Displaying similar documents to “Phase field method for mean curvature flow with boundary constraints”

Phase field method for mean curvature flow with boundary constraints

Elie Bretin, Valerie Perrier (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper is concerned with the numerical approximation of mean curvature flow  → () satisfying an additional inclusion-exclusion constraint  ⊂ () ⊂  . Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify...

Upper large deviations for maximal flows through a tilted cylinder

Marie Theret (2014)

ESAIM: Probability and Statistics

Similarity:

We consider the standard first passage percolation model in ℤ for  ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...

On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena

Similarity:

A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation ( + + + + ) = which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular...

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....

Nash equilibria for a model of traffic flow with several groups of drivers

Alberto Bressan, Ke Han (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are groups of drivers, The -th group consists of drivers, sharing the same departure and arrival costs (), (). For any given population sizes ,, , we prove the existence of a Nash equilibrium solution,...

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically ( ) where is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, 339 (2004) 71–76, C. Mouhot and L. Pareschi, 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which...

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in -norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate information of smoothness/sparsity on the inhomogeneity...

Regularity properties of optimal transportation problems arising in hedonic pricing models

Brendan Pass (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form () = ( + ) where is a convex function on ℝ. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely...

Local semiconvexity of Kantorovich potentials on non-compact manifolds

Alessio Figalli, Nicola Gigli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We prove that any Kantorovich potential for the cost function = /2 on a Riemannian manifold (, ) is locally semiconvex in the “region of interest”, without any compactness assumption on , nor any assumption on its curvature. Such a region of interest is of full -measure as soon as the starting measure does not charge – 1-dimensional rectifiable sets.

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

Luís Balsa Bicho, António Ornelas (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We prove of vector minimizers () =  (||) to multiple integrals ∫ ((), |()|)  on a  ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a  : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...

Model selection and estimation of a component in additive regression

Xavier Gendre (2014)

ESAIM: Probability and Statistics

Similarity:

Let  ∈ ℝ be a random vector with mean and covariance matrix where is some known  × -matrix. We construct a statistical procedure to estimate as well as under moment condition on or Gaussian hypothesis. Both cases are developed for known or unknown . Our approach is free from any prior assumption on and is based on non-asymptotic model selection methods....

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the variational problem         inf{ () +  () + (1 −  − ) () | Ω open in ℝ, || ≤ 1}, for  ∈ [0, 1],  +  ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( =   < 1), or is much greater than ( =   > 1). We consider all three cases. ...