Journal articles: 'Finite gain theory'

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Cavaleri, Matteo, and Alfredo Donno. "On cospectrality of gain graphs." Special Matrices 10, no. 1 (January 1, 2022): 343–65. http://dx.doi.org/10.1515/spma-2022-0169.

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Abstract We define G G -cospectrality of two G G -gain graphs ( Γ , ψ ) \left(\Gamma ,\psi ) and ( Γ ′ , ψ ′ ) \left(\Gamma ^{\prime} ,\psi ^{\prime} ) , proving that it is a switching isomorphism invariant. When G G is a finite group, we prove that G G -cospectrality is equivalent to cospectrality with respect to all unitary representations of G G . Moreover, we show that two connected gain graphs are switching equivalent if and only if the gains of their closed walks centered at an arbitrary vertex v v can be simultaneously conjugated. In particular, the number of switching equivalence classes on an underlying graph Γ \Gamma with n n vertices and m m edges, is equal to the number of simultaneous conjugacy classes of the group G m − n + 1 {G}^{m-n+1} . We provide examples of G G -cospectral switching nonisomorphic graphs and we prove that any gain graph on a cycle is determined by its G G -spectrum. Moreover, we show that when G G is a finite cyclic group, the cospectrality with respect to a faithful irreducible representation implies the cospectrality with respect to any other faithful irreducible representation, and that the same assertion is false in general.

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Mattos, Lucas Prado, Manuel Ernani Cruz, and Julián Bravo-Castillero. "Finite element computation of the effective thermal conductivity of two-dimensional multi-scale heterogeneous media." Engineering Computations 35, no. 5 (July 2, 2018): 2107–23. http://dx.doi.org/10.1108/ec-11-2017-0444.

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Purpose The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium. Design/methodology/approach The methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm. Findings The effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain. Research limitations/implications The present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization. Practical implications It is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media. Originality/value The novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.

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Sharma, Anshul, C. K. Susheel, Rajeev Kumar, and V. S. Chauhan. "Active Control of Thermally Induced Vibrations in Smart Structure Instrumented with Piezoelectric Materials." Applied Mechanics and Materials 612 (August 2014): 169–74. http://dx.doi.org/10.4028/www.scientific.net/amm.612.169.

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In this paper, a finite element model of piezolaminated composite shell structure is developed using nine-noded degenerated shell element. The stiffness, mass and thermo-electro-mechanical coupling effect is incorporated in finite element modeling using first order shear deformation theory and linear piezoelectric theory. The sensor voltage is calculated using the same formulation and fuzzy logic controller is used to calculate the actuator voltage. The fuzzy logic controller is designed as double input-single output (DISO) system using 49 If-Then rules. The performance of fuzzy logic controller is compared with convention constant-gain negative feedback controller. The simulation results illustrate the superiority of fuzzy logic controller over constant-gain negative feedback controller.

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Zhao, Zhanshan, Xiaomeng Li, Jing Zhang, and Yongzhen Pei. "Terminal sliding mode control with self-tuning for coronary artery system synchronization." International Journal of Biomathematics 10, no. 03 (February 20, 2017): 1750041. http://dx.doi.org/10.1142/s1793524517500413.

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A terminal sliding mode (TSM) control with self-tuning gain algorithm is proposed for the synchronization of coronary artery system under the existence of the unmodeled dynamics and the external disturbance. Considering the sliding mode dynamics of system, a criterion of selecting the parameters is derived to reach the point of equilibrium in the finite time. The theoretic analysis based on Lyapunov theory proved that the systems with the proposed TSM control with self-tuning scheme could be stabilized in finite time. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system in finite time. This information about the bound of unmodeled dynamics and the external disturbance is not needed in advance through self-tuning the gains of controller. The results for coronary artery system synchronization simulation show that the proposed TSM controller with self-tuning achieves better robustness and adaptation against unmodeled dynamics and the external disturbance, which offer the theory basis on curing myocardial infarction.

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Deng, Xiongfeng, Yiqing Huang, and Lisheng Wei. "Adaptive Fuzzy Command Filtered Finite-Time Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Unknown Input Saturation and Unknown Control Directions." Mathematics 10, no. 24 (December 8, 2022): 4656. http://dx.doi.org/10.3390/math10244656.

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This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law.

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Zhang, Xin Yu, and Li Kun Guan. "Stress Analysis and Structure Improvement on Arm of Ladle Turret." Applied Mechanics and Materials 597 (July 2014): 336–40. http://dx.doi.org/10.4028/www.scientific.net/amm.597.336.

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Static stress analysis on arm of ladle turret is based on finite element (FE) theory and shell theory by finite element software ANSYS. In this paper, an arm subjected to a multi-axial state of stress is examined both numerically and experimentally. The hot spot strains and stresses in the connection are determined through a detailed finite element analysis (FEA) of the joint. The arm geometry is accurately modeled using FE. Check the dangerous position on the side of the arm by different safety factor. For the experimental study, a test rig is designed and used to validate the FE model. Gain the impact factor of the arm. According to finite element calculations, assesses the fatigue strength by stress ratio method and stress amplitude method on the weld.Structural improvement is performed with increasing thickness and changing the location of the force.

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Brandt, Bastian B., Gergely Endrődi, and Sebastian Schmalzbauer. "QCD at finite isospin chemical potential." EPJ Web of Conferences 175 (2018): 07020. http://dx.doi.org/10.1051/epjconf/201817507020.

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We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.

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Ma, Xin, and Fang Zhu. "Prescribed Performance Synchronization Control of Chaotic Systems with Unknown Control Gain Signs." Journal of Control Science and Engineering 2021 (July 23, 2021): 1–7. http://dx.doi.org/10.1155/2021/5160768.

