The Wave Trace and Resonances of the Magnetic Hamiltonian with Singular Vector Potentials

Interference electron microscopy enables us to record the phase distribution of an electron wave on a hologram. The distribution is visualized as a fringe pattern in a micrograph by optical reconstruction. The phase is affected by electromagnetic potentials; scalar and vector potentials. Therefore, the electric and magnetic field can be reduced from the recorded phase. This study analyzes a leakage magnetic field from CoCr perpendicular magnetic recording media. Since one contour fringe interval corresponds to a magnetic flux of Φo(=h/e=4x10-15Wb), we can quantitatively measure the field by counting the number of finges. Moreover, by using phase-difference amplification techniques, the sensitivity for magnetic field detection can be improved by a factor of 30, which allows the drawing of a Φo/30 fringe. This sensitivity, however, is insufficient for quantitative analysis of very weak magnetic fields such as high-density magnetic recordings. For this reason we have adopted “fringe scanning interferometry” using digital image processing techniques at the optical reconstruction stage. This method enables us to obtain subfringe information recorded in the interference pattern.

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A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics

Fluids ◽

10.3390/fluids6030095 ◽

2021 ◽

Vol 6 (3) ◽

pp. 95

Author(s):

Stéphane Vincent ◽

Jean-Paul Caltagirone

Keyword(s):

Solid Mechanics ◽

Mechanical Energy ◽

Fluid Structure Interaction ◽

Equation Of Motion ◽

Discrete Equation ◽

Discrete Mechanics ◽

Fluid Structure ◽

Structure Interaction ◽

Vector Potentials

The unification of the laws of fluid and solid mechanics is achieved on the basis of the concepts of discrete mechanics and the principles of equivalence and relativity, but also the Helmholtz–Hodge decomposition where a vector is written as the sum of divergence-free and curl-free components. The derived equation of motion translates the conservation of acceleration over a segment, that of the intrinsic acceleration of the material medium and the sum of the accelerations applied to it. The scalar and vector potentials of the acceleration, which are the compression and shear energies, give the discrete equation of motion the role of conservation law for total mechanical energy. Velocity and displacement are obtained using an incremental time process from acceleration. After a description of the main stages of the derivation of the equation of motion, unique for the fluid and the solid, the cases of couplings in simple shear and uniaxial compression of two media, fluid and solid, make it possible to show the role of discrete operators and to find the theoretical results. The application of the formulation is then extended to a classical validation case in fluid–structure interaction.

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The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

Scientific Reports ◽

10.1038/s41598-021-83916-4 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Souma Jinno ◽

Shuji Kitora ◽

Hiroshi Toki ◽

Masayuki Abe

Keyword(s):

Numerical Method ◽

Time Domain ◽

Maxwell Equations ◽

Three Dimensional ◽

New Formalism ◽

Vector Potentials ◽

Lumped Parameter ◽

Radiation Theory ◽

Stable Solutions ◽

The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

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Retrieving Sun-Induced Chlorophyll Fluorescence from Hyperspectral Data with TanSat Satellite

Sensors ◽

10.3390/s21144886 ◽

2021 ◽

Vol 21 (14) ◽

pp. 4886

Author(s):

Shilei Li ◽

Maofang Gao ◽

Zhao-Liang Li

Keyword(s):

