1,893 research outputs found
Flux form Semi-Lagrangian methods for parabolic problems
A semi-Lagrangian method for parabolic problems is proposed, that extends
previous work by the authors to achieve a fully conservative, flux-form
discretization of linear and nonlinear diffusion equations. A basic consistency
and convergence analysis are proposed. Numerical examples validate the proposed
method and display its potential for consistent semi-Lagrangian discretization
of advection--diffusion and nonlinear parabolic problems
A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function
interpolation for approximating a curvature-related level set model, which has
been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces
from sparse, possibly noisy data sets. The main advantages of the proposed
scheme are the possibility to solve the level set method on unstructured grids,
as well as to concentrate the reconstruction points in the neighbourhood of the
data set, with a consequent reduction of the computational effort. Moreover,
the scheme is explicit. Numerical tests show the accuracy and robustness of our
approach to reconstruct curves and surfaces from relatively sparse data sets.Comment: 14 pages, 26 figure
An estimate for the multiplicity of binary recurrences
In this paper we improve drastically the estimate for the multiplicity of a
binary recurrence. The main contribution comes from an effective version of the
Faltings' Product Theorem
A generalization of the Subspace Theorem with polynomials of higher degree
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem
with arbitrary homogeneous polynomials of arbitrary degreee instead of linear
forms. Their result states that the set of solutions in P^n(K) (K number field)
of the inequality being considered is not Zariski dense. In our paper we prove
by a different method a generalization of their result, in which the solutions
are taken from an arbitrary projective variety X instead of P^n. Further, we
give a quantitative version which states in a precise form that the solutions
with large height lie ina finite number of proper subvarieties of X, with
explicit upper bounds for the number and for the degrees of these subvarieties.Comment: 31 page
A further improvement of the quantitative Subspace Theorem
In 2002, Evertse and Schlickewei obtained a quantitative version of the
so-called Absolute Parametric Subspace Theorem. This result deals with a
parametrized class of twisted heights. One of the consequences of this result
is a quantitative version of the Absolute Subspace Theorem, giving an explicit
upper bound for the number of subspaces containing the solutions of the
Diophantine inequality under consideration.
In the present paper, we further improve Evertse's and Schlickewei's
quantitative version of the Absolute Parametric Subspace Theorem, and deduce an
improved quantitative version of the Absolute Subspace Theorem. We combine
ideas from the proof of Evertse and Schlickewei (which is basically a
substantial refinement of Schmidt's proof of his Subspace Theorem from 1972,
with ideas from Faltings' and Wuestholz' proof of the Subspace Theorem.Comment: 93 page
Blended numerical schemes for the advection equation and conservation laws
In this paper we propose a method to couple two or more explicit numerical
schemes approximating the same time-dependent PDE, aiming at creating new
schemes which inherit advantages of the original ones. We consider both
advection equations and nonlinear conservation laws. By coupling a macroscopic
(Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of
multiscale numerical method
A fully semi-Lagrangian discretization for the 2D Navier--Stokes equations in the vorticity--streamfunction formulation
A numerical method for the two-dimensional, incompressible Navier--Stokes
equations in vorticity--streamfunction form is proposed, which employs
semi-Lagrangian discretizations for both the advection and diffusion terms,
thus achieving unconditional stability without the need to solve linear systems
beyond that required by the Poisson solver for the reconstruction of the
streamfunction. A description of the discretization of Dirichlet boundary
conditions for the semi-Lagrangian approach to diffusion terms is also
presented. Numerical experiments on classical benchmarks for incompressible
flow in simple geometries validate the proposed method
Supergravity and matrix theory do not disagree on multi-graviton scattering
We compare the amplitudes for the long-distance scattering of three gravitons
in eleven dimensional supergravity and matrix theory at finite N. We show that
the leading supergravity term arises from loop contributions to the matrix
theory effective action that are not required to vanish by supersymmetry. We
evaluate in detail one type of diagram---the setting sun with only massive
propagators---reproducing the supergravity behavior.Comment: 10 pages, 1 eps figure, it requires JHEP.cl
- …