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Event(s) on November 2016

  • Tuesday, 1st November, 2016

    Title: Ground State Patterns and Phase Transitions of of Spin-1 Bose-Einstein Condensates, Numerics and Analysis
    Speaker: Prof. I-Liang Chern, Department of Mathematics, National Taiwan University , Taiwan
    Time/Place: 10:30  -  11:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: "The ultra-cold dilute boson gases have apparent macroscopic quantum ground state, called Bose-Einstein condensates (BECs). In this talk, I will report our numerical and analytical results on such ground state patterns and their phase transitions of spin-1 BECs confined in a harmonic or box potential under the influence of a homogeneous magnetic field, based on a mean field model–a generalized Gross-Pitaevskii equation. For numerical studies, a pseudo-arclength continuation method with parameter switching technique is developed. A complete phase diagram of the ground state patterns are found with different quadratic Zeeman energy q and total magnetization M for both ferromagnetic and antiferromagnetic systems. For antiferromagnetic systems, two types of bifurcations are found. The first type is a transition from a two-component (2C) state to a three-component (3C) state. The second type is a symmetry breaking in the 3C state, followed by a phase separation of the spin components. For ferromagnetic systems, only the second type of phase transition is found. For analytic studies, we provide: (1) a complete characterization of ground states in the situation of no applied magnetic field; (2) a rigorous proof for the bifurcation from 2C to 3C for antiferromagnetic systems; and (3) a Γ-convergence theory in the semi-classical regime for antiferromagnetic systems on the whole parameter plane. In the first two parts, the key is a mass-redistribution lemma, which states that, a redistribution of the mass densities between different components can decrease bulk energy, but does not increase the kinetic energy. In the last part, the ground states and bifurcation curves in the Thomas-Fermi regime are given explicitly. The ground state patterns are determined by the zero mean curvature interfaces with contact angle determined by Young’s relation, a generalization of classical wetting theory to the quantum cases. "

  • Wednesday, 2nd November, 2016

    Title: Optimized Schwarz methods for heterogeneous problems
    Speaker: Dr. Sebastien Loisel, Department of Mathematics, Heriot-Watt University, UK
    Time/Place: 16:00  -  17:00
    FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: When a fluid flows through different media (e.g. sand vs stone), the flow rates can change dramatically; we call this a heterogeneous problem. One may solve a heterogeneous problem using domain decomposition. In this talk, we analyze the optimized Schwarz method (OSM) for heterogeneous problems. To tackle the heterogeneity, we propose two possible, completely different approaches. First, we prove that if we choose our subdomains such that the jump in diffusivity is aligned with the subdomain interfaces, then the OSM converges at a rate that is independent of the fine grid parameter h. Second, we prove that if we use a spectral coarse space (built from the eigenfunctions of subdomain D2N maps), we can obtain arbitrarily good convergence. Our theoretical results are supported by numerical experiments.

  • Friday, 4th November, 2016

    Title: Blind-source identification and decomposition of functions governed by the Adaptive Harmonic Model
    Speaker: Prof. Charles Chui, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The problem of decomposition or factorization of specific functions or of functions from certain function spaces has a long history in Mathematics, and is central to the recent development of Harmonic Analysis and Functional Analysis. However, for real-world problems, particularly in this era of Big Data, the functions of interest are usually not well-defined, but only governed by some nonlinear function models. In this presentation, we will only consider functions that represent real-world signals or time series. Such functions can always be modeled as the real part of certain exponential sums but with non-linear amplitude functions and with phase functions that are not necessarily linear polynomials. We will discuss the state-of-the-art approaches, with background from instantaneous frequency extraction and the problem of sparsed-data representation and super-resolution, originally proposed by David Donoho.

