In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for ...

In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indic...

in this paper, we consider a cahn-hillard/allen-cahn equation. by using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in h^k(0

I went to Carnegie Tech after spending my first 6 professional years designing computers at Digital Equipment Corporation to be part of the startup faculty of the computer science department. Allen Newell, Alan Perlis, and Rod Williams, who headed the Electrical Engineering Department, made this career changing choice easy for me. Like everyone who knew Allen, I feel deeply honored to have know...

The Allen Brain Atlas (http://www.brain-map.org) provides a unique online public resource integrating extensive gene expression data, connectivity data and neuroanatomical information with powerful search and viewing tools for the adult and developing brain in mouse, human and non-human primate. Here, we review the resources available at the Allen Brain Atlas, describing each product and data t...

Dry matter intake (DMI) is related to dietary NDF content (Mertens, 1987) and in vitro NDF digestibility (NDFD, % of NDF; Oba and Allen, 1999). The NRC (2001) summative energy equation is based on fiber digestibility calculated using lignin. Whole-plant lignin content was found to have a strong negative relationship with in-vitro NDFD within comparisons of brown midrib (bm3) hybrids to isogenic...

Originally proposed as a method for measuring the power gain of the cochlear amplifier, Allen-Fahey experiments compare intracochlear distortion products and ear-canal otoacoustic emissions (OAEs) under tightly controlled conditions. In this paper Allen-Fahey experiments are shown to place significant constraints on the dominant mode of reverse energy propagation within the cochlea. Existing Al...