# Browsing by Subject "EQUATION"

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Item Open Access Non-stokes drag coefficient in single-particle electrophoresis: New insights on a classical problem(Chinese Physics B, 2019-01-01) Liao, MJ; Wei, MT; Xu, SX; Daniel Ou-Yang, H; Sheng, PWe measured the intrinsic electrophoretic drag coefficient of a single charged particle by optically trapping the particle and applying an AC electric field, and found it to be markedly different from that of the Stokes drag. The drag coefficient, along with the measured electrical force, yield a mobility-zeta potential relation that agrees with the literature. By using the measured mobility as input, numerical calculations based on the Poisson-Nernst-Planck equations, coupled to the Navier-Stokes equation, reveal an intriguing microscopic electroosmotic flow near the particle surface, with a well-defined transition between an inner flow field and an outer flow field in the vicinity of electric double layer's outer boundary. This distinctive interface delineates the surface that gives the correct drag coefficient and the effective electric charge. The consistency between experiments and theoretical predictions provides new insights into the classic electrophoresis problem, and can shed light on new applications of electrophoresis to investigate biological nanoparticles.Item Open Access Numerical method for multi-alleles genetic drift problem(SIAM Journal on Numerical Analysis, 2019-01-01) Xu, S; Chen, X; Liu, C; Yue, XGenetic drift describes random fluctuations in the number of genes variants in a population. One of the most popular models is the Wright-Fisher model. The diffusion limit of this model is a degenerate diffusion-convection equation. Due to the degeneration and convection, Dirac singularities will always develop at the boundaries as time evolves, i.e., the fixation phenomenon occurs. Theoretical analysis has proven that the weak solution of this equation, regarded as measure, conserves total probability and expectations. In the current work, we propose a scheme for 3-alleles model with absolute stability and generalize it to N-alleles case (N > 3). Our method can conserve not only total probability and expectations, but also positivity. We also prove that the discrete solution converges to a measure as the mesh size tends to zero, which is the exact measure solution of the original problem. The simulations illustrate that the probability density decays to zero first on the inner nodes, then also on the edge nodes except at the three vertex nodes, on which the density finally concentrates. The results correctly predict the fixation probability and are consistent with theoretical ones and with direct Monte Carlo simulations.