Search results
Results From The WOW.Com Content Network
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 ...
Applications of the Kuramoto–Sivashinsky equation extend beyond its original context of flame propagation and reaction–diffusion systems. These additional applications include flows in pipes and at interfaces, plasmas, chemical reaction dynamics, and models of ion-sputtered surfaces. [9] [21]
The parameters depend on the physical system under consideration. In the context of fish skin pigmentation, the associated equation is a three field reaction–diffusion one in which the linear parameters are associated with pigmentation cell concentration and the diffusion parameters are not the same for all fields. [9]
Reaction–diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation. [5] [6] Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equations, there are often possibilities for an analytical treatment. [7] [8] [9]
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]
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 ...
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 ...
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation [1] occurring in various areas of applied mathematics, such as fluid mechanics, [2] nonlinear acoustics, [3] gas dynamics, and traffic flow. [4]