Date/Time : 03 Aug 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Lu Jian, South China Normal University

Minkowski type problems arise from modern convex geometry. In the smooth case, they are usually equivalent to solving a class of Monge-Ampere type equations defined on the unit hypersphere. These equations could be degenerate or singular in different conditions. We will talk about some new results on the existence, uniqueness, and regularity of solutions to several Minkowski type problems.

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Date/Time : 03 Aug 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Aijun An, York University

Generating revenue has been a significant issue for the news industry over the past decade. Due to the wide availability of numerous online news media, readers have many choices in selecting the news source. In a collaborative project with The Globe and Mail, we address the problem of user acquisition and engagement and investigate how data mining techniques can be used to solve the problem. In this talk, I will present two pieces of work in this project. One is a time-aware user subscription prediction model and the other is an adaptive paywall model. The goal of the time-aware user subscription prediction model is to identify potential subscribers and predict their prediction time so that effective targeted marketing can be used. We propose to learn a probabilistic model from user click streams that can predict the probability that a user subscribes the newspaper and estimate their subscription time. In the second piece of work, we address the problem of previous fixed paywall models that offer a non-subscribed reader a fixed number of free articles in a period of time. Such models treat all readers equally and do not consider the potential of a reader in becoming a subscriber. We propose an adaptive paywall model that considers the user’s browsing history in making paywall decisions. It provides potential subscribers with more free articles to engage them. I will present the models, the experimental results and the impact of our work.

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Date/Time : 01 Aug 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Chen Greif, The University of British Columbia

Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of associated applications and the challenge in developing efficient numerical solvers. In this talk we describe some of their numerical properties and make some distinctions between this family and the more well-established class of classical 2-by-2 block-structured saddle-point systems. We derive eigenvalue bounds, expressed in terms of extremal eigenvalues and singular values of block sub-matrices. The analysis includes bounds for preconditioned matrices based on block diagonal preconditioners using Schur complements, and it is shown that in this case the eigenvalues are clustered within a few intervals bounded away from zero. Analysis for approximations of Schur complements is included. We illustrate some of the numerical challenges and our findings on a Marker-and-Cell discretization of the Stokes-Darcy equations.

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Date/Time : 27 Jul 2023 16:30
Venue : S17 #04-05 (SR2)
Speaker : Li Yingzhou, Fudan University

We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H2, LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.

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Date/Time : 28 Jun 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Dai Shuyang, Wuhan University

In this talk, we present some modeling and simulations of heterogeneous structures in material sciences. The first part is the multiscale continuum model of defect structures in crystalline materials. The interface structure for twist, tilt and misfit grain boundaries are described by the dislocation network. The model incorporates both the anisotropy elasticity of each grain in crystalline materials and the molecular dynamics calculation informed interaction between two bulks, i.e., the nonlinear generalized stacking-fault energy. The second part is the simulations of dielectric inhomogeneous systems. We proposed several approaches to accelerate the calculation of static and dynamic properties of charged polymers in 3D dielectric inhomogeneity system.

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Date/Time : 04 May 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Zhen, Southern University of Science and Technology

We develop energy stable and bound preserving schemes for phase-field surfactant model with moving contact lines. The desired properties of the schemes are rigorously proved. We numerically validate the accuracies of the schemes and apply them in simulating droplet impact problems. Qualitative agreements with experiments are obtained. Moreover, surfactants are observed to have effects on enhancing droplet deformation and reducing dissipations.

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Date/Time : 27 Apr 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Franck Sueur, University of Bordeaux

In this talk, I will give an overview of some recent results on the so-called transport-Stokes system which describes sedimentation of inertialess particles in a viscous flow. This system couples a transport equation and the steady Stokes equations in the full 3D space. I will address the Cauchy problem, the regularity of the particle trajectories and the controllability issue. We will see that the system has some similarity to the incompressible Euler system. Some of the exposed results have been obtained in collaboration with Amina Mecherbet.

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Date/Time : 13 Apr 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Xavier Fernández-Real, Swiss Federal Institute of Technology Lausanne (EPFL)

In this talk we present an introduction to integro-differential operators and the obstacle problem, and how they interact with each other in what is known as the fractional obstacle problem.

In $\R^n$, the fractional obstacle problem with a given obstacle $\varphi\in C_c^\infty(\R^n)$ can be written as

\[\min\{(-\Delta)^s u, u – \varphi\} = 0\quad\text{in}\quad \R^n.\]

The set $\{u = \varphi\}$ is called the contact set, and its boundary $\partial\{u = \varphi\}$ is called the free boundary, which are unknowns of the problem. The free boundary can be divided into two sets: regular points (where it is regular) and degenerate points. In general, degenerate points can exist in any dimension.

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Date/Time : 06 Apr 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Quan Zhao, University of Regensburg, Germany

In this talk, I will consider the structure-preserving front-tracking methods for a sharp-interface model of two-phase flow in both the unfitted and fitted mesh approaches, meaning that the volume preservation and energy decay are satisfied on the discrete level. In the unfitted approach, the constructed method is based on an Eulerian weak formulation, while in the fitted approach, the method is devised in the arbitrary Lagrangian-Eulerian (ALE) framework. We compare the numerical results of the two approaches by using the example of a rising bubble.

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