General Topology Research Articles

Adaptive observer based-robust synchronization of switched fractional Rikitake systems with input nonlinearity

This paper mainly focuses on the robust synchronization of switched fractional-order improved Rikitake two-disk dynamo system which is a more general topology of the original Rikitake system. In particular, we first explore and design a simplified model very close to a real geophysical process which is described by an orbiting point, primarily using concepts from dynamical system theory. Dynamical properties, including symmetry, dissipation, stability of equilibria, Lyapunov exponents, and bifurcation, are analyzed on the basis of theoretical analysis and numerical simulation. Secondly, some less stringent conditions for adaptive control are derived when the system is subjected to external disturbances, parametric uncertainties and nonlinear input. The convergence of the state space trajectories with the overall robust asymptotic stability of the closed-loop system is obtained using the Lyapunov theory. To highlight our contribution, an illustrative example is presented to show the effectiveness and applicability of the proposed synchronization scheme. This proposal derives a systematic procedure for the design and control of a wide range of electromechanical systems. The results obtained in this work have not yet been reported in the literature to the best of the authors’ knowledge and thus deserve dissemination.

Distributed Bipartite Adaptive Event-Triggered Fault-Tolerant Consensus Tracking for Linear Multiagent Systems Under Actuator Faults.

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

Nonexistence of the NNSC-cobordism of Bartnik data

In this paper, we consider the problem of the nonnegative scalar curvature (NNSC)-cobordism of Bartnik data $$\left( {\sum _1^{n - 1},{{\rm{\gamma }}_1},{H_1}} \right)$$ and $$\left( {\sum _2^{n - 1},{{\rm{\gamma }}_2},{H_2}} \right)$$ . We prove that given two metrics γ1 and γ2 on Sn−1 (3 ⩽ n ⩽ 7) with H1 fixed, then (Sn−1, γ1, H1) and (Sn−1, γ2, H2) admit no NNSC-cobordism provided the prescribed mean curvature H2 is large enough (see Theorem 1.3). Moreover, we show that for n = 3, a much weaker condition that the total mean curvature $$\int_{{S^2}}^{} {{H_2}d{\mu _{{\gamma _2}}}} $$ is large enough rules out NNSC-cobordisms (see Theorem 1.2); if we require the Gaussian curvature of γ2 to be positive, we get a criterion for nonexistence of the trivial NNSC-cobordism by using the Hawking mass and the Brown-York mass (see Theorem 1.1). For the general topology case, we prove that $$\left( {\Sigma _1^{n - 1},{{\rm{\gamma }}_1},0} \right)$$ and $$\left( {{\rm{\Sigma }}_2^{n - 1},{{\rm{\gamma }}_2},{H_2}} \right)$$ admit no NNSC-cobordism provided the prescribed mean curvature H2 is large enough (see Theorem 1.5).

Researchers use LEGOs to decode intricate vibration patterns in quasi-crystalline matter

An experimental setup using LEGO pieces is proven to be a viable method for studying the general dynamics and topology of metastructures.

Implementation of Thermomechanical Multiphysics in a Large-Scale Three-Dimensional Topology Optimization Code

<div class="section abstract"><div class="htmlview paragraph">Due to the inherent computational cost of multiphysics topology optimization methods, it is a common practice to implement these methods in two-dimensions. However most real-world multiphysics problems are best optimized in three-dimensions, leading to the necessity for large-scale multiphysics topology optimization codes. To aid in the development of these codes, this paper presents a general thermomechanical topology optimization method and describes how to implement the method into a preexisting large-scale three-dimensional topology optimization code. The weak forms of the Galerkin finite element models are fully derived for mechanical, thermal, and coupled thermomechanical physics models. The objective function for the topology optimization method is defined as the weighted sum of the mechanical and thermal compliance. The corresponding sensitivity coefficients are derived using the direct differentiation method and are verified using the complex-step method. The design variables are updated using the method of moving asymptotes so that the objective function is minimized resulting in maximum performance of the structure. Solution of the linear systems of equation is scaled across several supercomputer nodes using the Portable, Extensible Toolkit for Scientific Computation (PETSc) developed by Argonne National Laboratory. The finite element models, sensitivity analysis, optimization algorithm, and solver are all implemented in a freeware, density-based, topology optimization code (written in C++) that has been modified for thermomechanical problems. As such, the implementation of the thermomechanical model is provided. The code is applied to solve an example problem under thermal, mechanical, and thermomechanical boundary conditions. The resulting topologies and field variables are shown with a corresponding discussion.</div></div>

