Group theoretical derivation of Liouville action for Regge surfaces

When rotary machines are running, acousto-mechanical signals acquired from the machines are able to reveal their operation status and machine conditions. Mechanical systems under periodic loading due to rotary operation usually respond in measurements with a superposition of sinusoids whose frequencies are integer (or fractional integer) multiples of the reference shaft speed. In this study we built an online real-time machine condition monitoring system based on the adaptive angular-velocity Vold-Kalman filtering order tracking (AV2KF_OT) algorithm, which was implemented through a DSP chip module and a user interface coded by the LabVIEW®. This paper briefly introduces the theoretical derivation and numerical implementation of computation scheme. Experimental works justify the effectiveness of applying the developed online real-time condition monitoring system. They are the detection of startup on the fluid-induced instability, whirl, performed by using a journal-bearing rotor test rig.

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Stress wave propagation in different number of fissured rock mass based on nonlinear analysis

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0301 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Xiaoming Lou ◽

Mingwu Sun ◽

Jin Yu

Keyword(s):

Numerical Simulation ◽

Rock Mass ◽

Confining Pressure ◽

Displacement Discontinuity ◽

Stress Wave Propagation ◽

Theoretical Derivation ◽

Mechanics Model ◽

Fissured Rock ◽

Deep Rock ◽

Theoretical Accuracy

AbstractThe fissures are ubiquitous in deep rock masses, and they are prone to instability and failure under dynamic loads. In order to study the propagation attenuation of dynamic stress waves in rock mass with different number of fractures under confining pressure, nonlinear theoretical analysis, indoor model test and numerical simulation are used respectively. The theoretical derivation is based on displacement discontinuity method and nonlinear fissure mechanics model named BB model. Using ABAQUS software to establish a numerical model to verify theoretical accuracy, and indoor model tests were carried out too. The research shows that the stress attenuation coefficient decreases with the increase of the number of fissures. The numerical simulation results and experimental results are basically consistent with the theoretical values, which verifies the rationality of the propagation equation.

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BMS field theories and Weyl anomaly

Journal of High Energy Physics ◽

10.1007/jhep07(2021)101 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Arjun Bagchi ◽

Sudipta Dutta ◽

Kedar S. Kolekar ◽

Punit Sharma

Keyword(s):

Three Dimensions ◽

Field Theories ◽

Partition Functions ◽

Two Dimensional ◽

Speed Of Light ◽

Asymptotically Flat ◽

Weyl Invariance ◽

Flat Spacetimes ◽

Liouville Action ◽

Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

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Integral barrier Lyapunov functions-based integrated guidance and control design for strap-down missile with field-of-view constraint

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220981329 ◽

2021 ◽

pp. 014233122098132

Author(s):

Bin Zhao ◽

Zhenxin Feng ◽

Jianguo Guo

Keyword(s):

Sliding Mode ◽

State Equation ◽

Field Of View ◽

Feedback Form ◽

Theoretical Derivation ◽

Guidance And Control ◽

Integrated Guidance And Control ◽

Twisting Algorithm ◽

And Control ◽

Special Time

The problem of the integrated guidance and control (IGC) design for strap-down missile with the field-of-view (FOV) constraint is solved by using the integral barrier Lyapunov function (iBLF) and the sliding mode control theory. Firstly, the nonlinear and uncertainty state equation with non-strict feedback form for IGC design is derived by using the strap-down decoupling strategy. Secondly, a novel adaptive finite time disturbance observer is proposed to estimate the uncertainties based on an improved adaptive gain super twisting algorithm. Thirdly, the special time-varying sliding variable is designed and the iBLF is employed to handle the problem of FOV constraint. Theoretical derivation and simulation show that the IGC system is globally uniformly ultimately bounded and the FOV angle constraint is also guaranteed not only during the reaching phase but also during the sliding mode phase.

