Date/Time : 28 Feb 2024 16:30
Venue : S17 #05-12 (SR4)
Speaker : Guo Ruchi, The Chinese University of Hong Kong

In physics and mathematics, a large class of PDE systems can be formulated as energy minimization problems subject to specific constraints. Lagrange multipliers are widely used for solving such problems, which however leads to min-max optimization problems known as saddle point systems. The development of fast solvers for saddle point systems, especially those nonlinear ones, presents considerable challenges in the sense that

(i) one has to consider the preconditioning in the primal and dual directions collectively;

(ii) the preconditioners have to evolve in iterations to accommodate the nonlinearity;

(iii) all the subsystems and subproblems cannot be solved exactly due to the high computational cost involved.

In this work, we develop an efficient transformed primal-dual (TPD) algorithm, and this is done by modifying the original gradient flow from the perspective of matrix factorization. We prove the global optimal linear convergence in terms of the condition numbers measured by variable metrics. To demonstrate the effectiveness of our approach, we apply the algorithm to a Darcy-Forchheimer model and a nonlinear ferromagnetic model, showing it is much more efficient than some traditional methods.

Add to calendar :

Date/Time : 14 Feb 2024 16:30
Venue : S17 #04-06 (SR1)
Speaker : Liu Xin, Chinese Academy of Sciences

We propose constraint dissolving approaches for optimization problems over a class of Riemannian manifolds. In these proposed approaches, solving a Riemannian optimization problem is transferred into the unconstrained minimization of a constraint dissolving function named CDF. Different from existing exact penalty functions, the exact gradient and Hessian of CDF are easy to compute. We study the theoretical properties of CDF and prove that the original problem and CDF have the same first-order and second-order stationary points, local minimizers, and Łojasiewicz exponents in a neighborhood of the feasible region. Remarkably, the convergence properties of our proposed constraint dissolving approaches can be directly inherited from the existing rich results in unconstrained optimization. Therefore, the proposed constraint dissolving approaches build up short cuts from unconstrained optimization to Riemannian optimization. Several illustrative examples further demonstrate the potential of the proposed approaches.

Add to calendar :

Date/Time : 19 Jan 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Linfeng Zhang, AI for Science Institute, Beijing, and DP Technology

The rapid development of artificial intelligence is driving significant changes in the field of molecular and materials modeling, simulation, and design. In this report, we will explore the breakthroughs and progress in AI-assisted molecular modeling, with a focus on the shift from multiscale methods to large pre-trained models and the resulting software, data, and model ecosystem. In particular, we will investigate the possibility of a large atomic model that covers the entire periodic table and, based on this, envision the future of the materials genome.

Add to calendar :

Date/Time : 17 Jan 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Sam Stechmann, University of Wisconsin–Madison

Sea ice floats on the surface of the Arctic Ocean, and plays an important role in Earth’s climate. Traditionally, sea ice has been modeled as a material, as a continuum, with various rheological models proposed. From a more detailed perspective, sea ice is a collection of many individual blocks of ice, called “floes.” In this talk, I will discuss approaches for floe-based (i.e., particle-based) models of sea ice, including multi-scale models to bridge the gap between floe-based and continuum-based models.

Add to calendar :

Date/Time : 22 Dec 2023 10:00
Venue : via Zoom
Speaker : Li Bowen, Duke University

Zoom link: https://nus-sg.zoom.us/j/81215174559?pwd=T21GRHJBSTRIMHhta0hVUlRrQVQvdz09

Meeting ID: 812 1517 4559
Passcode: 938817

In this talk, we discuss some recent results for photonic and quantum interacting systems. We first consider the scattering resonances in the wave interaction with nanoparticles of high refractive indices and their applications in imaging and material science. We will establish the existence and asymptotic behaviors of dielectric resonances and show that near a resonant frequency, a singular particle exhibits resonant magnetic dipole characteristics. We then discuss the topological properties of scattering resonances for the nanophotonic crystals. In particular, we prove the genericity of the Dirac dispersion cone for honeycomb lattice and the existence of embedded eigenvalue with Fano-type asymmetric peaks in transmission spectra. Further, we focus on two prototypical quantum interacting systems that are closely related to quantum optimal transport: the ground-state energy problem and open quantum dynamics. We will present an SDP relaxation hierarchy with optimized clusters for the ground-state energy of the quantum many-body Hamiltonian that admits a quantum embedding interpretation. For open quantum dynamics, we introduce quantum Beckner’s inequalities to quantify its long-time behavior with respect to convex entropies. We will discuss the properties of the Beckner constant in detail and provide a uniform lower bound in terms of the spectral gap. Moreover, we define a new class of quantum Wasserstein distances such that the quantum dynamic is a gradient flow and its convergence can be characterized by entropic Ricci curvature lower bound associated with the convex entropy. Some ongoing works and open questions will also be discussed.