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For a class of uncertain nonlinear chaotic systems with unknown control gain signs and saturated input, by means of Nussbaum function, a scheme of finite-time prescribed performance synchronization control is proposed. Here, Nussbaum function is used to eliminate the influence of unknown control gain signs, and fuzzy logic systems are used to estimate unknown functions. Lyapunov theory is used to prove that all synchronization errors converge to a predefined small performance range under the designed control method. Finally, simulation results are provided to illustrate the feasibility of the proposed method.

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Zhang, Chao, Qiang Guo, and Jing Wang. "Finite-Time Synchronizing Control for Chaotic Neural Networks." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/938612.

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This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.

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Jian, Xiong, Zengyun Wang, Aitong Xin, Yujing Chen, and Shujuan Xie. "An improved finite-time stabilization of discontinuous non-autonomous IT2 T-S fuzzy interconnected complex-valued systems: A fuzzy switching state-feedback control method." Electronic Research Archive 31, no. 1 (2022): 273–98. http://dx.doi.org/10.3934/era.2023014.

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<abstract><p>Based on the type-2 Takagi-Sugeno (IT2 T-S) fuzzy theory, a non-autonomous fuzzy complex-valued dynamical system with discontinuous interconnection function is formulated. Under the framework of Filippov, the finite-time stabilization (FTS) problem is investigated by using an indefinite-derivative Lyapunov function method, where the derivative of the constructed Lyapunov function is allowed to be positive. By designing a fuzzy switching state feedback controller involving time-varying control gain parameters, several sufficient criteria are established to determine the considered system's stability in finite time. Correspondingly, due to the time-varying system parameters and the designed time-dependent control gain coefficients, a more flexible settling time (ST) is estimated. Finally, an example is presented to confirm the proposed methodology.</p></abstract>

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Gao, Yanghua, Weidong Lou, Hailiang Lu, and Yonghua Jia. "Consensus Control of Multi-agent Robot System with State Delay Based on Fractional-Order Iterative Learning Control Algorithm." Journal Européen des Systèmes Automatisés 53, no. 6 (December 23, 2020): 771–79. http://dx.doi.org/10.18280/jesa.530603.

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This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.

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Aubrecht, Johannes, and Petros G. Voulgaris. "Minimization of the Peak-to-Peak Gain in Periodic Systems Under Full State Feedback1." Journal of Dynamic Systems, Measurement, and Control 123, no. 1 (November 8, 1985): 10–20. http://dx.doi.org/10.1115/1.1341199.

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The paper considers the minimization of the l∞-induced norm of the closed loop in linear periodically time varying (LPTV) systems when state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. It is shown that a memoryless periodically varying nonlinear controller can be constructed to achieve near-optimal performance. The construction involves the solution of several finite linear programs and generalizes to the periodic case earlier work on linear time-invariant systems (LTI).

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Sakthivel, Rathinasamy, Ramalingam Sakthivel, Boomipalagan Kaviarasan, Chao Wang, and Yong-Ki Ma. "Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling." Complexity 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/8546304.

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The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

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Thanh, Pham Tuan, Tran Xuan Tinh, Dao Phuong Nam, Dao Sy Luat, and Nguyen Hong Quang. "On finite-time output feedback sliding mode control of an elastic multi-motor system." International Journal of Power Electronics and Drive Systems (IJPEDS) 12, no. 1 (March 1, 2021): 10. http://dx.doi.org/10.11591/ijpeds.v12.i1.pp10-19.

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In this paper, the tracking control scheme is presented using the framework of finite-time sliding mode control (SMC) law and high-gain observer for disturbed/uncertain multi-motor driving systems under the consideration multi-output systems. The convergence time of sliding mode control is estimated in connection with linear matrix inequalities (LMIs). The input state stability (ISS) of proposed controller was analyzed by Lyapunov stability theory. Finally, the extensive simulation results are given to validate the advantages of proposed control design.

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Chen, Dechuan, Jin Li, Jianwei Hu, Xingang Zhang, and Shuai Zhang. "Optimal Channel Training Design for Secure Short-Packet Communications." Sensors 23, no. 3 (January 17, 2023): 1068. http://dx.doi.org/10.3390/s23031068.

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Physical layer security is a promising technique to ensure the confidentiality of short-packet communications, since no additional channel uses are needed. Motivated by the fact of finite coding blocklength in short-packet communications, we attempt to investigate the problem of how many the channel uses utilized for channel training should be allocated to perform secure communications. Based on the finite blocklength information theory, we derive a closed-form expression to approximate the average achievable secrecy throughput. To gain more insights, we also present the asymptotic average secrecy throughput under two special cases, i.e., high signal-to-noise ratio (SNR) and infinite blocklength. Moreover, we determine the optimal channel training length to maximize the average secrecy throughput under the reliability constraint and given blocklength. Numerical results are provided to validate the analysis and demonstrate that the performance gain achieved by the optimal channel training length is remarkable, relative to other benchmark schemes.

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Chuaqui, Tomás RC, Carla MC Roque, and Pedro Ribeiro. "Active vibration control of piezoelectric smart beams with radial basis function generated finite difference collocation method." Journal of Intelligent Material Systems and Structures 29, no. 13 (June 20, 2018): 2728–43. http://dx.doi.org/10.1177/1045389x18778363.

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A local collocation method based on finite difference generated radial basis functions considering supplementary polynomials is used to solve the governing equations of cantilever piezoelectric smart beams. The natural modes of vibration of a bimorph and a three-layered smart beam with an interior aluminium core are analysed for both open-circuit and closed-circuit electrical boundary conditions. Very accurate results are obtained at a low computational cost. Subsequently, a constant gain velocity feedback active vibration control system is implemented, and the time and frequency response functions of both beams subjected to initial impulse and displacement conditions are investigated. Different values of the applied gain and varying thickness of the piezoelectric layers are analysed. The governing equations are established using equivalent-single-layer first-order-shear-deformation theory with through-the-thickness quadratic layerwise electric potential for improved accuracy.

