Treating the motion of a dust particle suspended in a liquid as a random walk, Einstein in 1905 derived an equation describing the diffusion of the particle’s probability distribution in configuration space. Fokker and Planck extended this work to describe the velocity distribution of the particles. Their equation and its solutions have been applied to many problems in nature starting with the ...

A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on JKO type variational formulation naturally enforces solution positivity and energy law as continuous PNP system. fully discrete further formulated a constrained minimization problem, shown to be solvable, satisfy all three properties (mass conservati...

For ion channel gating, the appearance of two distinct conformational states and the discrete transitions between them are essential, and therefore of crucial importance to all living organisms. We show that the physical interplay between two structural elements that are commonly present in bacterial mechanosensitive channels--namely, a charged vestibule and a hydrophobic constriction--creates ...

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson-Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its...

Electrochemical flow cells have found widespread use in analytical chemistry due to their short response time, high sensitivity and selectivity [1, 2]. The geometrical flexibility and therefore, the ease of coupling the electrochemical to other experimental techniques has attracted considerable interest for applications in electrocatalytic research as well. Such coupling is far more cumbersome ...