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The orientation of a rigid body is described by a position‐tensor, composed of three unit vector axes fixed in the body; rotation is effected by tensor transformations in which a rotational operator is a Cartesian matrix, formed from the co‐ordinates of the pivot axis and components of the angle of rotation; rotational sequences are represented by matrix products. Three practical applications are discussed: sequences of aircraft manoeuvres, which include composite rotations of roll and pitch, or roll, pitch and yaw, applied simultaneously; the variation of sweep, incidence and dihedral of a wing moving on any axis fixed in the aircraft; the direction of the pivot axis and the angle of rotation in the motion of a retractable undercarriage between two specified positions.

In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM).

The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM).

The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (f_k) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in f_k, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS.

Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields.

Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.

The purpose of this paper is to study the effect of particle shapes (spherical particle and nonspherical fiber) on their orientation distributions in indoor environment.

This paper adopted a particle model to predict the fibrous particle flow and distribution, and analyzed the orientation distributions of nonspherical fiber particles and spherical particles in airflows like indoor places. Fokker-Planck model was employed to solve the orientation behavior of nonspherical fiber particles.

The simulation results discover that the nonspherical airborne fiber particles have very different characteristics and behaviors and their orientation distributions are totally different from the uniform distribution of spherical particles. The investigation of the particle orientation tensor and orientation strength indicates that the airflow field becomes more anisotropic due to the suspended fibers. The airborne fiber particles increase the viscosity of the room airflow due to the fiber induced additional viscosity.

Orientation tensor, strength and additional viscosity in fibrous flow are seldom investigated indoor. This research reveals that the particle shape has to be considered in the analysis of particle transport and distribution in indoor places as most suspended indoor particles are nonspherical.

With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively.

Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0° to 360°. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively.

This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement.

In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.

In any machining process, the surface profile of the workpiece is continuously changing with respect to time and input parameters. In a conventional machining process, input parameters are feed and depth of cut whilst other parameters are considered to be constant throughout the process.

The direct and indirect participation of this instantaneous curvature can be used to optimize the strategy of cutting operation in terms of different parameters like heat generation-induced stresses, etc. The concepts of the metric tensor and Riemannian curvature tensor are made use in this study as a representation of curvature itself. The objective of this study is to create a mathematical methodology that can be implemented on a highly flexible machining process to find an optimum cutting strategy for a particular output parameter.

The study also includes different case studies for the validation of this newly introduced mathematical methodology.

The study will also find its position in other mechanical processes like forging and casting where instantaneous curvature affects various mechanical properties.

IN Part I the motion of an aircraft, designated by the position‐tensor X, was considered relative to a fixed reference frame E. Now in our analysis of the motion of a wing, designated by the position‐tensor U, the relevant reference frame is X, though X is still free to move relative to E. The hinge on which the wing moves in the aircraft is denoted by the unit vector h, and for any specified hinge‐axis the components of h with respect to both U and X will have fixed values. The basic notation, following the principles adopted in Part I, Section (2), is therefore

Centres on the decomposition of the total electromagnetic torque of electrical machines for two components. The proposed idea of decomposition relies on the physical meaning of currents that appear in electromagnetic field region. The first torque component acts on external and conduction currents, the second on the material medium particles currents. Proves the main equations with the help of differential Maxwell’s equations. An example has been shown of the calculation of electromagnetic torque components for a synchronous salient‐pole generator.

This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the actual crack detection during welding process.

The paper studied the AE characteristics in welding using thermoelastic theory, which investigates the dynamical displacement field caused by a crack and the welding heating effect. In the calculation model, the crack initiation and extension are represented by moment tensor as the AE source, and the welding heat source is the Gauss heat flux distribution. The extended finite element method (XFEM) is implemented to calculate and solve the AE response of a thermoelastic plate with a crack during the welding heating effect. The wavelet transform is applied to the time–frequency analysis of the AE signals.

The paper provides insights about the changing rule of the acoustic radiation patterns influenced by the heating effect of the moving heat source and the AE signal characteristics in thermoelastic plate by different crack lengths and depths. It reveals that the time–frequency characteristics of the AE signals from the simulation are in good agreement with the theoretical ones. The energy ratio of the antisymmetric mode A0 to symmetric mode S0 is a valuable quantitative inductor to estimate the crack depth with a certain regularity.

This paper mainly discusses the application of XFEM to calculate and analyze thermoelastic problems, and has presented few cases based on a specified configuration. Further work will focus on the calculation and analysis under different plate configurations and conditions, which is to obtain more interesting and general conclusions for guiding practice.

The paper is a successful application of XFEM to solve the problem of AE response of a crack in the dynamic welding inhomogeneous heating effect. The paper provides an effective way to obtain the AE signal characteristics in monitoring the welding crack.

To develop a theory of concepts that solves the combination problem, i.e. to deliver a description of the combination of concepts. We also investigate the so‐called “pet fish problem” in concept research.

The set of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators and context and properties are orthogonal projections.

The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination problem is proposed. Using the tensor product, a natural product in Hilbert space mathematics, a procedure for describing combined concepts is elaborated. This procedure also provides a solution to the pet‐fish problem, and it allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.

The combination problem is considered to be one of the crucial unsolved problems in concept research. Also the pet‐fish problem has not been solved by earlier attempts of modeling.

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.