The role of one-dimensional diffusion in a growth model of the surface of a Kossel’s crystal

2006 ◽  
Vol 40 (3) ◽  
pp. 367-374
Author(s):  
A. M. Boĭko ◽  
R. A. Suris
2011 ◽  
Vol 9 (67) ◽  
pp. 222-233 ◽  
Author(s):  
Yoshimi Tanaka ◽  
Kentaro Ito ◽  
Toshiyuki Nakagaki ◽  
Ryo Kobayashi

Limbless crawling is a fundamental form of biological locomotion adopted by a wide variety of species, including the amoeba, earthworm and snake. An interesting question from a biomechanics perspective is how limbless crawlers control their flexible bodies in order to realize directional migration. In this paper, we discuss the simple but instructive problem of peristalsis-like locomotion driven by elongation–contraction waves that propagate along the body axis, a process frequently observed in slender species such as the earthworm. We show that the basic equation describing this type of locomotion is a linear, one-dimensional diffusion equation with a time–space-dependent diffusion coefficient and a source term, both of which express the biological action that drives the locomotion. A perturbation analysis of the equation reveals that adequate control of friction with the substrate on which locomotion occurs is indispensable in order to translate the internal motion (propagation of the elongation–contraction wave) into directional migration. Both the locomotion speed and its direction (relative to the wave propagation) can be changed by the control of friction. The biological relevance of this mechanism is discussed.


2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Igor Medved’ ◽  
Robert Černý

The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster.


2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.


2021 ◽  
Vol 22 (5) ◽  
pp. 2398
Author(s):  
Wooyoung Kang ◽  
Seungha Hwang ◽  
Jin Young Kang ◽  
Changwon Kang ◽  
Sungchul Hohng

Two different molecular mechanisms, sliding and hopping, are employed by DNA-binding proteins for their one-dimensional facilitated diffusion on nonspecific DNA regions until reaching their specific target sequences. While it has been controversial whether RNA polymerases (RNAPs) use one-dimensional diffusion in targeting their promoters for transcription initiation, two recent single-molecule studies discovered that post-terminational RNAPs use one-dimensional diffusion for their reinitiation on the same DNA molecules. Escherichia coli RNAP, after synthesizing and releasing product RNA at intrinsic termination, mostly remains bound on DNA and diffuses in both forward and backward directions for recycling, which facilitates reinitiation on nearby promoters. However, it has remained unsolved which mechanism of one-dimensional diffusion is employed by recycling RNAP between termination and reinitiation. Single-molecule fluorescence measurements in this study reveal that post-terminational RNAPs undergo hopping diffusion during recycling on DNA, as their one-dimensional diffusion coefficients increase with rising salt concentrations. We additionally find that reinitiation can occur on promoters positioned in sense and antisense orientations with comparable efficiencies, so reinitiation efficiency depends primarily on distance rather than direction of recycling diffusion. This additional finding confirms that orientation change or flipping of RNAP with respect to DNA efficiently occurs as expected from hopping diffusion.


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