Seminars

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2018

 Date Information
​18 May 2018 ​Title : Modeling, Analysis, & Augmented Strategy for Free Boundary/Moving Interface Problems

Professor Zhilin Li
Date:18 May 2018 (Friday)
Time: 3.00pm – 4.00pm

Abstract:
Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth, drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid methods such as Peskin's Immersed Boundary (IB) method, the Immersed Interface Method (IIM), and recent research on augmented approach.
There are several motivations or advantages using the augmented approach. It can be applied to decouple problems, to have accurate discretizations for complicated problems; and utilize fast solvers. We will present some new applications of the augmented approach including multi-scale interface problems and new ADI (alternating directional implicit) methods.

Host: Assistant professor Kelin Xia & Associate Professor Li-Lian Wang
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​11 May 2018  ​Title : A New and Robust Approach to Construct Energy Stable Schemes for Gradient Flows​

​​Professor Jie Shen

Time:  3.30pm – 4.30pm
Venue: MAS Executive Classroom 2 #03-07,
School of Physical and Mathematical Sciences

Abstract: 
We present in this talk the scalar auxiliary variable (SAV) approach and the multiple scalar auxiliary variables (MSAV) approach, to deal with nonlinear terms in a large class of gradient flows.  The technique is not restricted to specific forms of the nonlinear part of the free energy, it leads to linear and unconditionally energy stable second-order (or higher-order with weak stability conditions) schemes which only require solving decoupled  linear equations with constant coefficients. Hence, these schemes are extremely efficient as well as accurate. 
We apply the SAV approach to deal with  several challenging applications which cannot be easily handled by existing approaches, and present convincing numerical results to show that the new schemes are not only much more efficient and easy to implement, but also can better capture the physical properties in these models. ​
We shall also present a convergence and error analysis under mild assumptions on the nonlinear free energy.

Host: Associate Professor Wang Li-Lian
 Division of Mathematical Sciences, School of Physical and Mathematical Sciences
​7 May 2018 ​Title : Modeling and Inference of Local St​ationarity​

Professor Tailen Hsing ​
​Time : 2.00pm - 3.00pm
Venue: TR + 2 (SPMS-03-06)​
            School of Physical and Mathematical Sciences

Abstract:
Stationarity is a common assumption in spatial statistics. The justification is often that stationarity is a reasonable approximation to the true state of dependence if we focus on spatial data "locally." In this talk, we first review various known approaches for modeling nonstationary spatial data. We then examine a particular notion of local stationarity in more detail. To illustrate, we will focus on the multi-fractional Brownian motion, for which a thorough analysis could be conducted assuming data are observed on a regular grid. Finally, extensions to more general settings that relate to Matheron's intrinsic random functions will be briefly discussed.​

Host:  Prof Pan Guangming
           Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​6 April 2018 ​Titl​e : Coding for DNA Based Storage: Counting Profile Vectors
 
Dr Kiah Han Mao
Time : 9.30am – 10.30am
Venue : MAS Executive Classroom 1 #03-06,
School of Physical and Mathematical Sciences
​​
Abstract:
We consider the problem of storing and retrieving information from synthetic DNA media. We introduce the DNA storage channel and model the read process through the use of profile vectors. Using de Bruijn graphs and Ehrhart theory for rational polytopes, we first provide an asymptotic analysis of the number of profile vectors. We then provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $l$, and word length $n$. Consequently, we demonstrate that for $q\ge 2$ and $n \le q^{l/2−1}$, the number of profile vectors is at least $q^{kn}$ with $k$ very close to one.​

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences
27 February 2018
Title : Why spectral methods are preferred in PDE eigenvalue computations in some cases?
 
Professor Zhimin Zhang
Time : 3.30pm – 4.30pm
Venue : MAS Executive Classroom 1 #03-06,
School of Physical and Mathematical Sciences
 
Abstract:
When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that spectral methods can outperform traditional methods and the state-of-the-art method in 2-D problems even with singularities.

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
16 January 2018
Title : Limit theorems for the realised covariation of a bivariate Brownian semistationary process
 
Dr Andrea Granelli
Time : 11.00am – 12.00pm
Venue : MAS Executive Classroom 1 #03-06,
School of Physical and Mathematical Sciences
 
Abstract:
Within the realm of stochastic processes that fail to be a semimartingale, the recent literature has devoted particular attention to the Brownian semistationary process, a process that has originally been used in the context of turbulence modelling, but has subsequently been employed as a price process in energy markets.
This talk presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of the results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus.
This talk is based on joint work with Dr. Almut Veraart, reader in Statistics at Imperial College London.
 
Host: Dr Pun Chi Seng Patrick
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
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