  • Tuesday, 8th November, 2016

    Title: Some advancements on inverse problems for elastic and electromagnetic wave scattering
    Speaker: Ms. XIAO Jingni, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Inverse problems are of both theoretical and applied importance. We consider two types of inverse scattering problems, one for the time-harmonic elastic waves, and the other one for the electromagnetic waves. First, we consider the time-harmonic elastic wave scattering governed by the Lamé system associated with the third or fourth kind scatterers. It is known that the elastic wave field can be decomposed into the shear(S) and the pressure(P) parts which are generally coexisting. We derive two geometric conditions suggesting that the P and the S waves can be totally decoupled. Then we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far-field measurements. Second, we consider the "non-scatter energy" issue for electromagnetic scattering problems. The existence of the so called non-scattering energy provides a possible approach to partially coat a scatterer. We prove that a sufficiently regular inhomogeneous electromagnetic medium with a right corner shall always produce non-identically vanishing scattered field unless the incident field is from certain class.

  • Saturday, 12th November, 2016

    Title: An Adaptive Mode Solver for Varying Refractive-Index Profile's Waveguides with Modified Spectral Element Method
    Speaker: Prof. Jianxin Zhu, School of Mathematics, Zhejiang University, China
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: A mode solver based on the spectral element method with mesh adaptation is proposed to calculate the modal characteristics of a semivectorial field in open varying-index optical waveguides. General optical waveguides with varying refractive-indices are studied for the transverse electric and transverse magnetic cases, where perfectly matched layers (PMLs) are used to truncate the unbounded waveguides. The optical field expanded by a suitable set of orthogonal basis points (Gauss-Lobatto-Legendre (GLL) or Gauss-Chebyshev-Collocation (GCC) points) through spectral element method are all represented by processing of characterization of composite material through mesh adaptation. By this combined solver, a large number of accurate PML modes can be easily calculated. And our results are still found to be in good agreement with those produced by other various numerical methods, however, more efficiency. By the way, the relations of the PML modes distribution to the parameters of PMLs are analysed.

  • Tuesday, 15th November, 2016

    Title: HKBU 60th Anniversary Shun Hing Distinguished Lecture: Taming Infinities
    Speaker: Professor Martin Hairer, The University of Warwick, United Kingdom
    Time/Place: 14:30  -  16:00
    WLB103, Lam Woo International Conference Centre, Shaw Campus, Hong Kong Baptist University
    Abstract: Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! Various techniques, usually going under the common name of 'renormalisation' have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the mathematical aspects of these techniques and we will see how they have recently been used to make precise analytical statements about the solutions of some equations whose meaning was not even clear until now.

  • Friday, 18th November, 2016

    Title: Meta-analysis in Medical Decision Making (Western and Traditional medicine): Roles and Perspective
    Speaker: Dr. Yue Liu, China Academy of Chinese Medical Sciences, Xiyuan Hospital, China
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Meta-analysis is an important research method of evidence-based medicine and one of the best important sources of medical evidence. The medical profession reach a consensus that the importance of meta-analysis in medical decision making. In this lecture, I will address the definition, method, application and perspective of meta-analysis in medical decision making, including western and traditional medicine in many diseases.

  • Tuesday, 22nd November, 2016

    Title: A semiparametrically efficient estimator of the time-varying effects for survival data with time-dependent treatment
    Speaker: Prof. Huazhen Lin, Center of Statistical Research, School of Statistical, Southwestern University of Finance and Economics , China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The timing of time-dependent treatment---e.g., when to perform kidney transplantation---is an important factor for evaluating treatment efficacy. A naive comparison between the treatment and nontreatment groups, while ignoring the timing of treatment, typically yields results that might biasedly favor the treatment group, as only patients who survive long enough will get treated. On the other hand, studying the effect of time-dependent treatment is often complex, as it involves modeling treatment history and accounting for the possible time-varying nature of the treatment effect. We propose a varying-coefficient Cox model that investigates the efficacy of time-dependent treatment by utilizing a global partial likelihood, which renders appealing statistical properties, including consistency, asymptotic normality and semiparametric efficiency. Extensive simulations verify the finite sample performance, and we apply the proposed method to study the efficacy of kidney transplantation for end-stage renal disease patients in the U.S. Scientific Registry of Transplant Recipients (SRTR).

  • Tuesday, 29th November, 2016

    Title: On X-ray transform for asymptotically hyperbolic metrics
    Speaker: Prof. Colin Guillarmou, DMA, Ecole Normale Superieure, France
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We will discuss recent results X-ray transform for asymptotically hyperbolic metrics using analytic and spectral methods. 



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