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Study on Time Reversal Maximum Ratio Combining in Underwater Acoustic Communications

Applied Sciences ◽

10.3390/app11041509 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1509

Author(s):

Anbang Zhao ◽

Caigao Zeng ◽

Juan Hui ◽

Keren Wang ◽

Kaiyu Tang

Keyword(s):

Time Reversal ◽

Signal To Noise Ratio ◽

Spatial Diversity ◽

Single Element ◽

Noise Power ◽

Theoretical Derivation ◽

Underwater Acoustic ◽

Maximum Ratio Combining ◽

Weight Coefficients ◽

Output Snr

Time reversal (TR) can achieve temporal and spatial focusing by exploiting spatial diversity in complex underwater environments with significant multipath. This property makes TR useful for underwater acoustic (UWA) communications. Conventional TR is realized by performing equal gain combining (EGC) on the single element TR output signals of each element of the vertical receive array (VRA). However, in the actual environment, the signal-to-noise ratio (SNR) and the received noise power of each element are different, which leads to the reduction of the focusing gain. This paper proposes a time reversal maximum ratio combining (TR-MRC) method to process the received signals of the VRA, so that a higher output SNR can be obtained. The theoretical derivation of the TR-MRC weight coefficients indicates that the weight coefficients are only related to the input noise power of each element, and are not affected by the multipath structure. The correctness of the derivation is demonstrated with the experimental data of the long-range UWA communications conducted in the South China Sea. In addition, the experimental results illustrate that compared to the conventional TR, TR-MRC can provide better performance in terms of output SNR and bit error rate (BER) in UWA communications.

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Correction for the Partial Volume Effects (PVE) in Nuclear Medicine Imaging: A Post-Reconstruction Analytic Method

Applied Sciences ◽

10.3390/app11146460 ◽

2021 ◽

Vol 11 (14) ◽

pp. 6460

Author(s):

Fabio Di Martino ◽

Patrizio Barca ◽

Eleonora Bortoli ◽

Alessia Giuliano ◽

Duccio Volterrani

Keyword(s):

Nuclear Medicine ◽

Imaging System ◽

Tomographic Reconstruction ◽

Mathematical Expression ◽

Reconstruction Algorithm ◽

Volume Effect ◽

Nuclear Medicine Imaging ◽

Theoretical Derivation ◽

Reconstruction Process ◽

Partial Volume

Quantitative analyses in nuclear medicine are increasingly used, both for diagnostic and therapeutic purposes. The Partial Volume Effect (PVE) is the most important factor of loss of quantification in Nuclear Medicine, especially for evaluation in Region of Interest (ROI) smaller than the Full Width at Half Maximum (FWHM) of the PSF. The aim of this work is to present a new approach for the correction of PVE, using a post-reconstruction process starting from a mathematical expression, which only requires the knowledge of the FWHM of the final PSF of the imaging system used. After the presentation of the theoretical derivation, the experimental evaluation of this method is performed using a PET/CT hybrid system and acquiring the IEC NEMA phantom with six spherical “hot” ROIs (with diameters of 10, 13, 17, 22, 28, and 37 mm) and a homogeneous “colder” background. In order to evaluate the recovery of quantitative data, the effect of statistical noise (different acquisition times), tomographic reconstruction algorithm with and without time-of-flight (TOF) and different signal-to-background activity concentration ratio (3:1 and 10:1) was studied. The application of the corrective method allows recovering the loss of quantification due to PVE for all sizes of spheres acquired, with a final accuracy less than 17%, for lesion dimensions larger than two FWHM and for acquisition times equal to or greater than two minutes.

