A Quantitative Analytical Model for Predicting and Optimizing the Rate Performance of Battery Cells

An important objective of designing lithium-ion rechargeable battery cells is to maximize their rate performance without compromising the energy density, which is mainly achieved through computationally expensive numerical simulations at present. Here we present a simple analytical model for predicting the rate performance of battery cells limited by electrolyte transport without any fitting parameters. It exhibits very good agreement with simulations over a wide range of discharge rate and electrode thickness and offers a speedup of >10$^5$ times. The optimal electrode properties predicted by the model are of less than 10% difference from simulation results, suggesting it as an attractive computational tool for the cell-level battery architecture design. The model also offers important insights on practical ways to improve the rate performance of thick electrodes, including avoiding electrode materials such as LiFePO$_4$ and Li$_4$Ti$_5$O$_{12}$ whose open-circuit potentials are insensitive to the state of charge and utilizing lithium metal anode to synergistically accelerate electrolyte transport within thick cathodes

The multiplication theorem and bases in finite and affine quantum cluster algebras

We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \cite{fanqin}. We apply the formula to construct some $\mathbb{ZP}$-bases in quantum cluster algebras of finite and affine types. Under the specialization $q$ and coefficients to $1$, these bases are the integral bases of cluster algebra of finite and affine types (see \cite{CK1} and \cite{DXX}).Comment: 20 pages, the integral bases of cluster algebra of affine types are replace

The cluster character for cyclic quivers

We define an analogue of the Caldero-Chapoton map (\cite{CC}) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character (in the sense of \cite{Palu}) and satisfies some inductive formulas for the multiplication between the generalized cluster variables (the images of objects of the cluster category under the map). Moreover, we construct a $\mathbb{Z}$-basis for the algebras generated by all generalized cluster variables.Comment: 11 page

Notes on the cluster multiplication formulas for 2-Calabi-Yau categories

Y. Palu has generalized the cluster multiplication formulas to 2-Calabi-Yau categories with cluster tilting objects (\cite{Palu2}). The aim of this note is to construct a variant of Y. Palu's formula and deduce a new version of the cluster multiplication formula (\cite{XiaoXu}) for acyclic quivers in the context of cluster categories.Comment: 8 page

Model and Simulations of the Epitaxial Growth of Graphene on Non-Planar 6H-SiC Surfaces

We study step flow growth of epitaxial graphene on 6H-SiC using a one dimensional kinetic Monte Carlo model. The model parameters are effective energy barriers for the nucleation and propagation of graphene at the SiC steps. When the model is applied to graphene growth on vicinal surfaces, a strip width distribution is used to characterize the surface morphology. Additional kinetic processes are included to study graphene growth on SiC nano-facets. Our main result is that the original nano-facet is fractured into several nano-facets during graphene growth. This phenomenon is characterized by the angle at which the fractured nano-facet is oriented with respect to the basal plane. The distribution of this angle across the surface is found to be related to the strip width distribution for vicinal surfaces. As the terrace propagation barrier decreases, the fracture angle distribution changes continously from two-sided Gaussian to one-sided power-law. Using this distribution, it will be possible to extract energy barriers from experiments and interpret the growth morphology quantitatively.Comment: 6 pages, 7 figure

A quantum analogue of generic bases for affine cluster algebras

We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.Comment: The paper supersedes arXiv:1006.392

Phase Field Modelling of Submonolayer Epitaxial Growth

We report simulations of submonolayer epitaxial growth using a continuum phase field model. The island density and the island size distribution both show scaling behavior. When the capillary length is small, the island size distribution is consistent with irreversible aggregation kinetics. As the capillary length increases, the island size distribution reflects the effects of reversible aggregation. These results are in quantitative agreement with other simulation methods and with experiments. However, the scaling of the island total density does not agree with known results. The reasons are traced to the mechanisms of island nucleation and aggregation in the phase field model.Comment: 6 pages, 5 figure

Upper bound and shareability of quantum discord based on entropic uncertainty relations

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well accepted result that quantum discord is not monogamous.Comment: 5 pages, 1 figure, the final version as that published in Phys. Rev.

G/GG/G Gauged Supergroup Valued WZNW Field Theory

The $G/G$ gauged supergroup valued WZNW theory is considered. It is shown that for G=\OSP, the $G/G$ theory tensoring a ($b$, $c$, $\beta$, $\gamma$) system is equivalent to the non-critical fermionic theory. The relation between integral or half integral moded affine superalgebra and its reduced theory, the NS or R superconformal algebra, is discussed in detail. The physical state space, i.e. the BRST semi-infinite cohomology, is calculated, for the \OSP/\OSP theory.Comment: AS-ITP-93-2

Intermediate effective interactions and dynamical fermion mass generation of QCD

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate fermion-4 interactions is investigated. Of the 6 kinds of fermion-4 interactions generated by one-loop QCD, 4 kinds generate fermion mass while the other 2 kinds degenerate it. The net effect is fermion mass degeneration when dimensionless mass is large. Flow patterns on the $\tilde{m}^2_{\text{phys.}}-\tilde{g}^2$ plane are drawn.Comment: 6 pages, 5 figures, revtex