Coordinate Transformation Research Articles

Adaptive complementary neighboring sub-aperture beamforming for thermoacoustic imaging.

When applied to thermoacoustic imaging (TAI), the delay-and-sum (DAS) algorithm produces strong sidelobes due to its disadvantages of uniform aperture weighting. As a result, the quality of TAI images recovered by DAS is often severely degraded by strong non-coherent clutter, which restricts the development and application of TAI. To address this issue, we propose an adaptive complementary neighboring sub-aperture (NSA) beamforming algorithm for TAI. In NSA, we introduce a coordinate system transformation when calculating the normalized cross-correlation (NCC) matrix. This approach enables the computation of the NCC coefficient within the specified kernel without complex coordinate calculations. We first conducted the numerical simulation experiment to validate NSA using a tree branch phantom. In addition, we also conducted phantom (five sauce tubes), ex vivo (ablation needle in ex vivo porcine liver), and in vivo (human arm) TAI experiments using our TAI system with a center frequency of 3GHz. In the numerical simulation experiment, the structural similarity index (SSIM) value for NSA is increased from 0.37828 for DAS to 0.75492. In the point target phantom TAI experiment, the generalized contrast-to-noise ratio (gCNR) value for NSA is increased from 0.936 for DAS to 0.962. The experimental results show that NSA can recover clearer thermoacoustic images compared to DAS. In the ex vivo TAI experiment, the full width at half maxima (FWHM) of an ablation needle (diameter=1.5mm) for coherence factor (CF) weighted DAS and NSA are 0.9 and 1.3mm, respectively. Furthermore, in the in vivo TAI experiment, CF reduces the signals within the arm compared to NSA. Therefore, compared with CF, NSA can maintain the integrity of target information in TAI while effectively suppressing non-coherent background clutter. NSA can effectively reduce non-coherent background noise while ensuring the completeness of the target information. So, NSA offers the potential to provide high-quality thermoacoustic images and further advance their clinical application.

Internal Reliability of Planar Coordinate Transformations

Internal Reliability of Planar Coordinate Transformations

Dynamic Event-Based Adaptive Fixed-Time Control for Uncertain Strict-Feedback Nonlinear Systems With State Constraints.

In this article, the event-triggered fixed-time tracking control is investigated for uncertain strict-feedback nonlinear systems involving state constraints. By employing the universal transformed function (UTF) and coordinate transformation techniques into backstepping design procedure, the proposed control scheme ensures that all states are constrained within the time-varying asymmetric boundaries, and meanwhile, the undesired feasibility condition existing in other constrained controllers can be removed elegantly. Different from the existing static event-triggered mechanism, a dynamic event-triggered mechanism (DETM) is devised via constructing a novel dynamic function, so that the communication burden from the controller to actuator is further alleviated. Furthermore, with the aid of adaptive neural network (NN) technique and generalized first-order filter, together with Lyapunov theory, it is proved that the states of closed-loop system converge to small regions around zero with fixed-time convergence rate. The simulation results confirm the benefits of developed scheme.

Moyal product and generalized Hom-Lie-Virasoro symmetries in Bloch electron systems

We explore two variations of the Curtright-Zachos (CZ) deformation of the Virasoro algebra. Firstly, we introduce a scaled CZ algebra that inherits the scaling structure found in the differential operator representation of the magnetic translation (MT) operators. We then linearly decompose the scaled CZ generators to derive two types of Hom-Lie deformations of the W∞ algebra. We discuss ⁎-bracket formulations of these algebras and their connection to the Moyal product. We show that the ⁎-bracket form of the scaled CZ algebra arises from the Moyal product, while we obtain the second type of deformed W∞ through a coordinate transformation of the first type of Moyal operators. From a physical point of view, we construct the Hamiltonian of a tight binding model (TBM) using the Wyle matrix representation of the scaled CZ algebra. We note that the integer powers of q are linked to the quantum fluctuations that are inherent in the Moyal product.

Fracture modeling of curved composite shell structures using augmented finite element method

This paper presents an augmented finite element method for the fracture modeling of curved composite shell structures considering geometric nonlinear effects. We first derive the composite shell AFEM (CS-AFEM) formulation using a dynamic implicit algorithm, which enhances the numerical convergence when dealing with unstable crack propagations. Besides, the cohesive zone model featuring with shell kinematics is incorporated into the CS-AFEM to describe the quasi-brittle fracture behaviors of composite laminates. Furthermore, a coordinate transformation scheme is proposed to describe both the local material orientation and the crack evolving path in the curved shell structures. Finally, several benchmark examples are numerically investigated, and the capability of the proposed method in modeling the arbitrary evolving cracks in curved composite shell structures has been thoroughly demonstrated.

