In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded dis...In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded distribution functions such as in Q machines/plasma diodes or in the scrap-off layer of Tokamak fusion plasmas. The results are valid for functions of function spaces—Lebesgue spaces, which are defined using a natural generalization of the p-norm for finite-dimensional vector spaces, where is the real set, σs is the σ-algebra of Lebesgue measurable sets, and the μ Lebesgue measure. , so that . Note that, using a simpler notation, more natural/known to engineers, f could be considered any piecewise continuous function, that is: Here is a Euclidian space with the usual norm (inner product: ) given by: [1].展开更多
We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equat...We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.展开更多
文摘In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded distribution functions such as in Q machines/plasma diodes or in the scrap-off layer of Tokamak fusion plasmas. The results are valid for functions of function spaces—Lebesgue spaces, which are defined using a natural generalization of the p-norm for finite-dimensional vector spaces, where is the real set, σs is the σ-algebra of Lebesgue measurable sets, and the μ Lebesgue measure. , so that . Note that, using a simpler notation, more natural/known to engineers, f could be considered any piecewise continuous function, that is: Here is a Euclidian space with the usual norm (inner product: ) given by: [1].
基金supported by Ministerio de Ciencia e Innovacion(Spain)through projects PID2019-104927GB-C21 and PID2019-104927GB-C22,MCIN/AEI/10.13039/501100011033,ERDF(“A way of making Europe”)the support of the Conselleria d’Innovacio,Universitats,Ciencia i Societat Digital from the Generalitat Valenciana(Spain)through project CIAICO/2021/180.
文摘We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.