Add to calendar :

Date/Time : 22 Nov 2023 16:30
Venue : S17 #04-05 (SR2)
Speaker : Wu Hanxin, National University of Singapore

In this talk I purpose a diffuse-interface model for dynamic soft wetting problem with Shuttleworth effect. The model consists of Cahn-Hilliard-Navier-Stokes equations for two-phase fluid on a moving domain and linear elastic equation for soft substrate, and they are coupled on the free fluid-solid interface. An efficient numerical scheme is purposed by combining a monolith fluid-structure-interaction solver and linear convex splitting for Cahn-Hilliard equation on the moving domain. Theorems regarding energy-preserving property of the scheme are proved. We compare numerical results for moving contact line on soft and rigid substrate.

Add to calendar :

Date/Time : 15 Nov 2023 16:30
Venue : S17 #05-11 (SR5)
Speaker : Zou Guijin, Institute of High Performance Computing

At the nano-bio interface, mechanics can play important roles in the development of health-related technologies. In this talk, we will highlight two examples of such applications. First, we will examine how the mechanical properties of flexible nanomaterials affect their encapsulation in lipid vesicles. Through molecular dynamics simulations complemented by theoretical analysis, we have mapped out the phase diagram for these systems, revealing how nanomaterial stiffness and size relative to the vesicle dictate encapsulation outcomes. These results enhance our understanding of cell-nanomaterial interactions such as nano-toxicity, help guide the design of artificial cells and biohybrid microrobots. In the second example, we will introduce the emerging field of membrane targeting nanomedicine (MTN), an area where our mechanistic understanding is still at a primitive stage. Collaborating with experimental groups, we demonstrate how atomistic modelling and simulation facilitate the identification of membrane targeting antimicrobials (MTAs) capable of selectively penetrating and aggregating in bacterial lipid membranes, causing membrane permeability/rupture. These studies suggest a general simulation-assisted platform to accelerate discovery and innovation in nanomedicine.

Add to calendar :

Date/Time : 09 Nov 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Mengqi, National University of Singapore

Recent studies revealed that viscoelastic (polymeric) pipe flows can be linearly unstable, in contrast to the stability of the Newtonian pipe flows. The new linear instability was found to be a center mode with the eigenfunction concentrating in the center part of the pipe (Garg et al. 2018). We carried out linear stability analysis and transient energy growth analysis to further explore the linear dynamics of the center mode. It is found that an Orr mechanism(along with the critical-layer mechanism) is at play in the conformation tensor field, contributing to the total energy growth.

From a nonlinear point of view, the linear instability implies a possibility of supercritical bifurcation in viscoelastic pipe flows, again, in contrast to the subcritical Newtonian pipe flows. We applied a multiple-scale expansion method to study the bifurcation of the viscoelastic pipe flows. It is found that both supercritical and subcritical bifurcations exist in this flow. We calculated the boundary between the two bifurcations in terms of viscosity ratio (related to the polymer concentration) and our theoretical prediction gave a value about 0.785 (below which, the flow is supercritical; vice versa),qualitatively close to the experimental observation around 0.855. A scaling for the Landau coefficient has also been found.

Add to calendar :

Date/Time : 01 Nov 2023 16:30
Venue : S17 #05-11 (SR5)
Speaker : Lin Ting, Peking University

In this talk, I will introduce the construction of the $C^r$ finite element space in any dimension. We show that $C^r$ finite element in $\mathbb R^d$ can be constructed, with the local shape function space $\mathcal P_{k}$ ($k\ge 2^d r+1$). Moreover, we show that the assumptions in our construction are sharp. This is based on joint work with Jun Hu (PKU), Qingyu Wu (PKU), and Beihui Yuan (YMSC).

Add to calendar :