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Cai, Shan Bing, Jun Yan Liu, and Han Qing Cao. "Study on the Analysis and Pre-Control Technology of Vertical Deformation in Construction Process of the Super High-Rise Steel-Concrete Composite Structure." Applied Mechanics and Materials 578-579 (July 2014): 584–88. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.584.

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Puli central mall, with super high-rise steel-concrete composite structure, is one of the landmarks in the city of Jinan. During the construction process, the vertical deformation of the structure is crucial. This paper based on the finite element analysis software Ansys, uses the refined finite element method to numerically model the elastic, creep and shrinkage deformation during the construction process, in order to gain the vertical deformation and the difference of deformation between core and frame. The pre-control methods for reducing vertical deformation are proposed for design and construction based on the modeling results and the relevant theory, beneficial to guide the construction process for this project.

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Aşırım, Özüm Emre, and Mustafa Kuzuoğlu. "Numerical Study of Resonant Optical Parametric Amplification via Gain Factor Optimization in Dispersive Microresonators." Photonics 7, no. 1 (December 25, 2019): 5. http://dx.doi.org/10.3390/photonics7010005.

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The achievement of wideband high-gain optical parametric amplification has not been shown in micrometer-scale cavities. In this paper we have computationally investigated the optical parametric amplification process in a few micrometer-long dispersive microresonator. By performing a gain medium resonance frequency dependent analysis of optical parametric amplification, we have found that it is possible to achieve a wideband high-gain optical amplification in a dispersive microresonator. In order to account for the effects of dispersion (modeled by the polarization damping coefficient) and the resonance frequency of the gain medium on optical parametric amplification, we have solved the wave equation in parallel with the nonlinear equation of electron cloud motion, using the finite difference time domain method. Then we have determined the resonance frequency values that yield an enhanced or a resonant case of optical parametric amplification, via gain factor optimization. It was observed that if the microresonator is more dispersive (has a lower polarization damping coefficient), then there are more resonance frequencies that yield an optical gain resonance. At these gain resonances, a very wideband, high-gain optical amplification seems possible in the micron scale, which, to our knowledge, has not been previously reported in the context of nonlinear wave mixing theory.

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Nguyen, Van-Cuong, Phu-Nguyen Le, and Hee-Jun Kang. "An Active Fault-Tolerant Control for Robotic Manipulators Using Adaptive Non-Singular Fast Terminal Sliding Mode Control and Disturbance Observer." Actuators 10, no. 12 (December 15, 2021): 332. http://dx.doi.org/10.3390/act10120332.

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In this study, a fault-tolerant control (FTC) tactic using a sliding mode controller–observer method for uncertain and faulty robotic manipulators is proposed. First, a finite-time disturbance observer (DO) is proposed based on the sliding mode observer to approximate the lumped uncertainties and faults (LUaF). The observer offers high precision, quick convergence, low chattering, and finite-time convergence estimating information. Then, the estimated signal is employed to construct an adaptive non-singular fast terminal sliding mode control law, in which an adaptive law is employed to approximate the switching gain. This estimation helps the controller automatically adapt to the LUaF. Consequently, the combination of the proposed controller–observer approach delivers better qualities such as increased position tracking accuracy, reducing chattering effect, providing finite-time convergence, and robustness against the effect of the LUaF. The Lyapunov theory is employed to illustrate the robotic system’s stability and finite-time convergence. Finally, simulations using a 2-DOF serial robotic manipulator verify the efficacy of the proposed method.

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Xie, Jinhua, Rui Huo, Yanfeng Guan, and Zhen Zhou. "Application of Energy Finite Element Method in Active Vibration Control of Piezoelectric Intelligent Beam." Advances in Acoustics and Vibration 2012 (December 20, 2012): 1–10. http://dx.doi.org/10.1155/2012/819725.

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Based on the transmission and equilibrium relationship of vibration energy in beam-like structures, the Galerkin weighted residual method was applied to equation discretization. An equivalent transformation of feedback element was suggested to develop the Energy Finite Element model of a composite piezoelectric cantilever beam driven by harmonic excitation on lateral direction, with both systems with and without time delay being studied and the power input estimation of harmonic excitation was discussed for the resolution of Energy Finite Element function. Then the energy density solutions of the piezoelectric coupling beam through Energy Finite Element Method (EFEM) and classical wave theory were compared to verify the EFEM model, which presented a good accordance. Further investigation was undertaken about the influence of control parameters including the feedback gain and arrangement of piezoelectric patches on characteristics of system energy density distribution.

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Zhou, R., and L. Shafai. "Directivity enhancement by layered radomes." Canadian Journal of Physics 73, no. 7-8 (July 1, 1995): 444–51. http://dx.doi.org/10.1139/p95-064.

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Single and layered radomes are often used to protect radiating elements. A two-dimensional analysis is used to investigate their influence on the antenna directivity and radiation patterns. Image-theory and integral-equation methods are used to formulate the problem for a line source and layered dielectrics of finite length over a ground plane, and solved numerically using the moment method. It is shown that, for a sufficiently long single-layer slab, the directivity enhancement is approximately equal to the square root of its relative permittivity. Properly truncating the slab can even improve the directivity. The optimum length of a finite dielectric slab is determined to maximize the directivity. For multilayer slabs, the directivity enhancement is much greater and they can be used with low-permittivity dielectrics to simulate a single-layer one of higher permittivity. Frequency dependency of the enhanced gain is also studied. Useful information for how to incorporate the radome parameters into the antenna design and use it for gain or directivity enhancement is provided.

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Wang, Sheng Song, Ping Hu, and Hai Ni Yao. "Design of Test Bench for Flyweel of the Shaft-Seal Nuclear Coolant Pump and ANSYS Analysis." Applied Mechanics and Materials 644-650 (September 2014): 559–62. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.559.

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Due to the test requirements of flyweel of the shaft-seal nuclear coolant pump, design the structure of the test bench.Based on the theory of finite element analysis,use ANSYS software carries on its ststic analysis to gain the displacement and the stress form in order to check the strength and stiffness,and then carries on modal analysis to get its first six natural frequency and vibration in order to verify the rationality of design.CLC :TH122

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Cheng, Guifang, Zhishuai Ding, and Jianyin Fang. "Dissipativity Analysis of Linear State/Input Delay Systems." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/458243.

