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A convexity theory for interacting g...

McCann, Robert John.

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A convexity theory for interacting gases and equilibrium crystals.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A convexity theory for interacting gases and equilibrium crystals./
作者:	McCann, Robert John.
面頁冊數:	163 p.
附註:	Source: Dissertation Abstracts International, Volume: 55-10, Section: B, page: 4409.
Contained By:	Dissertation Abstracts International55-10B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9505121

A convexity theory for interacting gases and equilibrium crystals.
McCann, Robert John.

A convexity theory for interacting gases and equilibrium crystals. - 163 p.

Source: Dissertation Abstracts International, Volume: 55-10, Section: B, page: 4409.

Thesis (Ph.D.)--Princeton University, 1994.

A new set of variational inequalities is introduced, based on a novel but natural interpolation between Borel probability measures on Subjects--Topical Terms:

515831
Mathematics.

A convexity theory for interacting gases and equilibrium crystals.
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100 1 $a McCann, Robert John. $3 1938259
245 1 2 $a A convexity theory for interacting gases and equilibrium crystals.
300 $a 163 p.
500 $a Source: Dissertation Abstracts International, Volume: 55-10, Section: B, page: 4409.
500 $a Adviser: Elliott Lieb.
502 $a Thesis (Ph.D.)--Princeton University, 1994.
520 $a A new set of variational inequalities is introduced, based on a novel but natural interpolation between Borel probability measures on $\ rm\IR\sp{d} $. Used in lieu of convexity or rearrangement inequalities, these estimates lead to existence and uniqueness results concerning equilibrium states for (i) attracting gases; and (ii) plane crystals in an external field.
520 $a Consider a d-dimensional gas of particles interacting through a force which increases with distance and obeying an equation of state $ relating pressure to density. For $ non-decreasing, a unique energy minimizing state is shown to exist up to translation.
520 $a For a two-dimensional crystal in a convex potential, the equilibrium shape was known to consist of a countable disjoint union of closed convex sets. Here it is shown that each convex component minimizes the energy uniquely among convex sets of its area. Assuming symmetry under $x \leftrightarrow -x $, the crystal formed must be unique, convex and connected. The last result leads to a new proof that a convex crystal $ away from equilibrium remains convex and balanced under curvature-driven flow.
520 $a Incidental results include new generalisations of the Brunn-Minkowski inequality from sets to measures, and new derivations of inequalities due to Prekopa, Leindler, Brascamp and Lieb. A theorem of Brenier is improved to yield existence of a unique measure-preserving mapping with a convex potential between any pair of $ probability measures on $\ IR\sp{d} $; the potential satisfies a Monge-Ampere equation almost everywhere.
520 $a A separate section considers compressible fluid models for a rotating star. For fixed mass and large angular momentum, stable uniformly rotating solutions to the associated Navier-Stokes-Poisson system are constructed in the form of binary stars with specified mass ratio. A one-dimensional toy model admitting explicit solution is also introduced: to any specified number of components and their masses corresponds a single family of solutions, parameterized by angular velocity up to the point of equatorial break-up.
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Fluid and Plasma. $3 1018402
650 4 $a Physics, Astronomy and Astrophysics. $3 1019521
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710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 55-10B.
790 1 0 $a Lieb, Elliott, $e advisor
790 $a 0181
791 $a Ph.D.
792 $a 1994
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9505121