Diffusion from within a Spherical Body with Partially Blocked Surface: Diffusion through a Constant Surface Area

Diffusion from spherical bodies has been a subject of interest since the earliest times of modern sciences and a few equivalent analytical formulations of the problem are taught in engineering textbooks dealing with cooling rates of hot spheres. However, all these former studies assume that the diffusing material is transferable to/from the surrounding space through the whole surface of the spherical body. Conversely, the development of nanoscience and the improved knowledge of microscopic biological events have evidenced that diffusion from spherical bodies is a ubiquitous problem. It often occurs in situations where the nanosphere surfaces are not isotropic and partly impermeable to diffusing materials. This work elaborates on this issue and theoretically establishes that—with some specific allowance—the basic analytical equation of diffusion from/to fully accessible spherical bodies may be used.     

The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.     

The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L=4,6,8,10. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T_C=10.838(1), T_C=10.836(20) and T_C=10.835(1) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T_C=10.835(5). The value obtained for the critical exponent of the specific heat, i.e., =0.012(2) is also in agreement with =0 predicted by the theory.     

Transfer of pyrene-dietherphosphatidylcholine to serum lipoproteins

The nonhydrolyzable fluorescent diether analog of phosphatidylcholine, 1-O-hexadecyl-2-0-pyrenedecyl-sn-glycero-3-phosphocholine, has been synthesized as a stable probe for the determination of phospholipid transfer to different lipoprotein classes with potential phospholipase activities. After incubation of total human serum with the new probe at 37°C for 3 hours a characteristic partition equilibrium between the main lipoprotein fractions was observed. The fluorescent lipid was not degraded under these conditions and, therefore, served as a marker for choline glycerophospholipid distribution between and transport to serum lipoproteins.     

Exact scaling behavior of partially convex vesicles

We solve analytically for the perimeter-area generating functions for two models of vesicles. While from the solution of the first model, staircase polygons, one can easily extract the asymptotic scaling behavior, the exact solution of the second, column-convex polygons, is difficult to analyze. This leads us to apply a recently developed method for deriving the scaling behavior indirectly, utilizing a set of nonlinear differential equations. One result of this work is a nontrivial confirmation of the scaling/universality hypothesis.     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Rotators,periodicity, and absence of diffusion in cyclic cellular automata

Cyclic cellular automata are two-dimensional cellular automata which generalize lattice versions of the Lorentz gas and certain biochemistry models of artificial life. We show that rotators and time reversibility play a special role in the creation of closed orbits in cyclic cellular automata. We also prove that almost every orbit is closed (periodic) and the absence of diffusion for the flipping rotator model (also known as the ant).     

Evolution by damage spreading in Kauffman model

In Kauffman's Boolean automata model on the square lattice, the Darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next. Biological mutations are simulated by filpping one bit in the rule of one site. Selection of the fitter mutant then optimizes the whole lattice completely. This optimization is particularly effective near the critical point of the transition to chaos, but is in itself not a critical phenomenon. Also a two-dimensional spin glass can be optimized in this way.     

Self-averaging in complex brain neuron signals

Nonlinear statistical properties of Ventral Tegmental Area (VTA) of limbic brain are studied in vivo. VTA plays key role in generation of pleasure and in development of psychological drug addiction. It is shown that spiking time-series of the VTA dopaminergic neurons exhibit long-range correlations with self-averaging behavior. This specific VTA phenomenon has no relation to VTA rewarding function. Last result reveals complex role of VTA in limbic brain. Received 17 April 2002 / Received in final form 30 September 2002 Published online 31 December 2002