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Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary,imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
We study mean curvature flows (MCFs) coming out of cones. As cones are singular at the origin, the evolution is generally not unique. A special case of such flows is known as the self-expanders. We wi...
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
Mean curvature flow is the fastest way to decrease the area of surfaces. It is the model in many disciplines such as material science, fluid mechanism, and computer graphics. The translators are a spe...
Biologists believe they are one step closer to a long-held goal of making a cheap, widely available plant source for energy and fuel. One of the next big weapons in the battle against climate change m...
The last time Earth experienced both ice sheets and carbon dioxide levels within the range predicted for this century was a period of major sea level rise, melting ice sheets and upheaval of tropical ...
The task of determining dietary requirements for vitamin D intake is one of the key unresolved issues in vitamin- and mineral-related nutrition. The complexities of issues, including determining intak...
The advancement of satellite altimeter technology has generated many evolutions to oceanographic and geophysical studies. A multi-mission satellite altimeter consists with TOPEX, Jason-1 and Jason-2, ...
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
We study stationary quantum fluctuations around a mean field limit in trapped, dilute atomic gases of repulsively interacting bosons at zero temperature. Our goal is to describe quantum-mechanically t...

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