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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A structure-preserving parametric finite element method (PFEM) for geometric PDEs and applications
几何偏微分方程 结构保持 参数有限元
2023/4/17
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Volume preserving Gauss curvature flow of convex hypersurfaces in the hyperbolic space
双曲空间 凸超曲面 保体积 高斯曲率流
2023/5/15
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus
Averaging Markov Process Hamiltonian Flow
2015/9/29
We study deterministic and stochastic perturbations of incompressible flows on
a two-dimensional torus. Even in the case of purely deterministic perturbations,
the long-time behavior of such &...
Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus
Averaging Markov Process Hamiltonian Flow Gluing Conditions Diffusion on a Graph
2015/9/28
We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such ...
New Multiscale Transforms, Minimum Total Variation Synthesis: Applications to Edge-Preserving Image Reconstruction
Ridgelets curvelets wavelets pseudo-polar FFT Slant Stack Radon transform trigonometric interpolation total-variation edges edge-preserving tomography/deconvolution thresholding
2015/6/17
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
Discrete Kernel Preserving Model for 1D Electron-Optical Phonon Scattering
D Electron-Optical Phonon Scattering Discrete Kernel Preserving Model
2014/9/26
We investigate the discretization of of an electron-optical phonon scattering using
a nite volume method. The discretization is conservative in mass and is essentially
based on an energy point of v...
Motion by Volume Preserving Mean Curvature Flow Near Cylinders
Motion by Volume Mean Curvature Flow Cylinders Analysis of PDEs
2012/5/24
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces ...
Abstract: Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental prop...
A numerical study of infinitely renormalizable area-preserving maps
renormalizable area-preserving maps numerical study Dynamical Systems
2011/9/14
Abstract: It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equa...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12
Strong Stability Preserving, Hermite-Birkhoff Method SSP Coefficient Time Discretization Method of Lines Comparison with Other SSP Methods
2013/1/30
We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of ord...
Annular area preserving homeomorphisms which admit no interior compact invariant sets
Area preserving homeomorphisms rotation numbers fast approxi-mation by conjugation
2011/2/28
For any irrational number , there exists an ergodic area preserv-ing homeomorphism of the closed annulus which is isotopic to the identitity,admits no compact invariant set contained in the interior ...
Symmetry preserving self-adjoint extensions of Schrödinger operators with singular potentials
Symmetry preserving self-adjoint extensions Schrö dinger operators singular potentials
2011/1/21
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Prob-lems of this type naturally arise when considering two- and ...
The lattice structure of connection preserving deformations for q-Painleve equations I
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...
Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
Painleve system monodromy preserving deformation
2010/11/8
The higher order Painleve system of type D^{(1)}_{2n+2} is proposed by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry and expressed as a Hamiltonian sy...
