Posteriori Curving of [formula omitted] Tetrahedral Meshes

A new high-order mesh correction method is introduced. Using the simplex algorithm, it maximizes directly the minimum of all control coefficients depending on a control point. This method provides the global optimum as quickly as to evaluate the min 8 times on average. The basic principle is applicable to all common element types (tetrahedra, hexahedra pyramids, prisms) and degrees. Meshes are corrected globally using this simplex-based Jacobian corrector in iterative smoothing.Riemannian edge length minimization is presented for metric-based high-order mesh curving. It is consistent with log-Euclidean metric interpolation, which is extended to high-order meshes. The interpolated metric field is differentiated analytically, with applications to other geometric quantities (quality, Jacobian conformity). Edge length minimization is fast and flexible as it can be used with metrics deriving from adaptation or e.g. propagated surface metrics.The cavity operator is a general topological operator that can apply insertions, collapses and generalized swaps. It is extended to P2 meshes through a modular approach with curvature applied in two steps. Prescribed curvature is the result of CAD/P3 surrogate projection on the boundary and of metric-based curvature in the interior. Necessary curvature results from simplex-based correction of the curved cavity. Both curvature schemes can easily be replaced by alternatives.Several 3D numerical results on difficult academic and realistic CFD test-cases are presented. P2 tetrahedral meshes with up to 20M tetrahedra are corrected with curved boundary in between 10 s and 3 m30 s depending on target minimum Jacobian determinant.

Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

For a finite positive Borel measure $\mu$ on the unit circle, let $\mathcal{D}(\mu)$ be the associated harmonically weighted Dirichlet space. A shift invariant subspace $\mathcal{M}$ recognizes strong approximate spectral cosynthesis if there exists a sequence of shift invariant subspaces $\mathcal{M}_k$, with finite codimension, such that the orthogonal projections onto $\mathcal{M}_k$ converge in the strong operator topology to the orthogonal projection onto $\mathcal{M}$. If $\mu$ is a finite sum of atoms, then we show that shift invariant subspaces of $\mathcal{D}(\mu)$ admit strong approximate spectral cosynthesis.

Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief

Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief

Gurariĭ operators are generic

Answering a question of Garbulińska-Wȩgrzyn and Kubiś, we prove that Gurariĭ operators form a dense G_delta -set in the space mathcal B(mathbb G) of all nonexpansive operators on the Gurariĭ space mathbb G, endowed with the strong operator topology. This implies that universal operators on mathbb G form a residual set in mathcal B(mathbb G).

Decomposition, trivially-acting symmetries, and topological operators

Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry of the theory. That is, we regard such a symmetry as a mix of topological defect lines (TDLs) and topological point operators (TPOs). TDLs related by a trivially-acting symmetry can join at a TPO to form non-trivial two-way junctions. Upon gauging, the local operators at those junctions can become vacua in a disjoint union of theories. Examining the behavior of the TPOs under gauging therefore allows us to refine decomposition by tracking the trivially-acting symmetries of each universe. Mixed anomalies between the TDLs and TPOs provide discrete torsion-like phases for the partition functions of these orbifolds, modifying the resulting decomposition. This framework also readily allows for the consideration of trivially-acting non-invertible symmetries.

Weighted composition–differentiation operators in the uniformly closed algebra generated by weighted composition operators

Let $$\varphi $$ be an analytic self map of the open unit disc $$\mathbb {D}$$ . Assume that $$\psi $$ is an analytic map of $$\mathbb {D}$$ . Suppose that f is in the Hardy space of the open unit disc $$H^p$$ . The operator that takes f into $$\psi \cdot f \circ \varphi $$ is a weighted composition operator, and is denoted by $$C_{\psi ,\varphi }$$ . The operator that takes f into $$\psi \cdot f^\prime \circ \varphi $$ is a weighted composition-differentiation operator. We prove that some weighted composition-differentiation operators belong to the closed algebra generated by weighted composition operators in the uniform operator topology.

Finite dimensional approximations in operator algebras

A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an operator algebra is RFD if and only if every representation can be approximated by finite dimensional ones in the point weak operator topology. This is a non-self-adjoint version of a theorem of Exel and Loring for C⁎-algebras. Moreover, we construct an example of an operator algebra for which approximation in the point strong operator topology is not possible. As a consequence, the maximal C⁎-algebra generated by this operator algebra is not RFD. This answers questions of Clouâtre and Ramsey and of Clouâtre and Dor-On.

