Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.Comment: 18 pages, 4 figure

The geometry of spinors and the multicomponent BKP and DKP hierarchies

We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or DS) are reductions of the multicomponent BKP.Comment: 46 pages, Latex2

On multicomponent effects in stellar winds of stars at extremely low metallicity

We calculate multicomponent line-driven wind models of stars at extremely low metallicity suitable for massive first generation stars. For most of the models we find that the multicomponent wind nature is not important for either wind dynamics or for wind temperature stratification. However, for stars with the lowest metallicities we find that multicomponent effects influence the wind structure. These effects range from pure heating to possible fallback of the nonabsorbing wind component. We present a simple formula for the calculation of metallicity for which the multicomponent effects become important. We show that the importance of the multicomponent nature of winds of low metallicity stars is characterised not only by the low density of driving ions, but also by lower mass-loss rate

Quasichemical Models of Multicomponent Nonlinear Diffusion

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell--jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final published version

On rational solutions of multicomponent and matrix KP hierarchies

We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed.Comment: 15 pages, no figure

On the Maxwell-Stefan approach to multicomponent diffusion

We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and quasi-positive matrix which governs the flux-force relations and are able to show normal ellipticity of the associated multicomponent diffusion operator. This provides local-in-time wellposedness of the Maxwell-Stefan multicomponent diffusion system in the isobaric, isothermal case.Comment: Based on a talk given at the Conference on Nonlinear Parabolic Problems in Bedlewo, Mai 200

Multicomponent bi-superHamiltonian KdV systems

It is shown that a new class of classical multicomponent super KdV equations is bi-superHamiltonian by extending the method for the verification of graded Jacobi identity. The multicomponent extension of super mKdV equations is obtained by using the super Miura transformation

One-pot multicomponent synthesis of 2,3-dihydropyrans: new access to furanose–pyranose 1,3-C–C-linked-disaccharides

An efficient synthesis of 2,3-dihydropyrans starting from different terminal alkynes was developed. The 2,3-dihydropyrans were obtained in a few minutes through a microwave-assisted multicomponent enyne cross-metathesis/hetero-Diels–Alder reaction. Starting from C-ethynyl-ribofuranose, a new multicomponent approach to furanose–pyranose 1,3-C–C-linked disaccharides was also developed