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Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
, 1981
"... Several methods have been previously used to approximate free boundaries in finite difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other metho ..."
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Cited by 603 (3 self)
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Several methods have been previously used to approximate free boundaries in finite difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other
Free Boundaries
 in Viscous Flows, no. 61 in IMA
, 1994
"... Computational studies of the effect of wall temperature on hypersonic shockinduced ..."
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Cited by 1 (0 self)
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Computational studies of the effect of wall temperature on hypersonic shockinduced
CONVEXITY OF THE FREE BOUNDARY FOR AN EXTERIOR FREE BOUNDARY PROBLEM INVOLVING THE PERIMETER
, 2006
"... Convexity of the free boundary for an exterior free boundary problem involving the perimeter ..."
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Convexity of the free boundary for an exterior free boundary problem involving the perimeter
Homogenization of the free boundary velocity
 Arch. Rat. Mech. Anal
"... In this paper we investigate some free boundary problems with spacedependent free boundary velocities. Based on maximum principletype arguments, we show the uniform convergence of the solutions in the homogenization limit. The main step is to show the uniqueness of the limiting free boundary veloci ..."
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Cited by 7 (6 self)
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In this paper we investigate some free boundary problems with spacedependent free boundary velocities. Based on maximum principletype arguments, we show the uniform convergence of the solutions in the homogenization limit. The main step is to show the uniqueness of the limiting free boundary
FREE BOUNDARY ON A CONE
, 2013
"... We study two phase problems posed over a two dimensional cone generated by a smooth curve γ on the unit sphere. We show that when length(γ) < 2pi the free boundary avoids the vertex of the cone. When length(γ) ≥ 2pi we provide examples of minimizers such that the vertex belongs to the free bound ..."
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We study two phase problems posed over a two dimensional cone generated by a smooth curve γ on the unit sphere. We show that when length(γ) < 2pi the free boundary avoids the vertex of the cone. When length(γ) ≥ 2pi we provide examples of minimizers such that the vertex belongs to the free
ASYMPTOTIC SHAPES WITH FREE BOUNDARIES
, 908
"... Abstract. We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary. ..."
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Abstract. We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary.
On the convexity of some free boundaries
, 2009
"... We demonstrate that a method of Colesanti and Salani, which compares solutions of elliptic differential equations to their quasiconcave envelopes, can be extended to derive convexity of free boundaries. As examples we present the socalled dam problem, a free boundary problem modelling pollution and ..."
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Cited by 1 (0 self)
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We demonstrate that a method of Colesanti and Salani, which compares solutions of elliptic differential equations to their quasiconcave envelopes, can be extended to derive convexity of free boundaries. As examples we present the socalled dam problem, a free boundary problem modelling pollution
Remarks on positive and free boundary
, 2010
"... Abstract. The equation −∆u = χ{u>0} ( − 1 uβ +λf(x, u) in Ω with Dirichlet boundary condition on ∂Ω has a maximal solution uλ ≥ 0 for every λ> 0. For λ less than a constant λ ∗ the solution vanishes inside the domain, and for λ> λ ∗ the solution is positive and stable. We obtain optimal reg ..."
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regularity of uλ even in the presence of the free boundary. If 0 < λ < λ ∗ the solutions of the singular parabolic equation ut − ∆u + 1uβ = λf(u) quench in finite time, and for λ> λ ∗ the solutions are globally positively defined.
Free boundary problems in science and technology
 Notices Amer. Math. Soc
, 2000
"... Free boundary problems deal with solving partial differential equations (PDEs) in a domain, a part of whose boundary is unknown in advance; that portion of the boundary is called a free boundary. In addition to the standard boundary conditions that are needed in order to solve the PDEs, an additiona ..."
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Cited by 12 (0 self)
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Free boundary problems deal with solving partial differential equations (PDEs) in a domain, a part of whose boundary is unknown in advance; that portion of the boundary is called a free boundary. In addition to the standard boundary conditions that are needed in order to solve the PDEs
A Free Boundary Problem With Nonlinear Jump And Kinetics On The Free Boundaries
"... . In this paper we study a free boundary problem arising in modeling chemical vapor deposition in titanium. The problem involves two free boundaries, one of them is internal to the domain. The interface conditions at the interior free boundary consist of @u @n @v @n = k (u v) ; v = (u) and v u = V ..."
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. In this paper we study a free boundary problem arising in modeling chemical vapor deposition in titanium. The problem involves two free boundaries, one of them is internal to the domain. The interface conditions at the interior free boundary consist of @u @n @v @n = k (u v) ; v = (u) and v u
Results 1  10
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