多组分非线性扩散的拟化学模型
Quasichemical Models of Multicomponent Nonlinear Diffusion
摘要：
扩散保持了浓度的正性，因此，如果存在非对角项，多组分扩散应该是非线性的。各种各样的非线性多组分扩散方程应订购和特殊的工具，需要提供系统的建设的非线性扩散方程的多组分混合物与组分之间的显着相互作用。我们从化学动力学中借用反应机理的思想，发展了一种非线性多组分扩散的方法。化学动力学为过程建模提供了非常重要的工具。这是由简单动力学定律补充的化学计量代数。这项发明的结果现在被应用于许多科学领域，从粒子物理学到社会学。在我们的工作中，我们扩展到非线性多组分扩散的应用领域。我们证明，如何机制为基础的方法，多组分扩散可以纳入一般的热力学框架，并证明相应的耗散不等式。为了满足热力学的限制，基本过程的动力学定律不能有任意的形式。对于一般动力学定律（广义质量作用定律），证明了附加条件。细胞跳跃形式主义给出了直观清晰的表示的基本运输过程，并在同一时间，产生动力学有限元，数值模拟的工具。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