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This paper discusses dissipativity problem for system of linear state/input delay equations. Motivated by dissipativity theory of control systems, we choose a new quadratic supply rate. Using the concept of dissipativity, necessary and sufficient conditions for the linear state/input delay systems to be dissipative and exponentially dissipative are derived. The connection of dissipativity with stability is also considered. Finally, passivity and finite gain are explored, correspondingly. The positive-real and bounded-real lemmas are derived.

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Ye, Mengyang, Guoqin Gao, Junwen Zhong, and Qiuyue Qin. "Finite-Time Dynamic Tracking Control of Parallel Robots with Uncertainties and Input Saturation." Sensors 21, no. 9 (April 24, 2021): 2996. http://dx.doi.org/10.3390/s21092996.

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This paper considers the finite-time dynamic tracking control for parallel robots with uncertainties and input saturation via a finite-time nonsingular terminal sliding mode control scheme. A disturbance observer is designed to estimate the lumped disturbance in the dynamic model of the parallel robot, including modeling errors, friction and external disturbance. By introducing the fractional exponential powers into the existing asymptotic convergent auxiliary system, a novel finite-time convergent auxiliary system is constructed to compensate for input saturation. The finite-time nonsingular terminal sliding mode control is proposed based on the disturbance estimation and the state of the novel auxiliary system, so that the convergence performance, control accuracy and robustness are improved. Due to the estimation and compensation for the lumped disturbance, the inherent chattering characteristic of sliding mode control can be alleviated by reducing the control gain. The finite-time stability of the closed-loop system is proved with Lyapunov theory. Finally, simulation and experimental research on the dynamic control of a conveying parallel robot are carried out to verify the effectiveness of the proposed method.

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Yang, Yan Li, and Zhen Xing Zhang. "Sliding Mode Variable Structure Control of Active Magnetic Bearings Using Boundary Layer Approach." Advanced Materials Research 411 (November 2011): 213–17. http://dx.doi.org/10.4028/www.scientific.net/amr.411.213.

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To solve the chattering problem caused by the general sliding mode control in the active magnetic bearing control, a boundary layer approach is used in the controller design in this paper. The dynamic model of the active magnetic bearing is built firstly, and then a saturation function is employed to substitute for the sign function in the controller based on the Lyapunov theory to approximately realize infinite gain with finite gain. Finally, the performance of the controller is simulated, and compared with the general sliding mode control. The results show that the disadvantage of chattering can be effectively reduced by using the boundary layer approach, the rotor-s quick adjusting and steady levitation are achieved, and the controller has high tracking precision and good robustness.

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Liu, Jin, Gang Ding, and Zhan Shan Zhao. "Design Higher Order Sliding Mode Controller for a Class of SISO Uncertain Nonlinear System." Applied Mechanics and Materials 397-400 (September 2013): 1442–45. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1442.

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A higher order sliding mode control design is considered for a class of uncertain nonlinear systems with unknown bounded uncertainties. This method can be viewed as the finite time stabilization based on integral sliding mode control and geometric homogeneity. Based on the Lyapunov theory, the system trajectory is guaranteed to approach the sliding surface. Only one adaptive gain parameter is required. The stability and the robustness of the control system are proven. Numerical experiments illustrate the satisfactory performance of the proposed control methodology.

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Wang, Baofang, Sheng Li, and Qingwei Chen. "Robust adaptive finite-time tracking control of uncertain mechanical systems with input saturation and deadzone." Transactions of the Institute of Measurement and Control 41, no. 2 (May 3, 2018): 560–72. http://dx.doi.org/10.1177/0142331218767490.

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This paper addresses the problem of robust adaptive finite-time tracking control for a class of mechanical systems in the presence of model uncertainties, unknown external disturbances, and input nonlinearities containing saturation and deadzone. Without imposing any conditions on the model uncertainties, radial basis function neural networks are used to approximate unknown nonlinear continuous functions, and an adaptive tracking control scheme is proposed by exploiting the recursive design method. It is shown that the input saturation and deadzone model can be expressed as a simple linear system with a time-varying gain and bounded disturbance. An adaptive compensation term for the upper bound of the lumped disturbance is introduced. The semi-global finite-time uniform ultimate boundedness of the corresponding closed-loop tracking error system is proved with the help of the finite-time Lyapunov stability theory. Finally, an example is given to demonstrate the effectiveness of the proposed method.

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BAKRI, Ayoub EL, and Ismail Boumhidi. "Finite-Frequency Observer-Based Fault Estimation and Fault-Tolerant Control for Wind Turbine." International Journal on Electrical Engineering and Informatics 12, no. 3 (September 30, 2020): 571–85. http://dx.doi.org/10.15676/ijeei.2020.12.3.9.

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This paper deals with the design problem of a robust fault estimation (FE)/ faulttolerant control (FTC) scheme for wind turbines (WT) in the finite frequency domain (FF). First, an adaptive fuzzy H∞ observer is constructed to simultaneously reconstruct the WT states and faults within the FF range. Throughout the observer analysis, it is only assumed that faults, uncertainties, and disturbances are bounded, which coincide with the practical requirements. In the second stage, based on the observer information, an active FTC method is proposed to stabilize the faulty WT. The controller and observer gain matrices are extracted employing the Lyapunov theory, where constraints are expressed as a set of linear matrix inequalities (LMIs). The Simulation results illustrate the best performances of the suggested strategy.

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Marin, Marin, Aatef Hobiny, and Ibrahim Abbas. "The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method." Mathematics 9, no. 14 (July 7, 2021): 1606. http://dx.doi.org/10.3390/math9141606.

