1,387 research outputs found
Mean field equations, hyperelliptic curves and modular forms: II
A pre-modular form of weight is
introduced for each , where , such that for , every
non-trivial zero of , namely ,
corresponds to a (scaling family of) solution to the mean field equation
\begin{equation} \tag{MFE} \triangle u + e^u = \rho \, \delta_0 \end{equation}
on the flat torus with singular strength .
In Part I (Cambridge J. Math. 3, 2015), a hyperelliptic curve , the Lam\'e curve, associated to the MFE was
constructed. Our construction of relies on a detailed study
on the correspondence induced
from the hyperelliptic projection and the addition map.
As an application of the explicit form of the weight 10 pre-modular form
, a counting formula for Lam\'e equations of degree
with finite monodromy is given in the appendix (by Y.-C. Chou).Comment: 32 pages. Part of content in previous versions is removed and
published separately. One author is remove
Analytic Aspects of the Toda System: II. Bubbling behavior and existence of solutions
In this paper, we continue to consider the 2-dimensional (open) Toda system
(Toda lattice) for . We give a much more precise bubbling behavior of
solutions and study its existence in some critical casesComment: 33 pages, to appear in Comm. Pure Appl. Mat
A coordinated approach for supply-chain tracking in the liquefied natural gas industry
With the increased size and complexity of liquefied natural gas (LNG) projects, supplychain management has become a challenging process due to involvements of the remote location of the project site and the multiple stakeholders. The transparency and traceability of the supply-chain are critical as any surpluses or shortages of materials will put the project at risk. Currently, limited research has been conducted on LNG projects considering the total supply-chain perspective, which refers to all stages of materials tracking in off-site manufacturing, transportation, and site logistics. The purpose of this research is to propose a framework of a coordinated approach for supply-chain tracking in the LNG industry. Two focus group studies were organized to develop the proposed framework: One for LNG construction supply chain process development, and another for alternative tracking technologies selection. In addition, two experiments, namely off-site fabrication tracking and site logistics tracking, were conducted in a field to evaluate the feasibility of the proposed framework. Technology limitations were also discussed in terms of field implementation
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