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We attempt to consider a biological structure as an open nonequilibrium system the properties of which can be described on the basis of kinetic approach with the help of appropriate kinetic equations. This approach allows us to evaluate in principle scales of sizes and to connect these values to the inner characteristics of the processes of kinetic interaction and advection. One can compare the results with some empirical data concerning these characteristics for bio-systems, in particular mammals, and also for some parts of the systems, say sizes of green leaves. A sense of the nonequilibrium entropy as a measure of complexity of bio-organisms is discussed. Besides the estimations of bio-systems on a global scale, possible methods to describe restricted regions (associated e.g. with living cells) as nonequilibrium open structure with specific boundaries are also discussed. A new boundary 1D problem is formulated and solved for kinetic equations with the membrane-like boundaries conditions. Non-classical transport properties in the system are found. [ABSTRACT FROM AUTHOR]

Some new problems with nonequlibrium boundary conditions are formulated and solved. So-called nonuniform relaxation problem with nonequilibrium conditions on a free boundary for supersonic and subsonic cases are considered. Classical 1D heat transfer problem but with nonequilibrium boundary condition on one surface is also studied. Possible nonequilibrium flows with anomalous transport of momentum and heat are observed and discussed. [ABSTRACT FROM AUTHOR]

Oscillating Couette flow problem is studied for a wide range of Knudsen, Mach and Stokes numbers. From analysis of the free molecular solution, we obtained collisionless boundary layer of thickness proportional to the mean thermal velocity of the gas particles and inversely proportional to frequency of the wall oscillations. This boundary layer is quite different from the viscous layer formed near oscillating wall in the collisional regime, which is described by the Navier-Stokes equations. The velocity profiles in the boundary layers obtained from numerical solution of the Boltzmann and Navier-Stokes equations deviate considerably from each other when the boundary layer thickness becomes comparable or smaller than the mean free path. Considerable gas heating occurs when the wall velocity becomes comparable or larger than thermal velocities of the gas particles. In this case, large heat fluxes in both normal and longitudinal directions with respect to the wall have been obtained in our free-molecular solution and kinetic simulations. [ABSTRACT FROM AUTHOR]

New types of the kinetic problems for relaxation in space are generalized for a mixture of gases in 1D and 2D formulations. Nongradient transport processes inherent to supersonic flows with nonequilibrium boundary conditions are discussed. Boundary fluxes lead to resulting gradients of quantities (until the distribution approaches the equilibrium downstream). We show that the gradient of temperature can have the same sign as the heat flux and the velocity gradient can have the same sign as the appropriate nonequilibrium stress tensor component. Solutions for the Boltzmann equation with the full collision and for the model equation of the BGK type for gas mixtures are presented where these effects take place. [ABSTRACT FROM AUTHOR]