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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...
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...
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 ...
AN ALMOST PERIODIC NONCOMMUTATIVE WIENER’S LEMMA
ALMOST PERIODIC NONCOMMUTATIVE WIENER’S LEMMA
2015/9/29
We develop a theory of almost periodic elements in Banach algebras and present an abstract version of anoncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recentl...
A Limit Shape Theorem for Periodic Stochastic Dispersion
Space is periodic random flow order and an infinite linear speed
2015/9/28
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 mo...
Periodic Orbits of Hybrid Systems and Parameter Estimation via AD
Hybrid Systems Parameter Estimation via AD
2015/8/25
Rhythmic, periodic processes are ubiquitous in biological systems; for example,
the heart beat, walking, circadian rhythms and the menstrual cycle. Modeling
these processes with high delity as peri...
Computing Periodic Orbits and their Bifurcations with Automatic Differentiation
Automatic Differentiation Computing Periodic Orbits
2015/8/25
This paper examines algorithms for computing periodic orbits of dynamical systems. Our
goal is to explore the limits of accuracy that are attainable for these calculations within
the pragmatic conte...