Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.

Resonance and Bifurcation of Fractional Nonlinear Systems with Power Damping Term for Robot Grinding

A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot grinding.The robot,grinding wheel and steel bar are reduced to a spring-damping second-order system model.The implicit function equations of vibration amplitude of the dynamic system with coulomb friction damping,linear damping,square damping and cubic damping are obtained by average method.The stability of the system is analyzed and explained,and the stability condition of the system is proposed.Then,the amplitude-frequency characteristic curves of the system under different fractional differential orders,nonlinear stiffness parameters,fractional differential term coefficients and external excitation amplitude are analyzed.It is shown that the fractional differential term in the dynamic system is the damping characteristic.Then the influence of four kinds of damping on the vibration amplitude of the system under the same parameter is investigated and it is proved that the cubic damping suppresses the vibration of the system to the maximum extent.Finally,based on the idea that the equilibrium point of the system is the constant part of the Fourier series expansion term,the bifurcation behavior caused by the change of damping parameters in linear damping,square damping and cubic damping systems with different values of fractional differential order is investigated.

Developing Reliable Digital Healthcare Service Using Semi-Quantitative Functional Resonance Analysis

Since entering the era of Industry 4.0,the concept of Healthcare 4.0 has also been put forward and explored by researchers.How to use Information Technology(IT)to better serve people’s healthcare is one of the most featured emerging directions in the academic circle.An important field of Healthcare 4.0 research is the reliability engineering of healthcare service.Because healthcare systems often affect the health and even life of their users,developers must be very cautious in the design,development,and operation of these healthcare systems and services.The problems to be solved include the reliability of business process,system functions,and personal healthcare data.The Functional Resonance Analysis Method(FRAM)has been applied in reliability engineering for safety-critical systems in available studies,using both qualitative and quantitative approaches.However,the method has not been applied in the field of digital healthcare services development.Therefore,to narrow the gap,we present in this paper a semi-quantitative functional resonance analysis method to develop reliable healthcare services for diabetics.Moreover,this paper has tried to improve the reliability design of the service-oriented architecture(SOA)of traditional insulin pump therapy by system thinking.

Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.

Primary resonance of fractional-order Duffing–van der Pol oscillator by harmonic balance method

The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems.

Harmonic Resonance Analysis of Shale Gas Distribution Network with Phased Load

Based on the background of achieving carbon peaking and carbon neutrality, the development and application of new high-power compressors, electric grid drilling RIGS and electric fracturing pump system provide new equipment support for the electric, green and intelligent development of shale gas fields in China. However, the harmonic pollution of shale gas grid becomes more serious due to the converter and frequency conversion device in the system, which easily causes harmonic resonance problem. Therefore, the harmonic resonance of shale gas grid is comprehensively analyzed and treated. Firstly, the working mechanism of compressor, electric drilling RIGS of the harmonic impedance model of electric fracturing pump system is established. Secondly, the main research methods of harmonic resonance analysis are introduced, and the basic principle of modal analysis is explained. Modal analysis method was used to analyze. Finally, harmonic resonance is suppressed. The results show that there may be multiple resonant frequency points in the distribution network changes, but these changes are relatively clear;if the original resonant frequency point of the resonant loop does not exist, the resonant frequency point disappears. The optimal configuration strategy of passive filter can effectively suppress harmonic resonance of distribution network in shale gas field.

A method and device for online magnetic resonance multiphase flow detection

Most multiphase flow separation detection methods used commonly in oilfields are low in efficiency and accuracy,and have data delay.An online multiphase flow detection method is proposed based on magnetic resonance technology,and its supporting device has been made and tested in lab and field.The detection technology works in two parts:measure phase holdup in static state and measure flow rate in flowing state.Oil-water ratio is first measured and then gas holdup.The device is composed of a segmented magnet structure and a dual antenna structure for measuring flowing fluid.A highly compact magnetic resonance spectrometer system and intelligent software are developed.Lab experiments and field application show that the online detection system has the following merits:it can measure flow rate and phase holdup only based on magnetic resonance technology;it can detect in-place transient fluid production at high frequency and thus monitor transient fluid production in real time;it can detect oil,gas and water in a full range at high precision,the detection isn’t affected by salinity and emulsification.It is a green,safe and energy-saving system.

A decomposition method of nuclear magnetic resonance T2 spectrum for identifying fluid properties

Based on analysis of NMR T2 spectral characteristics,a new method for identifying fluid properties by decomposing T2 spectrum through signal analysis has been proposed.Because T2 spectrum satisfies lognormal distribution on transverse relaxation time axis,the T2 spectrum can be decomposed into 2 to 5 independent component spectra by fitting the T2 spectrum with Gauss functions.By analyzing the free relaxation response characteristics of crude oil and formation water,the dynamic response characteristics of the core mutual drive between oil and water,the petrophysical significance of each component spectrum is clarified.T2 spectrum can be decomposed into clay bound water component spectrum,capillary bound fluid component spectrum,micropores fluid component spectrum and macropores fluid component spectrum.According to the nature of crude oil in the target area,the distribution range of T2 component spectral peaks of oil-bearing reservoir is 165-500 ms on T2 time axis.This range can be used to accurately identify fluid properties.This method has high adaptability in identifying complex oil and water layers in low porosity and permeability reservoirs.

