Numerical Study of Poration and Ionic Conduction in Nanopores Caused by High-Intensity, Nanosecond Pulses in Cell

This dissertation focuses on the dynamics and bioeffects of electroporation of biological cell and ionic conduction in nanopores under high-intensity, nanosecond pulses. The electroporation model utilized the current continuity equation and the asymptotic Smoluchowski equation to explore the transmembrane potential and pore density of the plasma and intracellular membranes; the ionic conduction model employed the Poisson-Nernst-Planck equations and the Navier-Stokes equations to analyze the ionic current and ion concentration profile. Nanosecond electric pulses of high-intensity amplitude can initiate electroporation of intracellular organelles. The pulse parameters and cell electrical properties, that can selectively electroporate liposomes but keep the plasma and nuclear membranes intact, have been evaluated and optimized. This opens up the possibility of loading cell liposomes with potent drugs for subsequent release as part of a procedure for electrochemotherapy. The traditional spherical model ignores the geometric influence; therefore, the more realistic irregular shape of intracellular organelles is considered to explore the geometric impact on dynamics of electroporation. The results obtained here show that in the shorter pulse range, geometric dependence is very pronounced, and so short pulses could be very effective in highly irregularly shaped cells. In addition, nanopore transport is analyzed using a numerical method that couples the Nernst-Planck equations for ionic concentrations, the Poisson equation for the electric potential and Navier-Stokes equations for the fluid flow. Roles of the applied bias, the geometric asymmetry in the nanopore, as well as the charge distribution lining the membrane are comprehensively examined. The results show non-linear I-V characteristics that are in reasonable agreement with data, and suggest a bias-dependent expansion of an asymmetric pore, possibly arising from the enhanced flux of incident ions on the membrane walls

Super-reflection and Cloaking Based on Zero Index Metamaterial

A zero index metamaterial (ZIM) can be utilized to block wave (super-reflection) or conceal objects completely (cloaking). The "super-reflection" device is realized by a ZIM with a perfect electric (magnetic) conductor inclusion of arbitrary shape and size for a transverse electric (magnetic) incident wave. In contrast, a ZIM with a perfect magnetic (electric) conductor inclusion for a transverse electric (magnetic) incident wave can be used to conceal objects of arbitrary shape. The underlying physics here is determined by the intrinsic properties of the ZIM

Algorithms to test open set condition for self-similar set related to P.V. numbers

Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, \mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not

The Teaching of Highlighting Mathematical Culture from the Perspective of HPM ——Take the Teaching for "Letters Represent Numbers" as an Example

"Compulsory Education Mathematics Curriculum Standards (2022 Edition)" clearly states that attention should be paid to mathematics culture, but at present, mathematics textbooks and classrooms still do not attach importance to mathematics culture, and mathematics culture is not really integrated into mathematics classroom teaching. For further exploring how to integrate mathematical culture into mathematical classroom teaching, the traditional teaching design of Letters Represent Numbers is transformed from the perspective of HPM by taking Letters Represent Numbers as a case, and the history of mathematics is used to highlight the mathematical culture embedded in mathematical knowledge, and based on this, ideas and suggestions are put forward for teaching to highlight mathematical culture from the perspective of HPM. Keywords: HPM; Mathematical Culture; Letters Represent Numbers; Teaching Design DOI: 10.7176/JEP/13-35-07 Publication date: December 31st 2022