Segmented parabolic adjustment of the FAST reflector utilizing spatial coordinate rotation transformation

Abstract Since the middle of the twentieth century, the advent of radio telescopes has brought a whole new way and approach to astronomical observation. For Arecibo-type radio telescopes, the tuning optimization of the active reflecting surface (working paraboloid) is the main factor affecting the reflectance calibration. In this study, leveraging the transformation of spatial coordinates through rotation, we introduce an innovative optimization model specifically for the segmented paraboloid of the Five-hundred-meter Aperture Spherical radio Telescope (Hereinafter referred to as FAST) designed by China astronomer and scientist Nan Rendong. This research constructs the equation for an ideal paraboloid and adjusts the working paraboloid to fit within specified constraints such as the orientation of the target star, the adjustment limit of the actuator, and the spatial coordinates. The study employs a combination of coarse and fine grid searches to identify and record the optimal adjustment scheme of the main cable nodes at different angles and the corresponding 2226 actuator coordinates and telescoping length, based on which we build a back propagation model to continuously modify the adjustment scheme. A combination of geometric simulation and Monte Carlo tests were also used for verification. Furthermore, we delve into the impact of variations between adjacent nodes of the modulating actuators, as well as potential longitudinal and radial changes. Compared to the conventional conditioning model, the segmented solution idealized paraboloid we created increases the original reflection efficiency from 77.92% to 95.56% in the working area of 300 m aperture, it will contributes to enhancing the overall performance of FAST.

Dynamic spatial representation of self and others’ actions in the macaque frontal cortex

Modulation of neuronal firing rates by the spatial locations of physical objects is a widespread phenomenon in the brain. However, little is known about how neuronal responses to the actions of biological entities are spatially tuned and whether such spatially tuned responses are affected by social contexts. These issues are of key importance for understanding the neural basis of embodied social cognition, such as imitation and perspective-taking. Here, we show that spatial representation of actions can be dynamically changed depending on others' social relevance and agents of action. Monkeys performed a turn-taking choice task with a real monkey partner sitting face-to-face or a filmed partner in prerecorded videos. Three rectangular buttons (left, center, and right) were positioned in front of the subject and partner as their choice targets. We recorded from single neurons in two frontal nodes in the social brain, the ventral premotor cortex (PMv) and the medial prefrontal cortex (MPFC). When the partner was filmed rather than real, spatial preference for partner-actions was markedly diminished in MPFC, but not PMv, neurons. This social context-dependent modulation in the MPFC was also evident for self-actions. Strikingly, a subset of neurons in both areas switched their spatial preference between self-actions and partner-actions in a diametrically opposite manner. This observation suggests that these cortical areas are associated with coordinate transformation in ways consistent with an actor-centered perspective-taking coding scheme. The PMv may subserve such functions in context-independent manners, whereas the MPFC may do so primarily in social contexts.

Mathematical model for calculating steady-state conditions and static characteristics of salient-pole synchronous machines

Salient-pole synchronous machines occupy a paramount position in both the generation and consumption of electrical energy. Recent achievements in the design, manufacturing, and operation of salient-pole synchronous machines are the result of successful advancements in the fields of electromechanical engineering technology, semiconductor technology, and mathematical modeling. To calculate the nominal steady-state operation of salient-pole synchronous machines and their static characteristics (no-load, angular, V-shaped, regulatory, and external), a mathematical model has been developed. Its computer implementation enhances the technical and economic performance of synchronous pole machines. During the creation of the mathematical model, the following assumptions were made: the magnetic field of the machine is conditionally divided into a working field and scattered fields; the magnetic field of the machine is flat and parallel; the magnetic field in the active layer has only a radial component, while in the stator and rotor yokes, only a tangential one; the winding conductors are located in an infinitely thin layer and distributed along the slot according to a harmonic law; losses in the steel are absent. To create the mathematical model of salient-pole synchronous machine, a system of equations for the electrical and magnetic state is formulated. To obtain equations with coefficients independent of the rotor position, the coordinate transformation method (transformation to the dq0 rectangular coordinate system stationary with respect to the rotor) was employed.

Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.

Conformal field theory on TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed space and correlators from dynamical coordinate transformations

We study the map between two descriptions of the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document} deformation of conformal field theory (CFT): one is the defining description as a deformation of CFT by the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-operator. The other is an alternative description as the undeformed CFT on the dynamical TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed space that backreacts to the state or operator insertions, reminiscent of the theory of gravity. Instead of adopting the topological gravity description, we develop a more literal CFT-based operator formalism that facilitates systematic and straightforward computations of the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformation of the stress tensor, operators, and their correlators, while rederiving known results in the literature. Along the way, we discuss the backreaction to the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed space in response to local operators and exhibit the hard-disk and free-space structures in the UV-cutoff and Hagedorn phases, respectively, suggested by Cardy-Doyon and Jiang. To capitalize on the alternative description of the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFT, we focus on the correlators of semi-heavy operators, i.e., the operators of large conformal dimension ∆ ≫ c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{c} $$\\end{document}, and show an intuitive and simple way to obtain the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed correlators from those of the undeformed CFT on the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed space via dynamical coordinate transformations. This may have implications in the holographic dual description, pointing towards a working dictionary for a class of matter correlators in the cutoff AdS picture.