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In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

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Wang, Bing, Yan Ping Qian, and Yi Ming Zhang. "Hamiltonian Robust Controller Design of Permanent Magnet Wind Generators." Applied Mechanics and Materials 263-266 (December 2012): 709–12. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.709.

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In this paper, the dual-input nonlinear controller of permanent magnet wind generators was designed based on energy dissipation theory and Hamiltonian energy approach. Under the action of the Hamiltonian controller, the closed-loop system is asymptotically stable on case of no disturbances and finite-gain L2 stable in the presence of disturbances. The Hamiltonian energy approach provides us a physical insight and a new way to the controller design of nonlinear systems. The simulation results show the effectiveness of the proposed robust controller.

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HOVDEBO, JORDAN L., MARTÍN KRUCZENSKI, DAVID MATEOS, ROBERT C. MYERS, and DAVID J. WINTERS. "HOLOGRAPHIC MESONS: ADDING FLAVOR TO THE ADS/CFT DUALITY." International Journal of Modern Physics A 20, no. 15 (June 20, 2005): 3428–33. http://dx.doi.org/10.1142/s0217751x05026728.

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We study mesons in an [Formula: see text] super Yang-Mills theory with fundamental matter from its dual string theory on AdS5 × S5 with a D7-brane probe. For quarks with a finite mass mq, the meson spectrum is discrete and exhibits a mass gap of order [Formula: see text]. The spectrum of mesons with large spin J is obtained from semiclassical rotating open strings attached to the D7-brane. It displays Regge behaviour for [Formula: see text] whereas for [Formula: see text] it corresponds to that of two non-relativistic quarks bound by a Coulomb potential. We calculate 〈 Tr F2〉 around an isolated quark, to gain insight into the Regge behaviour of the spinning mesons.

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Sacher, William, and Peter Bartello. "Sampling Errors in Ensemble Kalman Filtering. Part I: Theory." Monthly Weather Review 136, no. 8 (August 1, 2008): 3035–49. http://dx.doi.org/10.1175/2007mwr2323.1.

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Abstract This paper discusses the quality of the analysis given by the ensemble Kalman filter in a perfect model context when ensemble sizes are limited. The overall goal is to improve the theoretical understanding of the problem of systematic errors in the analysis variance due to the limited size of the ensemble, as well as the potential of the so-called double-ensemble Kalman filter, covariance inflation, and randomly perturbed analysis techniques to produce a stable analysis—that is to say, one not subject to filter divergence. This is achieved by expressing the error of the ensemble mean and the analysis error covariance matrix in terms of the sampling noise in the background error covariance matrix (owing to the finite ensemble estimation) and by comparing these errors for all methods. Theoretical predictions are confirmed with a simple scalar test case. In light of the analytical results obtained, the expression of the optimal covariance inflation factor is proposed in terms of the limited ensemble size and the Kalman gain.

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Yang, Zi-Xian, Chia-Yu Kuo, and Gray Lin. "Simulation of Photonic-Crystal Surface-Emitting Lasers with Air-Hole and Air-Pillar Structures." Photonics 8, no. 6 (May 27, 2021): 189. http://dx.doi.org/10.3390/photonics8060189.

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Photonic-crystal surface-emitting lasers (PC-SELs), with and without regrowth, are theoretically simplified as air-hole and air-pillar structures, respectively. In this paper, square-latticed air-hole and air-pillar PC-SELs are simulated by a three-dimensional coupled-wave theory model and the design guideline is illustrated with a PC basis of a right isosceles triangular and double circular shapes. The optimum PC filling factor is determined by infinite PC cavity analysis and the slope efficiency of finite-size PC-SEL is then calculated for the lowest threshold band-edge mode. In comparison with air-hole PC-SEL, air-pillar PC-SEL exhibits lower threshold gain, larger gain discrimination but lower slope efficiency. To achieve slope efficiency of comparable value, the cavity area of air-pillar PC-SEL is about four times larger than that of air-hole PC-SEL.

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Naiemy, Yahiea Al, Taha Elwi, Lajos Nagy, and Thomas Zwick. "A Systematic Analysis and Design of a High Gain Microstrip Antenna based on a Single EBG Layer." Infocommunications journal, no. 4 (2018): 22–30. http://dx.doi.org/10.36244/icj.2018.4.4.

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In this paper, an Electromagnetic Band Gap (EBG) lens of a single layer is invented to improve the gain of a truncated slotted square patch antenna for the Wi-Fi applications. The proposed EBG lens is structured from 55 planar array. The individual unit cell is basically shaped as a couple of a split concave conductive patch. The proposed EBG struc- ture performance is tested numerically using Finite Integration Technique (FIT) formulations of CSTMWS and analytically using circuit theory. Then, the antenna performance in terms of |S11|, the boresight gain, and radiation patterns are reported and compared to the performance before introducing the EBG lens to identify the significant enhancements. The proposed EBG antenna is simulated numerically inside FIT formulations of CSTMWS time domain (TD) solver. A significant gain enhancement of 11.1 dBi at 2.45 GHz and a front to back ratio (F/B) about 22 dB are achieved after introducing the EBG lens. The antenna performance is validated using a frequency domain (FD) solver based CSTMWS formulations to obtain excellent agreements between the two invoked methods.

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Pashchenko, Dmitry V., Dmitry A. Trokoz, Alexey I. Martyshkin, Mihail P. Sinev, and Boris L. Svistunov. "Search for a substring of characters using the theory of non-deterministic finite automata and vector-character architecture." Bulletin of Electrical Engineering and Informatics 9, no. 3 (June 1, 2020): 1238–50. http://dx.doi.org/10.11591/eei.v9i3.1720.

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The paper proposed an algorithm which purpose is searching for a substring of characters in a string. Principle of its operation is based on the theory of non-deterministic finite automata and vector-character architecture. It is able to provide the linear computational complexity of searching for a substring depending on the length of the searched string measured in the number of operations with hyperdimensional vectors when repeatedly searching for different strings in a target line. None of the existing algorithms has such a low level of computational complexity. The disadvantages of the proposed algorithm are the fact that the existing hardware implementations of computing systems for performing operations with hyperdimensional vectors require a large number of machine instructions, which reduces the gain from this algorithm. Despite this, in the future, it is possible to create a hardware implementation that can ensure the execution of operations with hyperdimensional vectors in one cycle, which will allow the proposed algorithm to be applied in practice.