Crystallographic analysis of TarI and TarJ, a cytidylyltransferase and reductase pair for CDP-ribitol synthesis in Staphylococcus aureus wall teichoic acid biogenesis

The cell wall of many pathogenic Gram-positive bacteria contains ribitol-phosphate wall teichoic acid (WTA), a polymer that is linked to virulence and regulation of essential physiological processes including cell division. CDP-ribitol, the activated precursor for ribitol-phosphate polymerization, is synthesized by a cytidylyltransferase and reductase pair known as TarI and TarJ, respectively. In this study, we present crystal structures of Staphylococcus aureus TarI and TarJ in their apo forms and in complex with substrates and products. The TarI structures illustrate the mechanism of CDP-ribitol synthesis from CTP and ribitol-phosphate and reveal structural changes required for substrate binding and catalysis. Insights into the upstream step of ribulose-phosphate reduction to ribitol-phosphate is provided by the structures of TarJ. Furthermore, we propose a general topology of the enzymes in a heterotetrameric form built using restraints from crosslinking mass spectrometry analysis. Together, our data present molecular details of CDP-ribitol production that may aid in the design of inhibitors against WTA biosynthesis.

Loop-tree duality from vertices and edges

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of vertices. Interestingly, integrands considered in former studies, with up-to six vertices and L internal lines, display the same structure of up-to four-loop ones. The former is an insight that there should be a correspondence between vertices and the collection of internal lines, edges, that characterise a multi-loop topology. By virtue of this relation, in this paper, we embrace an approach to properly classify multi-loop topologies according to vertices and edges. Differently from former studies, we consider the most general topologies, by connecting vertices and edges in all possible ways. Likewise, we provide a procedure to generate causal representation of multi-loop topologies by considering the structure of causal propagators. Explicit causal representations of loop topologies with up-to nine vertices are provided.

A hybrid virtual–boundary element formulation for heterogeneous materials

In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary integral equations, employed as the original model of the represented physical problem. For several classes of problems, BEM offers some advantages over more popular techniques, namely the reduction of the dimensionality of the problem, with associated computational savings. In this study, the inherent advantages of VEM and BEM are simultaneously employed for the study of heterogeneous material microstructures.The method has been applied to i) the elastic analysis and ii) computational homogenization of fibre-reinforced composite materials and to iii) the analysis of composite unit cells exhibiting matrix isotropic damage. The discussed results show how the hybrid technique inherits the generality of VEM and the modelling simplification and accuracy of BEM, ensuring high accuracy and fast convergence and providing a versatile tool for the analysis of multiphase materials, also including non-linear behaviour such as material degradation. Further directions of research are identified and discussed after commenting on the presented results.

Renewable generation intermittence and economic dispatch control of autonomous microgrid with distributed sliding mode

This work addresses the Frequency Regulation (FR) and Economic Dispatch (ED) of autonomous Microgrid (MG) with distributed Renewable Energy Agents (REA). The MG possesses low inertia and lacks the natural synchronization capability requiring a fast-convergent control for FR and ED. Moreover, the nonlinear coupled dynamics of MG with unknown network parameter and network topology poses a critical control design challenge. The existing distributed control solutions; possess sluggish response against fluctuating power demand and system-disturbances, based on impractical assumptions and not applicable to generic network topologies. Moreover, the contemporary control schemes are unable to handle the renewable intermittence and fail to converge in presence of volatile production capacities of REA. A Distributed SMC based secondary control is proposed to fulfill the control requirements of MG. A novel decoupling technique is introduced that enables the application of control on generic network topologies with unknown network parameters. A constrained ED solution is derived for renewable agents possessing non-uniform and volatile production capacities and successfully achieved using the proposed control technique. The convergence of proposed control is proved using the Lyapunov Candidate function, while the performance is validated using IEEE 14 bus system and the results are compared with DAI control.