Homogenization for Locally Periodic Elliptic Problems on a Domain

Let $\Omega$ be a Lipschitz domain in $\mathbb R^d$, and let $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$ be a strongly elliptic operator on $\Omega$. We suppose that $\varepsilon$ is small and the function~$A$ is Lipschitz in the first variable and periodic in the second, so the coefficients of $\mathcal A^\varepsilon$ are locally periodic. Given $\mu$ in the resolvent set, we are interested in finding the rates of the approximations, as $\varepsilon\to0$, for $(\mathcal A^\varepsilon-\mu)^{-1}$ and $\nabla(\mathcal A^\varepsilon-\mu)^{-1}$ in the operator topology on $L_p$ for suitable~$p$. It is well-known that the rates depend on regularity of the effective operator~$\mathcal A^0$. We prove that if $(\mathcal A^0-\mu)^{-1}$ is bounded from $L_p(\Omega)^n$ to $W_p^{1+s}(\Omega)^n$ with $s\in(0,1]$, then the rates are, respectively, $\varepsilon^s$ and $\varepsilon^{s/p}$. The results are applied to the Dirichlet and Neumann problems for strongly elliptic operators with uniformly bounded and $\operatorname{VMO}$ coefficients.

On Two Intuitionistic Fuzzy Modal Topological Structures

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced previously, and some of its properties were studied. So far, there are two different IFMTSs based on the classical intuitionistic fuzzy operations: “union” (∪) and “intersection” (∩). In the present paper, two new IFMTSs are developed. They are based on new intuitionistic fuzzy topological operators from closure and interior types, introduced here for the first time, and on the two standard intuitionistic fuzzy modal operators □ and ◊. Some basic properties of the new IFMTSs are discussed. The newly presented IFMTSs could be considered as a basis for the next research on the IFMTSs. Some ideas for the future development of the IFMTS theory and open problems are formulated, related to the existence of other intuitionistic fuzzy operations that can generate new intuitionistic fuzzy topological operators and, respectively, new IFMTSs.

Voltage Operations on Maniplexes, Polytopes and Maps

Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags. In this paper we introduce the notion of voltage operations on maniplexes, as a way to unify the study of such operations and generalize them to other geometric and combinatorial structures such as abstract polytopes, hypermaps, maniplexes or hypertopes. This can be done since our technique provides a way to study classical operations in a graph theoretic setting, and thus to apply a voltage operation one only needs that the combinatorial structure in hand can be understood as an n-valent properly n-edge colored graph. For example, in the case of abstract polytopes, the partial order can be encoded into the so-called flag graph of the polytope and the voltage operation is therefore applied to such flag graph to then be recovered as a partial order. We focus on studying the interactions between voltage operations and the symmetries of the operated object, and show that these operations can be potentially used to build maniplexes with prescribed symmetry type graphs. Moreover, a complete characterization of when an operation can be seen as a voltage operation is given.

On two new intuitionistic fuzzy topological operators and four new intuitionistic fuzzy feeble modal topological structures

In the intuitionistic fuzzy sets theory there are some intuitionistic fuzzy topological operators. Here, two new operators are defined, some of their properties are shown and on their basis, four new intuitionistic fuzzy feeble modal topological structures are introduced and some of their properties are discussed.

B‐MIMO high step‐up DC/DC converter with high capability to control inputs

AbstractHere, a new bidirectional multi‐input‐multi‐output (B‐MIMO) high step‐up DC/DC converter with lower losses on switch/diode is proposed as suitable for electric vehicles. The proposed topology consists of five inputs and two outputs and the battery (energy storage) is considered one of the inputs. Due to the bidirectional nature of the proposed topology, different scenarios of it are described. In discharging mode, the stored energy of the battery is transferred to the output loads. In charging mode, the surplus energy by regenerative braking will be responsible for charging the battery in the related scenario. Also, each input can charge the battery separately in different scenarios. In general, the proposed topology is capable to work in different scenarios for bypassing/charging/discharging the battery. Other advantages of the proposed topology include continuous current of all the inputs, independent control of inputs from each other and lower normalized voltage stress on semiconductors. These features make the proposed bidirectional MIMO DC/DC converter (B‐MIMO‐C) suitable for electric vehicle applications. The proposed topology operation is provided in the laboratory testing for 870W prototype, and the obtained results confirm the theoretical calculations as well.

