128 research outputs found
Sub-Doppler supersonic jet spectra of the coupled 6a10 and 6b10 vibronic bands of the S1(1B2u) ← S0(1A1g) transition in monodeuterobenzene and their rovibrational analysis
Tightness for a stochastic Allen--Cahn equation
We study an Allen-Cahn equation perturbed by a multiplicative stochastic
noise which is white in time and correlated in space. Formally this equation
approximates a stochastically forced mean curvature flow. We derive uniform
energy bounds and prove tightness of of solutions in the sharp interface limit,
and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential
Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new.
It replaces and simplifies the old propositions 6.4-6.
On a linear programming approach to the discrete Willmore boundary value problem and generalizations
We consider the problem of finding (possibly non connected) discrete surfaces
spanning a finite set of discrete boundary curves in the three-dimensional
space and minimizing (globally) a discrete energy involving mean curvature.
Although we consider a fairly general class of energies, our main focus is on
the Willmore energy, i.e. the total squared mean curvature Our purpose is to
address the delicate task of approximating global minimizers of the energy
under boundary constraints.
The main contribution of this work is to translate the nonlinear boundary
value problem into an integer linear program, using a natural formulation
involving pairs of elementary triangles chosen in a pre-specified dictionary
and allowing self-intersection.
Our work focuses essentially on the connection between the integer linear
program and its relaxation. We prove that: - One cannot guarantee the total
unimodularity of the constraint matrix, which is a sufficient condition for the
global solution of the relaxed linear program to be always integral, and
therefore to be a solution of the integer program as well; - Furthermore, there
are actually experimental evidences that, in some cases, solving the relaxed
problem yields a fractional solution. Due to the very specific structure of the
constraint matrix here, we strongly believe that it should be possible in the
future to design ad-hoc integer solvers that yield high-definition
approximations to solutions of several boundary value problems involving mean
curvature, in particular the Willmore boundary value problem
Nonsmooth analysis of doubly nonlinear evolution equations
In this paper we analyze a broad class of abstract doubly nonlinear evolution
equations in Banach spaces, driven by nonsmooth and nonconvex energies. We
provide some general sufficient conditions, on the dissipation potential and
the energy functional,for existence of solutions to the related Cauchy problem.
We prove our main existence result by passing to the limit in a
time-discretization scheme with variational techniques. Finally, we discuss an
application to a material model in finite-strain elasticity.Comment: 45 page
Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension
We prove nonlinear asymptotic stability of steady spheres in the two-phase
Stefan problem with surface tension. Our method relies on the introduction of
appropriate orthogonality conditions in conjunction with a high-order energy
method.Comment: 25 pages, important references added, two remarks added, typos
correcte
Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
The qualitative behavior of a thermodynamically consistent two-phase Stefan
problem with surface tension and with or without kinetic undercooling is
studied. It is shown that these problems generate local semiflows in
well-defined state manifolds. If a solution does not exhibit singularities in a
sense made precise below, it is proved that it exists globally in time and its
orbit is relatively compact. In addition, stability and instability of
equilibria is studied. In particular, it is shown that multiple spheres of the
same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised
version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66
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