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Fabien, B. C. "Controller Gain Selection for an Electromagnetic Suspension Under Random Excitation." Journal of Dynamic Systems, Measurement, and Control 115, no. 1 (March 1, 1993): 156–65. http://dx.doi.org/10.1115/1.2897391.

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This paper considers the modeling and control of a single axis electromagnetic suspension for vibration isolation. Here, the nonlinear dynamic equations for the suspension are derived using a lumped-parameter model of the system that includes factors for flux leakage, fringing and finite permeability of the materials. To study the vibration isolation characteristics a set of linearized dynamic equations are used. The feedback signals considered are the air gap size, the absolute velocity of the isolated load and the current in the coil. Stability boundary plots that illustrate the domain of controller gains that will stabilize the system are presented. It is shown that feedback stabilization can be achieved without current feedback. The paper also considers the design of state feedback controllers that (i) minimize the mean square absolute displacement response of the suspension and (ii) minimize a measure of the system energy dissipation. In both cases the suspension system is assumed to be excited by random white noise disturbances. It is shown that near optimum disturbance attenuation and energy dissipation can be achieved without current feedback. Procedures for selecting these suboptimum controller gains are suggested. The paper compares the suboptimum controller gains with the state feedback gains obtained using Linear Quadratic optimal control theory. It is shown that the disturbance attenuation characteristics of the electromagnetic suspension can be made to be superior to that of a passive isolation system. Experimental results are also presented.

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Zhou, Zengcheng, Guoyuan Tang, Ruikun Xu, Lijun Han, and Maolin Cheng. "A Novel Continuous Nonsingular Finite–Time Control for Underwater Robot Manipulators." Journal of Marine Science and Engineering 9, no. 3 (March 3, 2021): 269. http://dx.doi.org/10.3390/jmse9030269.

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In this paper, the tracking control problem of underwater robot manipulators is investigated under the influence of the lumped disturbances, including unknown ocean current disturbances and parameter uncertainties. The proposed novel continuous nonsingular finite–time (CNFT) control method is twofold. Firstly, the modified adaptive super–twisting algorithm (ASTA) is proposed with a nonsingular fast terminal sliding mode (NFTSM) manifold to guarantee the finite–time convergence both in the sliding mode phase and the reaching phase. Secondly, a higher–order super–twisting disturbance observer (HOSTDO) is exploited to attenuate the effects of the lumped disturbances. Considering the time–varying gain matrix of the closed–loop control system, the bounded stability is strictly proved via the Lyapunov theory. Hence, the superiority of the proposed controller is singularity–free, fast convergence, chattering–free, high steady–state tracking performance, and good robustness by resorting to the methods of CNFT control and ASTA in combination with a disturbance observer. Finally, numerical simulations are conducted on a two degree–of–freedom (DOF) underwater robot manipulator to demonstrate the effectiveness and high tracking performance of the designed controller.

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Fan, Wenru, and Bailing Tian. "Adaptive Multivariable Super-Twisting Sliding Mode Controller and Disturbance Observer Design for Hypersonic Vehicle." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5291912.

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A multivariable super-twisting sliding mode controller and disturbance observer with gain adaptation, chattering reduction, and finite time convergence are proposed for a generic hypersonic vehicle where the boundary of aerodynamic uncertainties exists but is unknown. Firstly, an input-output linearization model is constructed for the purpose of controller design. Then, the sliding manifold is designed based on the homogeneity theory. Furthermore, an integrated adaptive multivariable super-twisting sliding mode controller and disturbance observer are designed in order to achieve the tracking for step changes in velocity and altitude. Finally, some simulation results are provided to verify the effectiveness of the proposed method.

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Zhang, Qiang, S. Shelley, and R. J. Allemang. "Active Damping Design of Flexible Structures Based on SISO and SIMO Noncollocated Sensor-Actuator Velocity Feedback." Journal of Dynamic Systems, Measurement, and Control 113, no. 2 (June 1, 1991): 259–66. http://dx.doi.org/10.1115/1.2896373.

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An active damping design technique based on single input velocity feedback is presented in this paper. The stability conditions for each individual mode in SISO and SIMO velocity feedback are demonstrated. Since these stability conditions are derived using modal information, it is appropriate to incorporate this technique with the commonly used dynamic analysis techniques, such as experimental modal analysis and finite element analysis, for active damping design. Based on these stability conditions, two active damping design algorithms are proposed: 1) Constrained Least Squares Feedback Gain Computation, and 2) Optimal Feedback Gain Computation With Flexible Damping Factors. The first algorithm is a straightforward method to find the feedback vector for the given damping factors and the modal frequencies. The second algorithm is based on an optimization process which allows freedom in chosing the desired damping factors. The problem of locating the actuator and sensors is also discussed in this paper. The stability theory and active damping design technique are verified by an experimental example.

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Bao, Wei Cheng, Hong Chen, and Yan Mei Liang. "Vibration Analysis on Convey Paper Belt of Infeed Unit." Applied Mechanics and Materials 262 (December 2012): 377–81. http://dx.doi.org/10.4028/www.scientific.net/amm.262.377.

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The precondition of improve the printing press velocity is to maintain the minimum vibration of infeed unit within the range of press speed. Taking advantage of the equivalent relation between the formula of infinitesimal energy and the classic beam theory, the vibration of convey paper belt can be converted into the problem of the beam be stretched and be compressed, and then we utilize the finite element simulation technology to conduct model analysis for the convey paper belt. When the numerical of the belt speed gain ,both the vibration and shape distortion reach the maximum, as well as speed of the infeed unit will be influenced most.

