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Jia-Ming Liou

Publications and source records attributed to Jia-Ming Liou.

5 recordsLinked to original sources
arXiv2017

An algebraic construction of a solution to the mean field equations on hyperelliptic Curves and its diabatic limit

In this paper, we give an algebraic construction of the solution to the following mean field equation $$ Δψ+e^ψ=4π\sum_{i=1}^{2g+2}δ_{P_{i}}, $$ on a genus $g\geq 2$ hyperelliptic curve $(X,ds^{2})$ where $ds^{2}$ is a canonical metric on $X$ and $\{P_{1},\cdots,P_{2g+2}\}$ is the set of Weierstrass points on $X.$ Furthermore, we study the rescaled equation $$ Δψ+γe^ψ=4πγ\sum_{i=1}^{2g+2}δ_{P_{i}} $$ and its adiabatic limit at $γ=0$.

math.DG↗
arXiv2015

Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves

We analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $\leq 6$. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for lower genera.

math.AG↗
arXiv2012

Local Conduction at the BiFeO3-CoFe2O4 Tubular Oxide Interface

In strongly correlated oxides, heterointerfaces, manipulating the interaction, frustration, and discontinuity of lattice, charge, orbital, and spin degrees of freedom, generate new possibilities for next generation devices. In this study, we went back to examine the existing oxide heterostructures and found the local conduction at the BiFeO3-CoFe2O4 vertical interface. In such hetero-nanostructure, the tubular interface, surrounding BiFeO3-CoFe2O4 vertical interface, can not only be the medium to the coupling between phases, but also be a new state of the matter. Our study demonstrates a novel concept on oxide interface design and opens a pathway alternative for the explorations of diverse functionalities in complex oxide interfaces.

cond-mat.mtrl-sci↗
arXiv2012

Moduli Spaces and Grassmannian

We calculate the homomorphism of the cohomology induced by the Krichever map of moduli spaces of curves into infinite-dimensional Grassmannian. This calculation can be used to compute the homology classes of cycles on moduli spaces of curves that are defined in terms of Weierstrass points.

math-ph↗