# Registered Data

Contents

- 1 [CT029]
- 1.1 [01022] Self similar solutions of fuzzy fractional vibration equation
- 1.2 [01224] Collision-induced amplitude dynamics of nD solitons in a perturbed saturable nonlinear medium
- 1.3 [02689] Double Dirac Cone in Subwavelength Bandstructure
- 1.4 [01390] Neural Operator for Multidisciplinary Engineering Design
- 1.5 [01424] Asymptotic behaviour of the tumor-immune chemotaxis system with inter-cellular competition

# [CT029]

## [01022] Self similar solutions of fuzzy fractional vibration equation

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this work, we consider the one dimensional fuzzy fractional vibration equation of large membrane. In order to find the self similar solution, we use scaling transformation to transform the fuzzy fractional vibration equation into the ordinary fractional differential equation with variable coefficients. Numerical examples are presented to show the effectiveness of developed theoretical results. The computation has been carried out using the MATHEMATICA software.**Classification**:__35C06__,__35R11__,__35R13__**Author(s)**:**PRAKASH PERIASAMY**(Periyar University, Salem - 636 011 INDIA)

## [01224] Collision-induced amplitude dynamics of nD solitons in a perturbed saturable nonlinear medium

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We study the amplitude dynamics of two-dimensional (2D) fast solitons in an interaction under a framework of coupled (2+1)D nonlinear Schrodinger equations with a saturable nonlinearity and weak perturbation. We derive a theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is mainly based on the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. The theoretical results are validated by numerical simulations with the coupled perturbed nonlinear Schrodinger equations with saturable nonlinearity.**Classification**:__35C08__,__35Q51__,__35Q60__,__78A10__,__78M10__**Author(s)**:**Quan Minh Nguyen**(International University, Vietnam National University Ho Chi Minh City)- Toan Thanh Huynh (Department of Mathematics, University of Medicine and Pharmacy at Ho Chi Minh City, Vietnam)

## [02689] Double Dirac Cone in Subwavelength Bandstructure

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this talk we wish to rigorously justify the existence of the double Dirac point for the super-honeycomb lattice in the subwavelength regime. First, we will give a rigorous characterization of the symmetry conditions. Then, representing the solution by periodic layer potentials when the frequency is nonzero, we can asymptotically solve the band structure by the periodic capacitance matrix. We also study how the perturbation to the inclusions affect the band structure numerically.**Classification**:__35C20__**Author(s)**:**Borui Miao**(Tsinghua University)- Yi Zhu (Yau Mathematical Sciences Center)

## [01390] Neural Operator for Multidisciplinary Engineering Design

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Deep learning surrogate models have shown promise in solving PDEs, which enable many-query computations in science and engineering. In this talk, I will first introduce a geometry-aware Fourier neural operator (Geo-FNO) to solve PDEs on arbitrary geometries, inspired by adaptive mesh motion and spectral methods. Furthermore, we study the cost-accuracy trade-off of different deep learning-based surrogate models, following traditional numerical error analysis. Finally, we demonstrate our approach on challenging engineering design problems.**Classification**:__35C99__,__65M99__,__65Z05__,__68T07__**Author(s)**:**Daniel Zhengyu Huang**(Caltech)- Andrew M. Stuart (Caltech)
- Zongyi Li (Caltech)
- Elizabeth Qian ( Georgia Tech)
- Maarten de Hoop (Rice University)
- Anima Anandkumar (Caltech)
- Burigede Liu (University of Cambridge)

## [01424] Asymptotic behaviour of the tumor-immune chemotaxis system with inter-cellular competition

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: This work mainly discusses the influence of the coefficient of inter-cellular competition $(\sigma_1, \sigma_2)$ on the following tumor-immune cell interaction system \begin{align*} \left\{ \begin{array}{rrll} \hspace*{-0.5cm}&&u_t=\Delta u-\chi \nabla\cdot(u \nabla v)+u(\mu_1-\sigma_1 u),\hspace*{0.5cm} &x\in\Omega,\, t>0,\\ \hspace*{-0.5cm}&&v_t= \Delta v+\alpha w-\beta v-\gamma u v, &x\in\Omega,\, t>0,\\ \hspace*{-0.5cm}&& w_t= \Delta w-\delta u w+ w(\mu_2-\sigma_2 w), &x\in\Omega,\, t>0,\\ \hspace*{-0.5cm}&&\frac{\partial u}{\partial\nu}=\frac{\partial v}{\partial\nu}=\frac{\partial w}{\partial\nu}=0, &x\in\partial\Omega,\, t>0,\\ \hspace*{-0.5cm}&&u(x,0)=u_0, \quad v(x,0)=v_0, \quad w(x,0)=w_0,&x\in\Omega, \end{array} \right.%\label{1} \end{align*} in an open, bounded domain $\Omega\subset\mathbb{R}^n, n\geq 1$ with smooth boundary $\partial\Omega$. By constructing a suitable Lyapunov functional, the convergence of the solution is asserted and the numerical simulations validate the asymptotic behaviour. Earlier results do not indicate the implications when $\sigma_1, \sigma_2\neq 1$, and this work addresses the issue by showing the predominant effects of $\sigma_1, \sigma_2 >0$ in the asymptotic behaviour.**Classification**:__35N25__,__35B40__,__65N06__,__65N12__**Author(s)**:**Gnanasekaran S**(Bharathiar University)