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ADAMS, S. D. M., K. D. CHEREDNICHENKO, R. V. CRASTER, and S. GUENNEAU. "High-frequency spectral analysis of thin periodic acoustic strips: Theory and numerics." European Journal of Applied Mathematics 21, no. 6 (July 27, 2010): 557–90. http://dx.doi.org/10.1017/s0956792510000215.

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This paper is devoted to the study of the asymptotic behaviour of the high-frequency spectrum of the wave equation with periodic coefficients in a ‘thin’ elastic strip Ση=(0, 1)×(−η/2, η/2), η > 0. The main geometric assumption is that the structure period is of the order of magnitude of the strip thickness η and is chosen in such a way that η−1 is a positive large integer. On the boundary ∂Ση, we set Dirichlet (clamped) or Neumann (traction-free) boundary conditions. Aiming to describe sequences of eigenvalues of order η−2 in the above problem, which correspond to oscillations of high frequencies of order η−1, we study an appropriately rescaled limit of the spectrum. Using a suitable notion of two-scale convergence for bounded operators acting on two-scale spaces, we show that the limiting spectrum consists of two parts: the Bloch (or band) spectrum and the ‘boundary’ spectrum. The latter corresponds to sequences of eigenvectors concentrating on the vertical boundaries of Ση, and is characterised by a problem set in a semi-infinite periodic strip with either clamped or stress-free boundary conditions. Based on the observation that some of the related eigenvalues can be found by solving an appropriate periodic-cell problem, we use modal methods to investigate finite-thickness semi-infinite waveguides. We compare our results with those for finite-thickness infinite waveguides given in Adams et al. (Proc. R. Soc. Lond. A, vol. 464, 2008, pp. 2669–2692). We also study infinite-thickness semi-infinite waveguides in order to gain insight into the finite-height analogue. We develop an asymptotic algorithm making use of the unimodular property of the modal method to demonstrate that in the weak contrast limit, and when wavenumber across the guide is fixed, there is at most one surface wave per gap in the spectrum. Using the monomode property of the waveguide we can consider the gap structure for the nth mode, when doing so, for traction-free boundaries, we find exactly one surface wave in each n-band gap.

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He, Yonghui, Jibin Jiang, Hischuan Huang, Shufang Zhuo, and Yanfeng Wu. "Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements." Discrete Dynamics in Nature and Society 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/1516028.

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The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena.

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YU, M., and Y. KAKEHASHI. "STRONG FERROMAGNETISM IN AMORPHOUS FE-NI ALLOYS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 930–33. http://dx.doi.org/10.1142/s0217979293002006.

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We elucidate the magnetic properties of amorphous Fe-Ni alloys by combining the geometrical-mean model for the ground-state electronic structure calculations of amorphous alloys with the finite-temperature theory of metallic magnetism. The numerical results show the strong ferromagnetism in the region 0.1≤c≤0.8 and the shift of the Curie-temperature maximum to the higher Fe concentration in agreement with the experimental data. We have clarified that these behaviors are not simply due to the volume change, but due to the change of electronic structure which causes the magnetic energy gain. The agreement between the calculated concentration dependence of effective Bohr magneton number and the experimental data for liquid alloys also supports our theoretical results.

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Barsotti, Jamison, and Rob Carman. "Burnside rings of fusion systems and their unit groups." Journal of Group Theory 23, no. 4 (July 1, 2020): 709–29. http://dx.doi.org/10.1515/jgth-2019-0145.

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AbstractFor a saturated fusion system {\mathcal{F}} on a p-group S, we study the Burnside ring of the fusion system {B(\mathcal{F})}, as defined by Matthew Gelvin and Sune Reeh, which is a subring of the Burnside ring {B(S)}. We give criteria for an element of {B(S)} to be in {B(\mathcal{F})} determined by the {\mathcal{F}}-automorphism groups of essential subgroups of S. When {\mathcal{F}} is the fusion system induced by a finite group G with S as a Sylow p-group, we show that the restriction of {B(G)} to {B(S)} has image equal to {B(\mathcal{F})}. We also show that, for {p=2}, we can gain information about the fusion system by studying the unit group {B(\mathcal{F})^{\times}}. When S is abelian, we completely determine this unit group.

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Zhang, Jianhua, Yang Li, and Wenbo Fei. "Neural Network-Based Nonlinear Fixed-Time Adaptive Practical Tracking Control for Quadrotor Unmanned Aerial Vehicles." Complexity 2020 (September 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/8828453.

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This brief addresses the position and attitude tracking fixed-time practical control for quadrotor unmanned aerial vehicles (UAVs) subject to nonlinear dynamics. First, by combining the radial basis function neural networks (NNs) with virtual parameter estimating algorithms, a NN adaptive control scheme is developed for UAVs. Then, a fixed-time adaptive law is proposed for neural networks to achieve fixed-time stability, and convergence time is dependent only on control gain parameters. Based on Lyapunov analyses and fixed-time stability theory, it is proved that the fixed-time adaptive neural network control is finite-time stable and convergence time is dependent with control parameters without initial conditions. The effectiveness of the NN fixed-time control is given through a simulation of the UAV system.

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Khatir, A., Z. Bouchama, S. Benaggoune, and N. Zerroug. "Indirect adaptive fuzzy finite time synergetic control for power systems." Electrical Engineering & Electromechanics, no. 1 (January 4, 2023): 57–62. http://dx.doi.org/10.20998/2074-272x.2023.1.08.

