Nanoparticle dynamics: A multiscale analysis of the Liouville equation

Article Abstract:

A theory of nanoparticle dynamics that is based on scaling arguments and the Liouville equation is presented. The results are obtained via formal asymptotic expansions in mass, size and other physical and kinetic parameter ratios.

Chemical reaction, Rate of, Chemical kinetics, Asymptotic expansions, Nanoparticles

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The backward Stochastic Liouville equation

Article Abstract:

The backward Stochastic Liouville equation (SLE) has advantages over the usual SLE with regard to obtaining numerical and analytical results. More analytic solutions for diffusion-controlled care is likely to surface.

Heat equation, Dirac equation

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Fractional diffusion based on Riemann-Liouville fractional derivatives

Article Abstract:

A fractional diffusion equation involving Riemann-Liouville fractional derivatives is solved exactly.

Differential equations

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