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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
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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 homogenisation for $\phi^4_2$
周期均匀化 \phi^4_2 奇异SPDE
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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 orbits and dynamical spectra
Periodic orbits dynamical spectra
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2015/9/29
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...
A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
Schrodinger equation Bloch decomposition time-splitting spectral method semiclassical asymptotics lattice potential
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2012/5/24
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics ...
Localization for quasi-periodic Schrodinger operators with dynamics defined by the skew-shift and potential in a Gevrey-class
Mathematical Physics Spectral Theory dynamics quasi-periodic Schrodinger operators
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2012/4/16
We consider the discrete one-dimensional Schr\"{o}dinger operator with quasi-periodic potential $v_n := \lambda v (\shift^n \, \xx)$, where $\shift : \T^2 \rightarrow \T^2, \, \shift \xx := (x_1+x_2, ...
Sensitivity computation of periodic and chaotic limit cycle oscillations
Sensitivity analysis linear response adjoint equation unsteady adjoint chaos statistical average
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2012/4/19
Sensitivity analysis can be a powerful tool for multi-disciplinary design optimization of nonlinear flow structure interaction. For computing sensitivity of time averaged quantities in chaotic oscilla...
Transition Temperatures of Superconductors estimated from Periodic Table Properties
estimating Tc superconductivity by design MSCD combinatorial-computational search for superconductors predicting superconductivity
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2012/4/19
Predicting the transition temperature, Tc, of a superconductor from Periodic Table normal state properties is regarded as one of the grand challenges of superconductivity. By studying the correlations...
Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces
Bloch-Floquet waves thin periodic bi-material strip Mathematical Physics
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2011/9/23
Abstract: We analyse an asymptotic low-dimensional model of anti-plane shear in a thin bi-material strip containing a periodic array of interfacial cracks. Both ideal and non-ideal interfaces are cons...
A Model connecting Quantum, Diffusion, Soliton, and Periodic Localized States under Brownian motion
connecting Quantum Diffusion Soliton Brownian motion Mesoscale and Nanoscale Physics
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2011/10/9
Abstract: We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but ...
Periodic Box FHNC calculations of neutron star crustal matter. (I)
Periodic Box FHNC calculations neutron star crustal matter
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2011/7/20
Neutron star crustal matter, whose properties are relevant in many models aimed at explaining observed astrophysical phenomena, has so far always been studied using a mean field approach. In order to ...
An O(N) Method for Rapidly Computing Periodic Potentials Using Accelerated Cartesian Expansions
Accelerated Cartesian Expansion ACE Fast Multipole Methods Periodic Systems
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2011/8/4
Abstract: The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation...
A charged particle in a homogeneous magnetic field accelerated by a time periodic Aharonov-Bohm flux
electron-cyclotron resonance Aharonov-Bohm flux quantum averaging method acceleration rate
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2011/9/6
Abstract: We consider a nonrelativistic quantum charged particle moving on a plane under the influence of a uniform magnetic field and driven by a periodically time-dependent Aharonov-Bohm flux. We ob...
Derivation of Invariant Varieties of Periodic Points from Singularity Confinement
integrable maps singularity confinement invariant variety of periodic points
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2011/8/31
Abstract: It was shown, in our previous works, that periodic points of $d$ dimensional rational integrable maps form varieties if the number of invariants $p$ is greater than $d/2$. In the case of 3 d...
Linear superpositions of gap solitons in periodic Kerr media
Linear superpositions gap solitons periodic Kerr media
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2011/8/3
Abstract: The existence of a novel type of solitons in periodic Kerr media constructed as superposition of noninteracting gap-solitons of different kinds (bright, dark and periodic) is first demonstra...
Spectral properties of a 2D scalar wave equation with 1D-periodic coefficients
2D scalar wave equation 1D-periodic coefficients
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2011/7/26
Spectral properties of a 2D scalar wave equation with 1D-periodic coefficients.