Preliminary analysis of resonance effect by Helmholtz Schrdinger method

The Helmholtz SchrSdinger method is employed to study the electric field standing wave caused by coupling through a simple slot. There is a good agreement between the numerical results and the resonant conditions presented by the Helmholtz-Schrodinger method. Thus, it can be used in similar cases where the amplitude of the electric field is the important quantity or eigenfunctions of the Schrodinger equation are needed for complicated quantum structures with hard wall boundary conditions.

Efficient Calculation of the Radar Cross Section at the Interior Resonance by the Inverse Power Method

It is well known that the incorrect results will be given using either the electric or magnetic field integral equation to calculate the radar cross section (RCS) of a closed body at the interior resonance. In this paper, an effective iterative technique is used to correct the calculated surface current density from the electric field integral equation. The radar cross section is computed for an infinite conducting circular cylinder at the interior resonance, and the obtained results are in good agreement with the analytical results. The backscattering cross section of an infinite triangular cylinder in the vicinity of a resonant frequency is also calculated. It is shown that the presence method is efficient and accurate.

The Verification of the Resonance Prediction Method for Great Earthquake Motion and its Prediction

More than 200 great (strong) earthquakes are examined in this thesis on the basis of the method for prediction of movement resonance of great earthquakes; and through the table of about 20 disastrous or representative earthquakes among them, it is proved that there is still room for breakthrough in the prediction of great (strong) earthquakes. At the end of 1996, I predicted that there would be a great earthquake with magnitude between 7.5 and 8.4 and a series of great earthquakes in Japan Trench in the following 1 or 2 years, and later this prediction was realized. Further study on this method resulted in the formula of epicentre prediction. Recently I also worked out that we can reduce the time of great earthquake prediction and epicentre prediction through the study of the early earthquakes with magnitude ≥≥of M 4. Written predictions on 7 earthquakes with magnitude of M 6 between January, 1998 to September 10, 1998 are proved successful in varying degrees, which will solve the —‘poser set by some authorities in international earthquake research field Short-time ’earthquake prediction is impossible on the basis of contemporary scientific technology.

Research on resonance parameters matching based on partitioned operation method of atmospheric pressure plasma reactor array

Matching optimization of resonant parameters among the high power inverters,low power transformers and plasma reactors have significant effects on the performance and output of the reactor array when applying the partitioned operation method.In this paper,the Matlab/Simulink electrical model was established based on the method of partitioned operation.The matching relation between resonant parameters is analyzed on the basis of experimental result.As a consequence,transformer leakage inductance and working frequency are the important parameters influencing the operational efficiency of system,leakage inductance of transformer should be adjusted based on the equivalent capacitance of plasma reactor to realize the matching optimization of resonant parameters.

Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy. Unlike the popular stream function method, the proposed method has design variables that are the distribution of conductive material. A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging（MRI） gradient coils, thus avoiding introducing a coil-winding pattern and simplifying the coil configuration. The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach. The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.

Linearized Proximal Alternating Direction Method of Multipliers for Parallel Magnetic Resonance Imaging

In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived.In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.

An efficient method for mapping the 12C+12C molecular resonances at low energies

The 12C+12C fusion reaction is famous because of its complication of molecular resonances,and it plays an important role in both nuclear structural research and astrophysics. It is extremely difficult to measure the cross sections of 12C+12C fusions at energies of astrophysical relevance because of the very low reaction yields. To measure the complicated resonant structure that exists in this important reaction, an efficient thick target method has been developed and applied for the first time at energies Ec.m.<5.3 MeV. A scan of the cross sections over a relatively wide range of energies can be carried out using only a single beam energy. The result of measurement at Ec.m.=4.1 MeV is compared with results from previous work.This method will be useful for searching for potentially existing resonances of 12C+12C in the energy range 1 MeV<Ec.m.<3 MeV.

A SIMPLE METHOD TO CALCULATE RESONANCE ENERGY

A very simple method to calculate resonance energies of conjugated hydrocarbons by counting carbon numbers was introduced.

ANALYSIS OF HUMAN PLACENTA BY ^(31)P NUCLEAR MAGNETIC RESONANCE AND THIN-LAYER CHROMATOGRAPHY SCANNING COMBINED WITH THE CORRECTIVE METHOD OF ABSORBANCE PROPORTIONAL COEFFICIENT

Five phospholipids in human placenta were determined by phosphorus 31 nuclear magnetic resonance(^(31)P NMR)spectroscopy and thin-layer chromatography(TLC) scanning combined with the corrective method of absorbance proportional coefficient. The NMR spectrometer used this investigation was a Bruker AM-500 spectrometer operating at 202.4 MHz for ^(31)P chemical shifts are relative to 85% phosphoric acid. TIC was carried out by silica gel H plate developed in chloroform-methanol-glacial acetic acid-ethanol-water(25:4:6:2:0.5),with Vaskovsky reagent as colour -developing agent of phospholipids.

Comparing High-resistance Grounding Method with Resonance Grounding Method for Large Generators

For large generators, the problem of high-resistance grounding method and the advantages of resonance, grounding method are discussed in detail, and an overall comparison is given in this paper. It is recommended that the latter should be adopted so as to increase the operation reliability of large generators and power systems.