Effects of Surface Transition and Adsorption on Ionic Liquid Capacitors

Room-temperature ionic liquids (RTILs) are synthetic electrolytes with electrochemical stability superior to that of conventional aqueous-based electrolytes, allowing a significantly enlarged electrochemical window for application as capacitors. In this study, we propose a variant of an existing RTIL model for solvent-free RTILs, accounting for both ion–ion correlations and nonelectrostatic interactions. Using this model, we explore the phenomenon of spontaneous surface charge separation in RTIL capacitors and find that this transition is a common feature for realistic choices of the model parameters in most RTILs. In addition, we investigate the effects of asymmetric preferential ion adsorption on this charge separation transition and find that proximity of the transition in this case can result in greatly enhanced energy storage. Our work suggests that differential chemical treatment of electrodes can be a simple and useful means for optimizing energy storage in RTIL capacitors

Localized direct CP violation in B±→ρ0(ω)π±→π+π−π±B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow \pi^+ \pi^-\pi^\pm

We study the localized direct CP violation in the hadronic decays $B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow\pi^+ \pi^-\pi^\pm$, including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between $\rho^0$ and $\omega$. We calculate the localized integrated direct CP violation when the low invariant mass of $\pi^+\pi^-$ [$m(\pi^+\pi^-)_{low}$] is near $\rho^0(770)$. For five models of form factors investigated, we find that the localized integrated direct CP violation varies from -0.0170 to -0.0860 in the ranges of parameters in our model when $0.750<m(\pi^+\pi^-)_{low}<0.800$\,GeV. This result, especially the sign, agrees with the experimental data and is independent of form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV are positive and negative, respectively. We find that $\rho$-$\omega$ mixing makes the localized integrated CP asymmetry move towards the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also model independent. We also calculate the localized integrated direct CP violating asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV and find that they agree with the experimental data in some models of form factors.Comment: 22 pages, 2 figures. arXiv admin note: text overlap with arXiv:hep-ph/0602043, arXiv:hep-ph/0302156 by other author

Analysis on Some Basic Ion Channel Modeling Problems

The modeling and simulation of ion channel proteins are essential to the study of many vital physiological processes within a biological cell because most ion channel properties are very difficult to address experimentally in biochemistry. They also generate a lot of new numerical issues to be addressed in applied and computational mathematics. In this dissertation, we mainly deal with some numerical issues that are arisen from the numerical solution of one important ion channel dielectric continuum model, Poisson-Nernst-Planck (PNP) ion channel model, based on the finite element approximation approach under different boundary conditions and unstructured tetrahedral meshes. In particular, we present the derivation of an improved PNP ion channel model using Dirichlet boundary value conditions and membrane surface charges, and obtain its variational formulations. To solve this PNP ion channel model numerically, we develop a fast finite element iterative method and program it as a software package by using effective numerical techniques. This work makes it possible for us to carry out numerical tests in order to study the affection of different boundary value conditions on the PNP numerical solutions. To solve a PNP ion channel model by the finite element method, one important task is to generate an interface fitted unstructured tetrahedral mesh but it is very challenging to complete since the PNP ion channel model involves three physical regions -- a protein region, a membrane region, and a solvent region, and the interfaces between these three regions are very complex. To address this mesh challenge, in this dissertation, we develop a new algorithm for generating a triangular surface mesh of a simulation box domain and a new algorithm for constructing a tetrahedral mesh of the membrane region, such that we can easily split a mesh of the simulation box domain into three submeshes --- the meshes of protein, membrane, and solvent regions in high quality. Remarkably, our membrane mesh generation algorithm works for an ion channel protein with an irregular ion channel pore provided that a triangular mesh of the interface between the membrane and protein regions does not have any hole. Furthermore, we implement these two new mesh algorithms based on the state-of-the-art package FEniCS, and then adapt them to one commonly-used ion channel mesh generation package. With our PNP ion channel program package, we study the impacts of boundary value conditions, membrane surface changes, and simulation box sizes on the quality of a PNP ion channel model. Such studies are done numerically by using crystallographic molecular structures of ion channel proteins in a solution of multiple ionic species. We visualize the three-dimensional electrostatic potential and ionic concentrations not only in color mapping on a cross-section of protein, membrane, or solvent region but also in two-dimensional curves with curve values being the average values of potential and concentration functions over a block partition of the solvent region along the membrane normal direction. %We also test whether the channel conductance and charge selectivity obtained from the PNP ion channel model could be sensitive to some mutations of an ion channel protein