For motions in liquid

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  • Soft matter (or soft condensed matter) refers to a group of systems that includes polymers, colloids, amphiphiles, membranes, micelles, emulsions, dendrimers, liquid crystals, polyelectrolytes, and their mixtures. Soft matter systems usually have structural length scales in the region from a nanometer to several hundred nanometers and thus fall within the domain of “nanotechnology.” The soft matter length scales are often characterized by interactions that are of the order of thermal energies so that relatively small perturbations can cause dramatic structural changes in them.

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  • Besides the blowing dust and the heavenly bodies, little else moves on the Martian landscape. This lack of movement might seem to be strangest of all, for we humans are used to motion. Almost from birth, infants follow motion with their eyes, and from then on we are continually aware of things moving about, starting, stopping, turning, bouncing. On earth we see liquids flowing, people moving, and the wind stirring the leaves of trees. Although we can not see them, we know that the very atoms and molecules of matter are continuously in motion. Even mosses and lichens that...

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  • Annals of Mathematics We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler’s equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a “physical condition”, related to the fact that the pressure of a fluid has to be positive. ...

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  • There have been some attempts to explain theoretically the behavior of the stock return volatility. Veronesi (1999) constructs a model with regime shifts in the endowments in which investors will- ingness to hedge against their own uncertainty on the true regime generates overreaction to good news in bad times and volatility clustering. In contrast to that paper, I assume that the exogenous state variables are not subject to regimes, neither do they exhibit mean-reversion.

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