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Burst pressure prediction of fiber-reinforced flexible pipes with arbitrary generatrix

Journal of Engineered Fibers and Fabrics ◽

10.1177/1558925021990812 ◽

2021 ◽

Vol 16 ◽

pp. 155892502199081

Author(s):

Guo-min Xu ◽

Chang-geng Shuai

Keyword(s):

Transfer Matrix ◽

Linear Equations ◽

Burst Pressure ◽

Fiber Reinforced ◽

Flexible Pipe ◽

Theoretical Derivation ◽

Design And Optimization ◽

Flexible Pipes ◽

Novel Method ◽

Winding Angle

Fiber-reinforced flexible pipes are widely used to transport the fluid at locations requiring flexible connection in pipeline systems. It is important to predict the burst pressure to guarantee the reliability of the flexible pipes. Based on the composite shell theory and the transfer-matrix method, the burst pressure of flexible pipes with arbitrary generatrix under internal pressure is investigated. Firstly, a novel method is proposed to simplify the theoretical derivation of the transfer matrix by solving symbolic linear equations. The method is accurate and much faster than the manual derivation of the transfer matrix. The anisotropy dependency on the circumferential radius of the pipe is considered in the theoretical approach, along with the nonlinear stretch of the unidirectional fabric in the reinforced layer. Secondly, the burst pressure is predicted with the Tsai-Hill failure criterion and verified by burst tests of six different prototypes of the flexible pipe. It is found that the burst pressure is increased significantly with an optimal winding angle of the unidirectional fabric. The optimal result is determined by the geometric parameters of the pipe. The investigation method and results presented in this paper will guide the design and optimization of novel fiber-reinforced flexible pipes.

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On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

Abstract and Applied Analysis ◽

10.1155/2013/681523 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Sendren Sheng-Dong Xu ◽

Chih-Chiang Chen

Keyword(s):

Control Systems ◽

Linear Systems ◽

Switched Systems ◽

The Other ◽

Linear Control ◽

Linear Control Systems ◽

Problem Statement ◽

Theoretical Derivation ◽

Control Laws ◽

Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

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Erratum: “A New Group-Theoretical Derivation of the Bravais Lattices”

Journal of the Physical Society of Japan ◽

10.1143/jpsj.47.1732 ◽

1979 ◽

Vol 47 (5) ◽

pp. 1732-1732 ◽

Cited By ~ 1

Author(s):

Masahiko Hosoya

Keyword(s):

Theoretical Derivation

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The relationship between photometric and spectroscopic oscillation amplitudes from 3D stellar atmosphere simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab337 ◽

2021 ◽

Author(s):

Yixiao Zhou ◽

Thomas Nordlander ◽

Luca Casagrande ◽

Meridith Joyce ◽

Yaguang Li ◽

...

Keyword(s):

Radial Velocity ◽

Three Dimensional ◽

Quantitative Relationship ◽

Stellar Atmospheres ◽

Spectral Lines ◽

Wavelength Shift ◽

The Sun ◽

Theoretical Derivation ◽

Velocity Amplitude ◽

Good Agreement

Abstract We establish a quantitative relationship between photometric and spectroscopic detections of solar-like oscillations using ab initio, three-dimensional (3D), hydrodynamical numerical simulations of stellar atmospheres. We present a theoretical derivation as proof of concept for our method. We perform realistic spectral line formation calculations to quantify the ratio between luminosity and radial velocity amplitude for two case studies: the Sun and the red giant ε Tau. Luminosity amplitudes are computed based on the bolometric flux predicted by 3D simulations with granulation background modelled the same way as asteroseismic observations. Radial velocity amplitudes are determined from the wavelength shift of synthesized spectral lines with methods closely resembling those used in BiSON and SONG observations. Consequently, the theoretical luminosity to radial velocity amplitude ratios are directly comparable with corresponding observations. For the Sun, we predict theoretical ratios of 21.0 and 23.7 ppm/[m s−1] from BiSON and SONG respectively, in good agreement with observations 19.1 and 21.6 ppm/[m s−1]. For ε Tau, we predict K2 and SONG ratios of 48.4 ppm/[m s−1], again in good agreement with observations 42.2 ppm/[m s−1], and much improved over the result from conventional empirical scaling relations which gives 23.2 ppm/[m s−1]. This study thus opens the path towards a quantitative understanding of solar-like oscillations, via detailed modelling of 3D stellar atmospheres.

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