The standard and high-order Gaussian beam solutions for gravitational wave is obtained in the linear approximation of vacuum Einstein equation under harmonic conditions.
When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correc...When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correction of the classical D’Alembert equation. Later on, WoinowskyKrieger (Nash & Modeer) incorporated this correction in the classical Euler-Bernoulli equation for the beam (plate) with hinged ends.Here a new equation for the small transverse vibrations of a simply supported beam is proposed. Such equation takes into account Kirchhoff’s correction, as well as the correction for rotary inertia of the cross section Of the beam and the influence of shearing strains, already present in the Timoshenko beam equation (of the Mindlin-Timoshenko equation for the plate).The model is inspired by a remark of Rayleigh, and by a joint paper with Panizzi & Paoli. It looks more complicated than the one proposed by Sapir & Reiss, but as a matter of fact it is easier to study if a suitable change of variables is performed.The author proves the local well-posedness of the initial-boundary value problem in Sobolev spaces of order ≥2.5. The technique is abstract, i.e. the equation is rewritten as a fourth order evolution equation in Hilbert space (thus the results could be applied also to the formally analogous equation for the plate).展开更多
In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major ax...In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation.Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed.It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.展开更多
We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential dep...We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.展开更多
A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using M...A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.展开更多
文摘The standard and high-order Gaussian beam solutions for gravitational wave is obtained in the linear approximation of vacuum Einstein equation under harmonic conditions.
文摘When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correction of the classical D’Alembert equation. Later on, WoinowskyKrieger (Nash & Modeer) incorporated this correction in the classical Euler-Bernoulli equation for the beam (plate) with hinged ends.Here a new equation for the small transverse vibrations of a simply supported beam is proposed. Such equation takes into account Kirchhoff’s correction, as well as the correction for rotary inertia of the cross section Of the beam and the influence of shearing strains, already present in the Timoshenko beam equation (of the Mindlin-Timoshenko equation for the plate).The model is inspired by a remark of Rayleigh, and by a joint paper with Panizzi & Paoli. It looks more complicated than the one proposed by Sapir & Reiss, but as a matter of fact it is easier to study if a suitable change of variables is performed.The author proves the local well-posedness of the initial-boundary value problem in Sobolev spaces of order ≥2.5. The technique is abstract, i.e. the equation is rewritten as a fourth order evolution equation in Hilbert space (thus the results could be applied also to the formally analogous equation for the plate).
文摘In the present work,nonlinear interaction of elliptical laser beam with collisional plasma is studied by using paraxial ray approximation.Nonlinear differential equations for the beam width parameters of semi-major axis and semi-minor axis of elliptical laser beam have been set up and solved numerically to study the variation of beam width parameters with normalized distance of propagation.Effects of variation in absorption coefficient and plasma density on the beam width parameters are also analyzed.It is observed from the analysis that extent of self-focusing of beam increases with increase/decrease in plasma density/absorption coefficient.
基金Supported by the Fundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China under Grant No.10904111
文摘We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.
文摘A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.
