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.

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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.

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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.

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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.

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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).

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Date/Time : 25 Oct 2023 16:00
Venue : S16 #03-06
Speaker : Yin Jianyuan, National University of Singapore

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the two-dimensional rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional with the constraint. A solution landscape method is introduced with the constrained high-index saddle dynamics. Various excited states and their connections at different rotational frequencies are revealed with solution landscapes. Four excitation mechanisms are identified: vortex addition, rearrangement, merging, and splitting. We demonstrate changes in the ground state with increasing rotational frequencies and decipher the stability evolution of ground states.

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Date/Time : 16 Oct 2023 16:00
Venue : S16 #04-35
Speaker : Lin Yi-Hsuan, National Yang Ming Chiao Tung University

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce the nonlocal parabolic inverse problems to the corresponding local inverse problems by using the extension problem for nonlocal parabolic equations. This talk is based on joint works with Ching-Lung Lin and Gunther Uhlmann.

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