Chlorophyll Fluorescence ◽

Fluorescence Spectrum ◽

Singular Vector ◽

Low Frequency ◽

Information Criterion ◽

Hyperspectral Data ◽

High Spectral Resolution ◽

Remotely Sensed Data ◽

Spectral Window ◽

Vector Decomposition

A series of algorithms for satellite retrievals of sun-induced chlorophyll fluorescence (SIF) have been developed and applied to different sensors. However, research on SIF retrieval using hyperspectral data is performed in narrow spectral windows, assuming that SIF remains constant. In this paper, based on the singular vector decomposition (SVD) technique, we present an approach for retrieving SIF, which can be applied to remotely sensed data with ultra-high spectral resolution and in a broad spectral window without assuming that the SIF remains constant. The idea is to combine the first singular vector, the pivotal information of the non-fluorescence spectrum, with the low-frequency contribution of the atmosphere, plus a linear combination of the remaining singular vectors to express the non-fluorescence spectrum. Subject to instrument settings, the retrieval was performed within a spectral window of approximately 7 nm that contained only Fraunhofer lines. In our retrieval, hyperspectral data of the O2-A band from the first Chinese carbon dioxide observation satellite (TanSat) was used. The Bayesian Information Criterion (BIC) was introduced to self-adaptively determine the number of free parameters and reduce retrieval noise. SIF retrievals were compared with TanSat SIF and OCO-2 SIF. The results showed good consistency and rationality. A sensitivity analysis was also conducted to verify the performance of this approach. To summarize, the approach would provide more possibilities for retrieving SIF from hyperspectral data.

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Large Lorentz scalar and vector potentials in nuclei

Nuclear Physics A ◽

10.1016/s0375-9474(00)00146-9 ◽

2000 ◽

Vol 673 (1-4) ◽

pp. 298-310 ◽

Cited By ~ 31

Author(s):

R.J. Furnstahl ◽

Brian D. Serot

Keyword(s):

Vector Potentials ◽

Lorentz Scalar

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Approximate treatment of the Dirac equation with scalar and vector potentials of rectangular shapes

Physical Review A ◽

10.1103/physreva.50.29 ◽

1994 ◽

Vol 50 (1) ◽

pp. 29-33 ◽

Cited By ~ 2

Author(s):

M. E. Grypeos ◽

C. G. Koutroulos ◽

G. J. Papadopoulos

Keyword(s):

Dirac Equation ◽

Vector Potentials ◽

Approximate Treatment

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Ensemble Construction and Verification of the Probabilistic ENSO Prediction in the LDEO5 Model

Journal of Climate ◽

10.1175/2010jcli3453.1 ◽

2010 ◽

Vol 23 (20) ◽

pp. 5476-5497 ◽

Cited By ~ 16

Author(s):

Yanjie Cheng ◽

Youmin Tang ◽

Peter Jackson ◽

Dake Chen ◽

Ziwang Deng

Keyword(s):

High Frequency ◽

Singular Vector ◽

Southern Oscillation ◽

Initial Perturbation ◽

Probabilistic Prediction ◽

Construction Methods ◽

Sea Surface Temperature Anomaly ◽

Probabilistic Forecasts ◽

Construction Strategy ◽

Construction Strategies

Abstract El Niño–Southern Oscillation (ENSO) retrospective ensemble-based probabilistic predictions were performed for the period of 1856–2003 using the Lamont-Doherty Earth Observatory, version 5 (LDEO5), model. To obtain more reliable and skillful ENSO probabilistic predictions, first, four ensemble construction strategies were investigated: (i) the optimal initial perturbation with singular vector of sea surface temperature anomaly (SSTA), (ii) the realistic high-frequency anomalous winds, (iii) the stochastic optimal pattern of anomalous winds, and (iv) a combination of the first and the third strategy. Second, verifications were conducted to examine the reliability and resolution of the probabilistic forecasts provided by the four methods. Results suggest that reliability of ENSO probabilistic forecast is more sensitive to the choice of ensemble construction strategy than the resolution, and a reliable and skillful ENSO probabilistic prediction system may not necessarily have the best deterministic prediction skills. Among these ensemble construction methods, the fourth strategy produces the most reliable and skillful ENSO probabilistic prediction, benefiting from the joint contributions of the stochastic optimal winds and the singular vector of SSTA. In particular, the stochastic optimal winds play an important role in improving the ENSO probabilistic predictability for the LDEO5 model.

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EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

Modern Physics Letters A ◽

10.1142/s0217732308026686 ◽

2008 ◽

Vol 23 (35) ◽

pp. 3005-3013 ◽

Cited By ~ 14

Author(s):

A. REZAEI AKBARIEH ◽

H. MOTAVALI

Keyword(s):

Exact Solutions ◽

Gordon Equation ◽

Bound State ◽

S Wave ◽

Vector Potentials ◽

Klein Gordon ◽

The One ◽

Uvarov Method ◽

Equal Scalar ◽

Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

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