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Introduction. Budget constraints in a world ravenous for electrical power have led utility companies to operate generating stations with full power and sometimes at the limit of stability. In such drastic conditions the occurrence of any contingency or disturbance may lead to a critical situation starting with poorly damped oscillations followed by loss of synchronism and power system instability. In the past decades, the utilization of supplementary excitation control signals for improving power system stability has received much attention. Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp low-frequency oscillations caused by load disturbances or short-circuit faults. Problem. Adaptive power system stabilizers have been proposed to adequately deal with a wide range of operating conditions, but they suffer from the major drawback of requiring parameter model identification, state observation and on-line feedback gain computation. Power systems are nonlinear systems, with configurations and parameters that fluctuate with time that which require a fully nonlinear model and an adaptive control scheme for a practical operating environment. A new nonlinear adaptive fuzzy approach based on synergetic control theory which has been developed for nonlinear power system stabilizers to overcome above mentioned problems. Aim. Synergetic control theory has been successfully applied in the design of power system stabilizers is a most promising robust control technique relying on the same principle of invariance found in sliding mode control, but without its chattering drawback. In most of its applications, synergetic control law was designed based on an asymptotic stability analysis and the system trajectories evolve to a specified attractor reaching the equilibrium in an infinite time. In this paper an indirect finite time adaptive fuzzy synergetic power system stabilizer for damping local and inter-area modes of oscillations for power systems is presented. Methodology. The proposed controller design is based on an adaptive fuzzy control combining a synergetic control theory with a finite-time attractor and Lyapunov synthesis. Enhancing existing adaptive fuzzy synergetic power system stabilizer, where fuzzy systems are used to approximate unknown system dynamics and robust synergetic control for only providing asymptotic stability of the closed-loop system, the proposed technique procures finite time convergence property in the derivation of the continuous synergetic control law. Analytical proofs for finite time convergence are presented confirming that the proposed adaptive scheme can guarantee that system signals are bounded and finite time stability obtained. Results. The performance of the proposed stabilizer is evaluated for a single machine infinite bus system and for a multi machine power system under different type of disturbances. Simulation results are compared to those obtained with a conventional adaptive fuzzy synergetic controller.

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Dular, Patrick, Patrick Kuo-Peng, Mauricio Valencia Ferreira da Luz, and Laurent Krahenbuhl. "Model refinements of transformers via a subproblem finite element method." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 1 (January 3, 2017): 309–19. http://dx.doi.org/10.1108/compel-03-2016-0125.

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Purpose This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings. Design/methodology/approach The progressive modeling of transformers is performed via a subproblem (SP) FE method. A complete problem is split into SPs with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, one-dimensional to two-dimensional to three-dimensional models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings and homogenized to fine models of cores and coils, with any coupling of these changes. Findings The proposed unified procedure efficiently feeds each SP via interface conditions (ICs), which lightens mesh-to-mesh sources transfers and quantifies the gain given by each refinement on both local fields and global quantities, with a clear view on its significance to justify its usefulness, if any. It can also help in education with a progressive understanding of the various aspects of transformer designs. Originality/value Models of different accuracy levels are sequenced with successive additive corrections supported by different adapted meshes. The way the sources act at each correction step, up to the full models with their actual geometries, is given a particular care and generalized, allowing the proposed unified procedure. For all the considered corrections, the sources are always of IC type, thus only needed in layers of FE along boundaries, which lightens the required mesh-to-mesh projections between subproblems.

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Diamond, Phil, Peter Kloeden, and Igor Vladimirov. "Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices." Journal of Applied Mathematics and Stochastic Analysis 16, no. 3 (January 1, 2003): 209–31. http://dx.doi.org/10.1155/s1048953303000169.

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Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

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Selby, John H., Carlo Maria Scandolo, and Bob Coecke. "Reconstructing quantum theory from diagrammatic postulates." Quantum 5 (April 28, 2021): 445. http://dx.doi.org/10.22331/q-2021-04-28-445.

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A reconstruction of quantum theory refers to both a mathematical and a conceptual paradigm that allows one to derive the usual formulation of quantum theory from a set of primitive assumptions. The motivation for doing so is a discomfort with the usual formulation of quantum theory, a discomfort that started with its originator John von Neumann. We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbone of quantum theory concerns the manner in which systems and processes compose. Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. Therefore we first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the ‘fully quantum’ systems as the final step. We propose two novel alternative manners of doing so, ‘no-leaking’ (roughly that information gain causes disturbance) and ‘purity of cups’ (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups & caps. Additionally, we show how the standard purification postulate can be seen as an immediate consequence of the symmetric purification postulate and purity of cups. Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a. CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can be subsumed under process theories. Secondly, we argue that the ‘sharp dagger’ is indeed the right choice of a dagger structure as this sharpness is vital to the reconstruction.

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Wang, Yu, Fu Gang Yan, P. Wang, Cai Xu Yue, and Xian Li Liu. "Finite Element Analysis of Precision Hard Cutting Using Different Cutting Edge Preparation." Applied Mechanics and Materials 10-12 (December 2007): 353–58. http://dx.doi.org/10.4028/www.scientific.net/amm.10-12.353.

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Machining hardened steels has become an important manufacturing process, particularly in the automotive and bearing industries. Hardened steel GCr15 with its harness between HRC50 and HRC65 is one kind of more difficult machining material. Abrasive processes such as grinding have typically been required to machine hardened steels, but advances in machine tools and a new cutting material of polycrystalline cubic boron nitride (PCBN) have allowed hard turning on modern lathes to seems to gain an ever increasing industrial acceptance as an economically and environmentally friendly alternative to many grinding applications. In this paper, based on large deformation theory and updated Lagrangian procedure, a coupled thermo-mechanical plane strain orthogonal precision cutting model with general finite element analysis software is developed to the influence of cutting edge preparation on the cutting of GCr15 with PCBN tool, such as cutting forces, shear angle, and cutting temperature. The three major designs of cutting edge preparation are used on most commercial cutting inserts: a) sharp edge, b) honed edge, and c) chamfer edge. The friction between the tool and the chip is assumed to follow a shear model and the local adaptive remeshing technique is used for the formation of chip. The calculated principle cutting forces are compared with published data and found to be in good agreement. The simulation results can be used as a practical tool both by researchers and toolmakers to design new tools with rational tool edge and to optimize the cutting process.

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Journal articles on the topic 'Finite gain theory'

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