Distributed MPC for economic dispatch and intermittence control of renewable based autonomous microgrid

This work addresses secondary level control of Autonomous Microgrid composed of Distributed Renewable Energy Sources (DRES). The interconnection of DRES forms a nonlinear system with coupled dynamics, unknown network parameters, and network topologies. The challenging features of DRES, such as low inertia, large number, volatile production capacities, and geographically wide distribution pose critical control design challenges for Economic Dispatch (ED) and frequency regulation. Whereas the distributed control schemes proposed in contemporary research are too slow to provide ED in the presence of fluctuating power demand, based on impractical assumptions or too restrictive in terms of network topology to have practical significance. Moreover, the control schemes are unable to handle the intermittent and uncertain nature of DRES and lead to instability in the presence of volatile power production capacities. Considering the above, we propose Secondary Distributed Model Predictive Control that provides fast and robust convergence and avoids impractical assumptions. A unique decoupling technique enables the application of control to generic network topologies. A constrained ED solution is derived and successfully achieved in presence of volatile production capacities of DRES. The Lyapunov stability of control is proved through terminal constraints. The performance of the proposed control is validated using an IEEE 14-Bus System.

Topology optimization of hyperelastic structures with anisotropic fiber reinforcement under large deformations

Fiber-reinforced soft materials have emerged as promising candidates in various applications such as soft robotics and soft fibrous tissues. To enable a systematic approach to design fiber-reinforced materials and structures, we propose a general topology optimization framework for the computational optimized design of hyperelastic structures with nonlinear and anisotropic fiber reinforcements under large deformations. This framework simultaneously optimizes both the material distribution in the matrix phase and the orientations of the underlying fiber reinforcements, by parameterizing matrix and fiber phases individually using two sets of design variables. The optimized distribution of fiber orientations is chosen from a set of discrete orientations defined a priori, and several fiber orientation interpolation schemes are studied. In addition, this work proposes a novel anisotropic material interpolation scheme, which integrates both matrix and fiber design variables (both with material nonlinearity) into the stored-energy function. To improve the computational efficiency of both optimization and nonlinear structural analysis, we derive a fully decoupled fiber-matrix update scheme that performs parallel updates of the matrix and fiber design variables and employ the virtual element method (VEM) together with a tailored mesh adaptivity scheme to solve the finite elasticity boundary value problem. Design examples involving three objective functions are presented, demonstrating the efficiency and effectiveness of the proposed framework in designing anisotropic hyperelastic structures under large deformations.

Asymmetric Structure of Uranus' Magnetopause Controlled by IMF and Planetary Rotation

AbstractTo investigate the diurnal variations of the magnetopause boundary under different Interplanetary Magnetic Field (IMF) orientations during the solstice season, we implemented a multifluid magnetohydrodynamic model of Uranus' magnetosphere in combination with Voyager 2 observations, which provided a good ability to simulate and predict the variability of the magnetospheric boundaries. In this study, we quantitatively studied Uranus' magnetopause in terms of the subsolar stand‐off distance and the flaring parameter and tracked the variation in cusp indentation, which are good indicators to describe the general topology of the boundary. During this season, the stand‐off distance fluctuated within a small range. In contrast, the flaring parameter and cusp indentation were strongly impacted by Uranus' rotation. Meanwhile, the IMF orientation also modulated the variation of the flaring parameter and cusp indentation. These results show that the asymmetry of the magnetopause is highly dependent on the rotation of Uranus and its IMF orientations.

Compact condensations of Hausdorff spaces

We continue to study one of the classic problems in general topology raised by P. S. Alexandrov: when a Hausdorff space X has a continuous bijection (a condensation) onto a compactum? We concentrate on the situation when not only X but also $$X\setminus Y$$ can be condensed onto a compactum whenever the cardinality of Y does not exceed certain $$\tau$$ .

Beta- Star- Continuity and Beta- Star- Contra- Continuity

In 2014 Mubarki, Al-Rshudi, and Al- Juhani introduced and studied the notion of a set in general topology called β*-open set and investigated its fundamental properties and studied the relationships between β*-open set and other topological sets including β*-continuity in topological spaces. We introduce and investigate several properties and characterizations of a new class of functions between topological spaces called β*- open, β*- closed, β*- continuous and β*- irresolute functions in topological spaces. We also introduce slightly β*- continuous, totally β*- continuous and almost β*- continuous functions between topological spaces and establish several characterizations of these new forms of functions. Furthermore, we also introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra β*- continuous, and almost contra β*-continuous functions along with their several properties, characterizations and natural relationships. Moreover, we introduce new types of closed graphs by using β*- open sets and investigate its properties and characterizations in topological spaces.

New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations

In this paper, we prove a new common fixed point in a general topological space with a $tau-$distance. Then we deduce two common fixed point theorems for two new classes of contractive selfmappings in complete bounded metric spaces. Moreover, an application to a system of differential equations is given.

