Seminars

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2018

 Date Information
23 July 2018 Title:  Mathematical Analysis and Numerical Methods for an Underground Oil Recovery Model

Prof Ying Wang
Date: 23 July 2018 (Monday)
Time: 10.30am – 11.30am

Abstract:
In this talk, I will discuss an underground oil recovery model which includes a third-order mixed derivatives term resulting from the dynamic effects in the pressure difference between the two phases. Analytic study on the computational domain reduction will be provided. A variety of numerical examples in both one and two space dimensions will be given. They show that the solutions may have many different saturation profiles depending on the initial conditions, diffusion parameter, and the third-order mixed derivatives parameter. The results are consistent with the study of traveling wave solutions and their bifurcation diagrams.

Host: Assistant Professor Kelin Xia 
Division of Mathematical Sciences, School of Physical and Mathematical Sciences 
17 July 20 18 Title: On eigenvalues of graphs

Prof Jongyook Park 
Date:17 July 2018 (Tuesday)
Time: 2.00pm – 3.00pm

Abstract:
In this talk, we introduce association schemes and a generalization of distance-regular graphs. We will study eigenvalues of graphs to classify a certain class of association schemes.  This talk is designed to be accessible.

Host: Dr Gary Greaves
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
28 June 2018 Title: A 2-stage Adaptive Design to Evaluate the Intra-subject Variability of Glucodynamic Parameters

Dr Yeo Kwee Poo
Date: 28 June 2018 (Thursday)
Time: 9.30am – 10.30am

Abstract:
n typical clinical trials the design is fixed and the statistician does not analyze the data until the study is terminated. Often the size of the trial is powered based on the assumptions about the effect size that cannot be verified until the actual trial has commenced. An adaptive design allows the study team to modify the sample size for the trial based on interim results. Although adaptive design is not new, most publications in the literature discussed mainly on the inference of mean. In this talk, we propose a 2-stage procedure to analyze variance based on conditional probability. We will also discuss how the overall Type I error is preserved. 

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

18 June 2018 Title : Mathematical Modeling for HIV-1 Viral Capsid Structure and Assembly

Professor Jiangguo James Liu
Date:18 June 2018 (Monday)
Time: 10.00am – 11.00am

Abstract:
Human immunodeficiency virus type 1 (HIV-1) is a retrovirus that causes acquired immunodeficiency syndrome (AIDS), a condition in humans in which the immune system fails progressively.  Understanding the structure and assembly of the HIV-1 virus will help find cures for AIDS.  In this talk, we discuss mathematical models for characterizing the structure and formation of HIV-1 conical capsid.  Particularly, we focus on three aspects: (1) generating vectors for the lattice structure of the conical shell; (2) curvature concentrations on the narrow end of the cone; (3) dynamical system models for the nucleation stage of the conical capsid. Comparison of modeling results with biological experimental data will be presented.  
This talk is based on the joint work with Farrah Sadre-Marandi at Ohio State University (USA), Chaoping Chen and Simon Tavener at Colorado State University, Yuewu Liu and Xiufen Zou at Wuhan University (China) .

Host : Assistant Professor Kelin Xia 
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
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
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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