Sampled‐data cooperative semi‐global robust practical output regulation for nonlinear multi‐agent systems with an uncertain leader

AbstractThis article explores the problem of sampled‐data cooperative robust practical output regulation for nonlinear multi‐agent systems whose leader system is unknown. In this study, the nonlinearities of the follower systems are not constrained by the linear growth condition. Based on the robust control technology and the adaptive control technology, a distributed output‐based sampled‐data control protocol is developed to deal with the uncertainty of the exosystem which can belong to any large known compact set. We first perform the coordinate transformation of closed‐loop system to obtain the so‐called augmented system, and then perform the stability analysis for this system. As a result, it is proven that the steady‐state tracking errors are in any small given neighborhood of the origin. Finally, the performance of the proposed controller is validated by a numerical example.

Study on rigid-flexible coupling modeling of planetary gear systems: Incorporation of the pass effect and random excitations

A rigid-flexible coupling model for the planetary gear system is developed, in which the flexibility of the ring gear, input shaft, and carrier are considered. Subsequently, rotational modal projection is proposed to simulate the meshing of the flexible ring gear at any angle of planet gear revolution, and the coordinate transformation equations are presented to establish the coupling between rigid body and rotating flexible body. These two approaches incorporate the pass effect into the coupling model. Additionally, a method employing pre-emphasized noise to simulate random excitations is introduced. The model is validated by comparing computed modal frequencies and dynamic responses with those from ANSYS software and experiment, respectively. Results indicate that the proposed method accurately simulates the modulation signal observed in the experiment. Closely matched resonances excited by random excitations are apparent in experimental and simulated acceleration spectra, highlighting the validity of the proposed method and aiding in the determination of operational system modes. In addition, analyses of parameter influences are conducted, which further reveal the dynamic characteristics of the system.

Conformal 3D Printing Algorithm for Surfaces and Its In Situ Repair Applications.

Conformal 3D printing can construct specific three-dimensional structures on the free-form surfaces of target objects, achieving in situ additive manufacturing and repair, making it one of the cutting-edge technologies in the current field of 3D printing. To further improve the repair efficacy in tissue engineering, this study proposes a conformal path planning algorithm for in situ printing in specific areas of the target object. By designing the conformal 3D printing algorithm and utilizing vector projection and other methods, coordinate transformation of the printing trajectory was achieved. The algorithm was validated, showing good adherence of the printing material to the target surface. In situ repair experiments were also conducted on human hands and pig tibia defect models, verifying the feasibility of this method and laying a foundation for further research in personalized medicine and tissue repair.

Research on the optimization methods of common points layout for survey and alignment of particle accelerators

As a fourth-generation synchrotron light source based on a diffraction-limited storage ring, Hefei Advanced Light Facility (HALF) puts forward higher requirements for the alignment accuracy of the main components. Aggregated common points result in a loss of accuracy during the coordinate transformation required by accelerator alignment. To address this challenge, we proposed two methods: “aggregated points centralization (APC)" and “uniformity-weighted algorithm (UWA)" according to different usage scenarios. APC combines uniformity with the K-means algorithm to enhance the accuracy of coordinate transformation while reducing the number of common points. UWA calculates the uniformity in different directions and assigns weights to common points, reducing the accuracy loss. Simulations demonstrate that these two methods have strong superiority and stability with significantly improved accuracy. Applications of these 2 methods in the magnet unit pre-alignment experiment and tunnel network measurement show promising results. APC in pre-alignment can reduce the cost of building common points by 26% while maintaining the coordinate conversion accuracy. In tunnel network measurement, accuracy can be increased by 28% using UWA. The methods proposed offer broad applicability in the field of particle accelerator alignment and guiding alignment solutions for HALF.

Adjustable Ultra-Light Mechanical Negative Poisson's Ratio Metamaterials with Multi-Level Dynamic Crushing Effects.