Scientific instrument for creation of effective Cooper pair mass spectroscopy

We describe electronic instruments for creation of effective Cooper pair spectroscopy. The suggested spectroscopy requires study of electric field effects on the surface of cleaved superconductors. The electronic instrument reacquires low noise amplifier with 106 amplitude amplification which we have formerly used for study of Johnson-Nyquist and Schottky noises. The nonspecific amplifier is followed by high-Q tunable resonance filter based on schematics of general impedance converter topology which is also and innovative device. The work of the device is based on the Manhattan equation of operational amplifier. After a final nonspecific amplification the total amplification can exceed 109 and in such a way sub-nano-volt signals can be reliably detected. In short the observation of new effects in condensed matter physics leads to creation of new generation of electronic equipment.

Analyzing the impact of the number of nodes on the performance of the routing protocols in manet environment

Mobile Ad-hoc Networks (MANETs) are independent systems that can work without the requirement for unified controls, pre-setup to the paths/routes or advance communication structures. The nodes/hubs of a MANET are independently controlled, which permit them to behave unreservedly in a randomized way inside the MANET. The hubs can leave their MANET and join different MANETs whenever the need arises. These attributes, in any case, may contrarily influence the performance of the routing conventions (or protocols) and the general topology of the systems. Along these lines, MANETs include uniquely planned routing conventions that responsively as well as proactively carry out the routing. This paper assesses and looks at the effectiveness (or performance) of five directing conventions which are AOMDV, DSDV, AODV, DSR and OLSR in a MANET domain. The research incorporates executing a simulating environment to look at the operation of the routing conventions dependent on the variable number of hubs. Three evaluation indices are utilized: Throughput (TH), Packet Delivery Ratio (PDR), and End-to-End delay (E2E). The assessment outcomes indicate that the AODV beats other conventions in the majority of the simulated scenarios.

WITHDRAWN: Alexandroff soft topological spaces

In this paper, we characterized another kind of topological space known as Alexandroff Soft Topological space. It is characterized over a general set X alongside an arbitrary set of parameters. This space satisfies a more grounded condition that an arbitrary intersection of open sets are open. We have likewise contemplated different ideas like basis of a topology, sub base, subspace, closure of a space and so on. Further, different separation axioms known as Alexo Ti-spaces have been presented alongside their properties. This space is also the parametrized type of general topology.

Bi-interior Ideal Elements in ∧e-semigroups

All the results on semigroups obtained using only sets, can be written in an abstract form in a more general setting. Let us consider a recent paper to justify what we say. The bi-interior ideals of semigroups introduced and studied by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. in 2018, follow for more general statements about ordered semigroups. The same holds for every result of this sort on semigroups based on right (left) ideals, bi-ideals, quasi-ideals, interior ideals etc. for which we use sets. As a result, we have an abstract formulation of the results on semigroups obtained by sets that is in the same spirit with the abstract formulation of general topology (the so-called topology without points) initiated by Koutsk ́y, Nöbeling and, even earlier, by Chittenden, Terasaka, Nakamura, Monteiro and Ribeiro. As a consequence, results on ordered Γ-hypersemigroups and on similar simpler structures can be obtained.

Full-scale topology optimization for fiber-reinforced structures with continuous fiber paths

Fiber-reinforced composite (FRC) structure design by topology optimization has become a hot spot in recent years. Nevertheless, the existing researches reveal several unfavorable issues including the fiber dis-continuity, the length scale separation, the decreased design freedom, as well as the complicated fiber orientation optimization. Thus, this paper proposes a full-scale fiber-reinforced structure topology optimization method that is capable of simultaneous design for the structural topology, continuous fiber path, and its morphology (i.e., fiber volume, spacing and thickness). The method builds upon a bi-material element-wise density-based topology optimization framework, where the matrix material and fiber material are considered in a uniform finite element model without the scale separation. Furthermore, a novel fiber generation scheme is developed, in which the bi-material constraint method is introduced by combining the total solid (composite) volume constraint and local fiber proportion constraint, so as to drive the evolution of the general topology, continuous fiber path and fiber morphology, respectively. In this way, it can avoid the above existing issues of the current FRC designs. The fiber-reinforced structures can be naturally generated with continuous fiber paths. Several numerical examples for compliance minimization problems are provided to show the merits of the full-scale optimization method for fiber-reinforced structures. The interpretation design procedure and post-processing error simulation analysis are also presented to further validate the applicability of the proposed method.