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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost periodic function and rotation number of the Schrodinger operator
薛定谔算子 几乎周期函数 旋转数
2023/4/25
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Periodic Phenomena in homotopy theory
同伦理论 周期现象
2023/4/25
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The N-periodic wave solutions of some coupled bilinear equations
耦合 双线性方程 N周期波解
2023/4/26
In this talk, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation, the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation and the mKdV-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Linked periodic orbits of disc homeomorphisms
圆盘同胚 连锁 周期轨道
2023/5/8
In 1990, Gambaudo introduced the notion of linking of two invariant sets of a surface self-map. Most of the known results of linked periodic orbits are about an orbit linked with a fixed point. In thi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Periodic homogenisation for $\phi^4_2$
周期均匀化 \phi^4_2 奇异SPDE
2023/5/10
We consider a periodic homogenisation problem for $\phi^4_2$, a toy model that combines both renormalisation in singular SPDEs and homogenisation. In this case, we show that two different orders of th...
Periodic Table of Ecological Niches Could Aid in Predicting Effects of Climate Change（图）
periodic table ecological niches aid climate change
2017/9/19
A group of ecologists has started creating a periodic table of ecological niches similar to chemistry’s periodic table. And just as chemists have used their periodic table as a point of reference to u...
BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
We study stationary quantum fluctuations around a mean field limit in trapped, dilute atomic gases of repulsively interacting bosons at zero temperature. Our goal is to describe quantum-mechanically t...
ERRATUM:BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
This is a correction to the author’s article [Multiscale Model. Simul.,10 (2012), pp.383–417].
BOSE-EINSTEIN CONDENSATION AT FINITE TEMPERATURES:MEAN FIELD LAWS WITH PERIODIC MICROSTRUCTURE
quantum dynamics Bose-Einstein condensation periodic homogenization finite temperatures two-scale expansion mean field limit
2015/10/16
At finite temperatures below the phase transition point, the Bose-Einstein condensation, the macroscopic occupation of a single quantum state by particles of integer spin, is not complete. In the lang...
Homogenization of a Hele-Shaw problem in periodic and random media
Free boundary problem Hele-Shaw equation Obstacle problem Viscosity solution Homogenization
2015/10/15
We investigate the homogenization limit of a free boundary problem with space-dependent free boundaryvelocities. The problem under consideration has a well-known obstacle problem transformation, forma...
Homogenization of one-phase Stefan-type problems in periodic and random media
one-phase Stefan-type periodic random
2015/10/15
We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) medium are considered. The proof relies on the...
Basic results in the rigorous theory of weighted dynamical zeta functions
or dynamically defined generalized Fredholm determinants are presented. Analytic
properties of the zeta functions or d...
JOINTLY PERIODIC POINTS IN CELLULAR AUTOMATA:COMPUTER EXPLORATIONS AND CONJECTURES
JOINTLY PERIODIC POINTS CELLULAR AUTOMATA COMPUTER EXPLORATIONS AND CONJECTURES
2015/9/29
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, con...
ANOMALOUS CURRENT IN PERIODIC LORENTZ GASES WITH INFINITE HORIZON
PERIODIC LORENTZ GASES INFINITE HORIZON
2015/9/29
We study electrical current in two-dimensional periodic Lorentz gas in the presence of a weak homogeneous etric field.When the horizon is finite, i.e. the free flights between
colli...
A Limit Shape Theorem for Periodic Stochastic Dispersion
Periodic Stochastic Dispersion Shape
2015/9/29
We consider the evolution of a connected set on the plane carried by a space
periodic incompressible stochastic flow. While for almost every realization of
the stochastic flow at time t ...