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.

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.

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.

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.

Application of the N + 2 Transversal Network Method to the Study of a Coupled Resonator Filter

This paper presents a new approach to synthesize admittance function polynomials and coupling matrices for coupled resonator filters. The N + 2 transversal network method is applied to study a coupled resonator filter. This method allowed us to determine the polynomials of the reflection and transmission coefficients. A study is made for a 4 poles filter with 2 transmission zeros between the N + 2 transversal network method and the one found in the literature. A MATLAB code was designed for the numerical simulation of these coefficients for the 6, 8, and 10 pole filter with 4 transmission zeros.

An Effective Method for Solving the Induced Surface Current for Arbitrary Conducting Bodies at the Interior Resonance

The incorrect surface current may be obtained in the vicinity of the resonant frequencies when the method of moments is used to solve either the electric or magnetic field surface integral equation. An effective method is presented to determine the correct surface current, i.e., the correct surface current, i.e., the correct surface current is composed of the non-resonant mode current and the normalized resonant mode current multiplied by an unknown complex factor. The unknown complex factor can be obtained by employing the condition that the total field inside the conducting closed body must be zero at specified interior points. A numerical example is given for an infinitely long and perfectly conducting circular cylinder at the interior resonance, and the calculated surface currents are in good agreement with the analytical ones. The validity and accuracy of the presented method is thus verified.

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.

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.

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.

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.

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.

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.

Nonlinear principal resonance of magneto-electro-elastic thin plate

Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare （L-P） method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different condi- tions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parame- ter e, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2 04, different magneto-electro-elastic ma- terials of BaTiO3/CoFe2 04 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects in- volve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.