Equilibrium states for the massive Sine-Gordon theory in the Lorentzian signature

In this paper we investigate the massive Sine-Gordon model in the ultraviolet finite regime in thermal states over the two-dimensional Minkowski spacetime. We combine recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes to construct the correlation functions of the equilibrium state of the Sine-Gordon theory in the adiabatic limit. First of all, the observables of the Sine-Gordon theory are seen as functionals over the free configurations and are obtained as a suitable combination of the S−matrices of the interaction Lagrangian restricted to compact spacetime regions over the free massive theory. These S−matrices are given as power series in the coupling constant with values in the algebra of fields over the free massive theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we prove that these power series converge when evaluated on a generic field configuration. The latter observation implies convergence in the strong operator topology in the GNS representations of the considered states. In the second part of the paper, adapting the cluster expansion technique to the Lorentzian case, we prove that the correlation functions of the interacting equilibrium state at finite temperature (KMS state) can be constructed also in the adiabatic limit, where the interaction Lagrangian is supported everywhere in space.

Five Generalized Rough Approximation Spaces Produced by Maximal Rough Neighborhoods

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the system of maximal neighborhood systems. We benefit from the symmetry between rough approximations (lower and upper) and topological operators (interior and closure) to structure the current generalized rough approximation spaces. First, we display two novel types of rough set models produced by maximal neighborhoods, namely, type 2 mξ-neighborhood and type 3 mξ-neighborhood rough models. We investigate their master properties and show the relationships between them as well as their relationship with some foregoing ones. Then, we apply the idea of adhesion neighborhoods to introduce three additional rough set models, namely, type 4 mξ-adhesion, type 5 mξ-adhesion and type 6 mξ-adhesion neighborhood rough models. We establish the fundamental characteristics of approximation operators inspired by these models and discuss how the properties of various relationships relate to one another. We prove that adhesion neighborhood rough models increase the value of the accuracy measure of subsets, which can improve decision making. Finally, we provide a comparison between Yao’s technique and current types of adhesion neighborhood rough models.

Brushless Operation of Wound-Rotor Synchronous Machine Based on Sub-Harmonic Excitation Technique Using Multi-Pole Stator Windings

This paper presents a topology for the brushless operation of a wound-rotor synchronous machine based on the subharmonic excitation technique by using two sets of multi-pole windings on the armature as well as on the rotor. The armature windings consist of a four-pole three-phase main winding and a two-pole single-phase additional winding, responsible for the generation of fundamental and subharmonic components of magnetomotive force (MMF), respectively. The rotor contains four-pole field winding and two-pole excitation winding. From the generated air gap MMF, the additional winding is responsible for induction in excitation winding, which feeds DC to the field winding through a rotating rectifier without the need of brushes. Then, the interaction of the magnetic field from the main and the field windings produces torque. The proposed topology is analyzed using 2D finite element analysis (FEM). From the analysis, the generation of the subharmonic component of MMF is verified, which helps in achieving the brushless operation of the wound-rotor synchronous machine. Furthermore, the performance of the proposed brushless multi-pole topology is compared with the existing dual three-phase winding multi-pole topology in terms of current due to induction, output torque, torque ripples, and efficiency.

PMOS‐only pW‐power voltage reference with sub‐10 ppm/°C trimmed temperature coefficient and sub‐100 ppm/V line sensitivity

SummaryIn this paper, a new ultra‐low‐power voltage reference based on a two‐stage, all‐pMOS topology operating in the subthreshold region is proposed to uniquely meet the pW‐power range power consumption requirements of emerging Internet‐of‐Things applications without significantly compromising the temperature coefficient (TC) and the line sensitivity (LS) performance. The proposed circuit consists of the LS regulator, TC corrector, and TC trimming sections. Based on post‐layout Monte Carlo simulations in 180‐nm CMOS, the proposed circuit operates with 0.8‐ to 2.4‐V supply potential and generates a reference voltage of 206 mV with a process spread of 7.8%, achieving an average calibrated TC of 4.4 ppm/°C in the temperature range of −20°C to 80°C, and an average LS of 51.5 ppm/V with a power consumption of 25.9 pW at 25°C (469.1 pW at 80°C).

The étale open topology over the fraction field of a Henselian local domain

AbstractSuppose that R is a local domain with fraction field K. If R is Henselian, then the R‐adic topology over K refines the étale open topology. If R is regular, then the étale open topology over K refines the R‐adic topology. In particular, the étale open topology over agrees with the ‐adic topology for any field L and .