Well-defined Physical Meaning Research Articles

Study of Numerical Method for Magnetic Shielding Problem Considering Actual Measurement of Magnetic Environment

A critical consideration in the optimal design of magnetically shielded rooms is the manner in which an external magnetic field, which should be shielded, is imposed on a target area. In this paper, we examined the possibility of applying the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method (the method of which the magnetic field <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> in the analyzed region is given) to the shielding problem with a measurement-based magnetic field, which includes an irrotational field component as noise, and, therefore, is inconsistent with Maxwell's equations. We show that the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method has a well-defined physical meaning for such an irrotational field component. Furthermore, we explain why the convergence and the accuracy of the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method are better than those of the A method.

A Phenomenological Model for Decay Process of Long-Persistent Phosphorescence

A sum of two or more exponential decay functions is empirically adopted nowadays to analyze the decay curve of long-persistent phosphor. However, the fitting parameters of this empirical model lack well-defined physical meanings, especially when the number of exponential decay function is greater than two. We propose a phenomenological model to describe the decay curve of long-persistent phosphor based on an analysis of the relationship between carrier concentration and light-emitting intensity. This model has a few fitting parameters with well-defined physical meanings as compared to the current empirical one. With this model, we quantitatively analyze the decay processes of typical long-persistent phosphors of SrAl2O4:Eu,Dy and obtain reasonable fitting results.

A decomposition of the number of effectively unpaired electrons and its physical meaning

We report a procedure which allows one to decompose the number of effectively unpaired electrons corresponding to an N-electron system into two components with well-defined physical meaning. One of these terms represents the number of net unpaired electrons arising from the spin. The second one accounts for the partial split of electron pairs that appears when multideterminantal correlated wave functions are used.

Identification of nonlinear elastic structures using empirical mode decomposition and nonlinear normal modes

The empirical mode decomposition (EMD) method is well-known for its ability to decompose a multi-component signal into a set of intrinsic mode functions (IMFs). The method uses a sifting process in which local extrema of a signal are identified and followed by a spline fitting approximation for decomposition. This method provides an effective and robust approach for decomposing nonlinear and non-stationary signals. On the other hand, the IMF components do not automatically guarantee a well-defined physical meaning hence it is necessary to validate the IMF components carefully prior to any further processing and interpretation. In this paper, an attempt to use the EMD method to identify properties of nonlinear elastic multi-degree-of-freedom structures is explored. It is first shown that the IMF components of the displacement and velocity responses of a nonlinear elastic structure are numerically close to the nonlinear normal mode (NNM) responses obtained from two-dimensional invariant manifolds. The IMF components can then be used in the context of the NNM method to estimate the properties of the nonlinear elastic structure. A two-degree-of-freedom shear-beam building model is used as an example to illustrate the proposed technique. Numerical results show that combining the EMD and the NNM method provides a possible means for obtaining nonlinear properties in a structure.

Transferable ab Initio Intermolecular Potentials. 1. Derivation from Methanol Dimer and Trimer Calculations

An intermolecular potential was derived from ab initio calculations on methanol dimers and trimers. Ninety-four methanol dimer geometries and seventeen trimer geometries have been studied using an interaction-optimized basis set. Because we aimed at transferability, all terms of the model were fitted separately, in order to obtain a potential in which these energy terms have a well-defined physical meaning. Electrostatic interactions were described by atomic multipole moments obtained by fitting to the monomer electrostatic potential. The polarization energy was modeled using atomic dipole polarizabilities. Scaled empirical polarizabilities reproduced the energy nonadditivity in methanol trimers very accurately. The dispersion energy was described by a damped r-6 atom−atom potential, which was fitted to separately calculated dispersion energies. Exchange energy and remaining short-ranged terms were modeled by an exponential repulsion term, including some anisotropic features. This repulsion model was fitt...

Focusing fan-out elements based on phase-matched Fresnel lenses

A novel approach for designing and fabricating focusing fan-out elements is presented. It is based on an area-sharing arrangement of planar lenses. Due to the low number of parameters and their well-defined physical meaning, it is possible to find solutions with both a high efficiency and a low uniformity error using simple and fast optimization procedures. Results of numerical simulations and experiments agree well. Conspicuous properties include a high fabrication fault tolerance, the suitability for low-cost mass production, and the possibility of realizing very compact microoptical systems.

Quark and gluon content of the proton spin.

We examine the role of quarks and gluons in polarized deep-inelastic scattering in connection with the famous European Muon Collaboration experimental result. The gluon contribution generated by the axial anomaly is shown to have a well-defined physical meaning and its gauge-invariance properties are fully clarified. We also emphasize the role of the ghost contribution in the generalized Goldberger-Treiman relation and give a detailed calculation of the correction due to unequal quark masses and to ${\ensuremath{\pi}}^{0}\ensuremath{-}\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing.

A semiempirical equation of state for non-polar and polar substances on the basis of perturbation theory.

A new semiempirical equation of state applicable both to non-polar and to polar substances was developed, by a modification of the perturbation theory. This equation is composed of four terms, each characterized by one of the four kinds of interactions: repulsion, symmetric, non-polar asymmetric and polar asymmetric interactions. For the first one, the hard convex fluid equation of Boublík was used. The functional forms of the second and third ones were determined by analogy to the Padé function of Stell and the second virial coefficient equation of Tsonopoulos. The last one was approximated by the polar deviation function of Stell. The universal constants of the second and third terms were obtained by use of the P-V-T data of the reference substances having the corresponding interaction. Four characteristic parameters, with well-defined physical meaning, were required to characterize the pure substances. The values of these parameters are presented for non-polar and polar substances. The proposed equation produced good correlation results for the P-V-T relations of the non-polar and polar substances, except in the critical region of polar substances.

ON THE PROBLEM OF THE ENERGY OF GRAVITATIONAL FIELD

In this paper, we discuss the problem of the local energy content in gravitational fields. A new total energy-momentum density pseudo-tensor of gravitational field is given In this paper. The energy content in any part of a gravitational field given by the new pseudo-tensor is an invariant under arbitrary purely spatial transformation, hence the local energy content in the gravitational field has a well-defined physical meaning. For the energy and momentum of a Schwarzschild gravitational field, the results given by the new pseudo-tensor are more reasonable than those given by other pseudo-tensors pro-posed in the literatures of the general theory of relativity.The relation between mass and energy in the theory of gravitation is also discussed.

Influence of Vibrations on Molecular Structure Determinations. II. Average Structures Derived from Spectroscopic Data

Formulas are given which enable structural parameters for the average molecular configuration in the ground vibrational state to be calculated for some simple types of molecules. The data required are the observed effective moments of inertia and harmonic force constants. No knowledge of anharmonic constants is necessary. The average structural parameters have a well-defined physical meaning and are directly comparable with diffraction results. Polyatomic molecules for which explicit calculations are given are CO2, CS2, H2O, SO2, O3, NO2, CH4, HCN, and C2H2. It is found that the average bond lengths involving H are usually 0.003–0.005 Å longer than the corresponding D bond. For bonds involving heavier elements isotopic differences are smaller but nonetheless significant. Implications of the results for the general problem of structural determination are discussed.