Mathematical Problems of Collaborating Robotic Vehicle Traffic

Предложен подход для моделирования динамики транспортных потоков для взаимодействующих аппаратов на основе теории самосогласованного поля, основанного на уравнениях А.А. Власова. Сформулированы проблемы применимости таких моделей для описания коллективных явлений трафика в связи с задачами поведения «стаи» роботизированных однородных взаимодействующих аппаратов в фазовом пространстве на основе кинетического подхода. An approach to the simulation of time-dependent collaborating vehicle traffic flows based on the self-consistent field theory and A. Vlasov equations are proposed. The problems of the simulation model applicability to collaborative traffic processes such as the behavior of a swarm of identical collaborating vehicles in phase space using the kinetic approach are stated.

Polymer Brush in a Nanopore: Effects of Solvent Strength and Macromolecular Architecture Studied by Self-Consistent Field and Scaling Theory

To study conformational transition occuring upon inferior solvent strength in a brush formed by linear or dendritically branched macromolecules tethered to the inner surface of cylindrical or planar (slit-like) pore, a self-consistent field analytical approach is employed. Variations in the internal brush structure as a function of variable solvent strength and pore radius, and the onset of formation of a hollow channel in the pore center are analysed. The predictions of analytical theory are supported and complemented by numerical modelling by a self-consistent field Scheutjens–Fleer method. Scaling arguments are used to study microphase segregation under poor solvent conditions leading to formation of a laterally and longitudinally patterned structure in planar and cylindrical pores, respectively, and the effects of confinement on "octopus-like" clusters in the pores of different geometries.