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Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
The simplest model to describe a non-linear effect, the ML 2 model involves a metal system (M) with two chiral ligands, L R and L S. In addition to the catalyzed reaction of interest, the model accounts for a steady state equilibrium between the unbound and bound catalyst complexes. [ 3 ]
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
While some studies have found that vitamin D 3 raises 25(OH)D blood levels faster and remains active in the body longer, [44] [45] others contend that vitamin D 2 sources are equally bioavailable and effective for raising and sustaining 25(OH)D. [46] [47] If digestive disorders compromise absorption, then intramuscular injection of up to ...
Examples of anomalous diffusion in nature have been observed in ultra-cold atoms, [3] harmonic spring-mass systems, [4] scalar mixing in the interstellar medium, [5] telomeres in the nucleus of cells, [6] ion channels in the plasma membrane, [7] colloidal particle in the cytoplasm, [8] [9] [10] moisture transport in cement-based materials, [11 ...
A stirred BZ reaction mixture showing changes in color over time. The discovery of the phenomenon is credited to Boris Belousov.In 1951, while trying to find the non-organic analog to the Krebs cycle, he noted that in a mix of potassium bromate, cerium(IV) sulfate, malonic acid, and citric acid in dilute sulfuric acid, the ratio of concentration of the cerium(IV) and cerium(III) ions ...
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
If spatial effects are taken into account through a reaction–diffusion equation, long-range correlations and spatially ordered patterns arise, [6] such as in the case of the Belousov–Zhabotinsky reaction. Systems with such dynamic states of matter that arise as the result of irreversible processes are dissipative structures.