Search results for "ddc:510"

Projective metrics and mixing properties on towers

2001

An Itô Formula for rough partial differential equations and some applications

2020

AbstractWe investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form $\partial _{t}u-A_{t}u-f=(\dot X_{t}(x) \cdot \nabla + \dot Y_{t}(x))u$ ∂ t u − A t u − f = ( X ̇ t ( x ) ⋅ ∇ + Y ̇ t ( x ) ) u on $[0,T]\times \mathbb {R}^{d}.$ [ 0 , T ] × ℝ d . To do so, we introduce a concept of “differential rough driver”, which comes with a counterpart of the usual controlled paths spaces in rough paths theory, built on the Sobolev spaces Wk,p. We also define a natural notion of geometricity in this context, and show how it relates to a product formula for controlled paths. In the case of transport noise (i.e. when Y = 0), we use this framework to prove a…

The spectrum of weakly coupled map lattices

1998

We consider weakly coupled analytic expanding circle maps on the lattice Zd (for d 2 l), with small coupling strength c and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (Perron-Frobenius) transfer operators. We give a FrCchet space on which the operator associated to the full system has a simple eigenvalue at 1 (corresponding to the SRB measure p* previously obtained by Bricmont-Kupiainen (BKl)) and the rest of the spectrum, except maybe for continuous spectrum, is inside a disc of radius smaller than one. For d = 1 we also construct Banach spaces of densities with respect to pr on which perturbation theory, applied to the diff…

Automorphisms of $mathbb{A}^{1}$-fibered affine surfaces

2011

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface S of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of S is generated by automorphisms preserving these fibrations.

Existence of dynamical low-rank approximations to parabolic problems

2021

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

Algebraic (2, 2)-transformation groups

2009

This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an algebraically closed field $\sf k$, which operate transitively, but not primitively, on a variety $\Omega$, provided the following conditions are fulfilled. We ask that the (non-effective) action of $G$ on the variety of blocks is sharply 2-transitive, as well as the action on a block $\Delta$ of the normalizer $G_\Delta$. Also we require sharp transitivity on pairs $(X,Y)$ of independent points of $\Omega$, i.e. points contained in different blocks.

Particle transport in recirculated liquid metal flows

2008

PurposeAims to present recent activities in numerical modeling of turbulent transport processes in induction crucible furnace.Design/methodology/approach3D large eddy simulation (LES) method was applied for fluid flow modeling in a cylindrical container and transport of 30,000 particles was investigated with Lagrangian approach.FindingsParticle accumulation near the side crucible boundary is determined mainly by the ρp/ρ ratio and according to the presented results. Particle settling velocity is of the same order as characteristic melt flow velocity. Particle concentration homogenization time depends on the internal flow regime. Separate particle tracks introduce very intensive mass exchang…

Monothetic algebraic groups

2007

AbstractWe call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.

Construction de Triplets Spectraux à Partir de Modules de Fredholm

1998

Soit (A, H, F) un module de Fredholm p-sommable, où l'algèbre A = CT est engendrée par un groupe discret Gamma d'éléments unitaires de L(H) qui est de croissance polynomiale r. On construit alors un triplet spectral (A, H, D) sommabilité q pour tout q > p + r + 1 avec F = signD. Dans le cas où (A, H, F) est (p, infini)-sommable on obtient la (q, infini)-sommabilité de (A, H, D)pour tout q > p + r + 1. Let (A, H, F) be a p-summable Fredholm module where the algebra A = CT is generated by a discrete group of unitaries in L(H) which is of polynomial growth r. Then we construct a spectral triple (A, H, D) with F = signD which is q-summable for each q > p + r + 1. In case (A, H, F) is (p, infini…

An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models

2022

We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing the connectivity graph of the ancestry of mesh cells. Due to the employed rectangular mesh structure, the identification of the siblings and the neighbouring cells is greatly simplified. The administration technique is particularly designed for smooth meshes, where the smoothness is dynamically used in the matrix operations. It has a small memory footprint that makes it affordable for a wide range of mesh resolutions over a large class of problems. We pre…