Mechanical metamaterials with multi-level dynamic crushing effects (MM-MLs) are designed in this study through coordinate transformation and mirror arrays. The mechanical effects of the diameter and length ratio of the struts and connecting rods, the Euler angles, and the cell numbers on the mechanical properties are investigated separately. MM-ML can exhibit significant two-level platform stress, and the local cells in the first platform stress stage undergo rotational motion, while the second platform stress stage mainly involves collapse compression and bending. Although increasing the length of the connecting rods can increase the range of Poisson's ratio, it will reduce the level of platform stress and energy absorption. Increasing the Euler angle will reduce the strain interval of the first platform stress and can improve the energy absorption capacity. In addition, increasing the cell number while maintaining a constant relative density can effectively enhance energy absorption. MM-ML has significant parameter controllability, can achieve different platform stress regions, different ranges of Poisson's ratios, and energy absorption requirements according to the application scenario, and can demonstrate functional diversity compared to existing research. The design scheme can provide ideas for adaptive crushing protection requirements.

Enhancing ballet posture Teaching: Evaluation of a scientific computing model with motion capture integration

To improve the effect of ballet teaching, this study used the scientific computing model integrated with motion capture to analyze and evaluate the teaching of ballet dance postures, so as to improve the intelligence of modern ballet teaching. Moreover, this study employed the coordinate transformation and D-H method to model and analyze the forward and inverse kinematics of the ballet posture teaching model, and used the Monte Carlo method to verify the correctness of the exoskeleton motion space analysis. In addition, this study established a dynamic model, and used the Lagrangian equation method for a dynamic solution to obtain the relationship between the position, velocity and torque of each component. The data analysis indicated that the ballet posture teaching system, which is based on the scientific computing model and integrated with motion capture, can play an important role in ballet teaching.

Inverse scattering transform for integrable nonisospectral hierarchy associate with Camassa-Holm equation

We initiate the process by introducing a nonisospectral Lax pair, from which we derive an integrable nonisospectral hierarchy associate with Camassa-Holm equation. Through the inverse scattering transform method, we obtain parameter expressions for the N-soliton solution of the integrable nonisospectral hierarchy associate with Camassa-Holm equation. To derive the precise expression of the solution without the parameters, a coordinate transformation is performed. In order to work out accurately the soliton solution through the Gel'fand-Levitan-Marchenko equation. Finally, we present the graphical representation of the 1-soliton solution and analyze its dynamic behavior.

Event-Triggered Adaptive Finite-Time Control Using a Fuzzy State Observer for Nonlinear Cyber-Physical Systems Under Deception Attacks.

This article presents a new event-triggered adaptive finite-time control strategy using a fuzzy state observer for a class of nonlinear cyber-physical systems (CPSs) under malicious deception attacks with a more general form. Compared with the traditional assumptions on the deception attacks in the existing results, a more general assumption on deception attacks is given in this article. During the design process, real system states are initially estimated by developing an improved state observer, which effectively addresses the problem of state unavailability. Then, a coordinate transformation technology, in which the estimated states of observer are considered, is presented to stabilize the studied system. By constructing the singularity-free finite time virtual controls, the singularity problem in the traditional finite time design algorithms is cleverly avoided. Furthermore, to minimize communication overhead, a final finite-time controller is established by using a relative threshold event-triggered scheme. The developed event-triggered adaptive finite-time control strategy guarantees that all signals in the closed-loop system are semi-globally bounded in finite time without Zeno behavior. Finally, the correctness of the proposed control strategy is validated through two simulation results.

Primary Resonances in Inclined Cantilever Beam with Tip-Mass: A Parameter-Splitting Multiple-Scales Approach

The transverse static load, resultant from self-weight, significantly impacts both the response and the nonlinear dynamic behavior of a flexible inclined cantilever with a large lumping tip mass under harmonic base motion. However, the transverse static load was not taken into account and the mode shape of a pure cantilever beam was directly adopted during Galerkin’s procedure in the formulations of a cantilever carrying a large lumping tip mass in many previous studies. In this paper, (1) the static load effect caused by the self-weight in an inclined cantilever is considered by using a coordinate transformation, (2) the efficacy of adopting a pure cantilever beam mode shape to analyze a cantilever beam carrying a large lumping mass is studied and (3) a recently proposed semi-analytical method named parameter-splitting multiple-scales method is extended to analyze the cantilever studied to examine its effectiveness. First, the extended Hamilton’s principle is utilized to formulate the equation of motion of the cantilever studied. After that, the mode shape of a pure cantilever and the exact mode shape of a cantilever carrying a lumping mass are separately adopted in Galerkin’s method to transform the partial differential equation into ordinary differential equations. The frequency-response curves of the discretized nonlinear differential equations obtained by the numerical continuation method and the parameter-splitting multiple-scales method are compared to address ① the transverse static load effect on the frequency-response and nonlinear dynamical behavior of the beam, ② the discrepancies between the resultant frequency-response curves obtained by using two different mode shapes and ③ the efficacy of the parameter-splitting multiple-scales method on solving strongly nonlinear practical problem.

Constitutive behavior of asymmetric multi-material honeycombs with bi-level variably-thickened composite architecture

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.