WHERE:

MR2 - CMSCambridge, United Kingdom

WHEN:

2 May 19from 10:30 to 17:00

Cambridge Student Chapter

WHERE:

MR2 - CMSCambridge, United Kingdom

WHEN:

2 May 19from 10:30 to 17:00

SPEAKERS:

Professors Alain Goriely, Xue-Mei Li, Coralia Cartis, Edriss S. Titi and Christoph OrtnerPROGRAM

10:30 Welcome

10:40**Modelling Dementia (Prof Alain Goriely, MR2)**

11:25**Perturbation, Noise, and Averaged Dynamics (Prof Xue-Mei Li, MR2)**

12:10 Break

12:20**Optimization with expensive and uncertain data – challenges and improvements (Prof Coralia Cartis, MR2)**

13:05 Lunch

14:00** Analysis of Oceanic and Tropical Atmospheric with Moisture Models: Global Regularity, Finite-time Blowup and Singular Limit Behavior (Prof Edriss S. Titi, MR2)**

14:45** Hybrid Modelling of Interatomic Forces (Physics+Data+Mathematics) (Prof Christoph Ortner, MR2)**

15:30 Tea break

16:00*Grad moment method for dilute granular gases of inelastic Maxwell*

molecules, Vinay Kumar Gupta (MR2)

16:15*The physics of regularized Stokeslets, Andy Zhao* (MR2)

16:30*An Anisotropic Interaction Model for Simulating Fingerprints, Lisa Maria Kreusser* (MR2)

16:45*Towards an ideal synthetic system for active matter, Debasish Das* (MR2)

17:00 End

10:40

11:25

12:10 Break

12:20

13:05 Lunch

14:00

14:45

15:30 Tea break

16:00

molecules, Vinay Kumar Gupta

16:15

16:30

16:45

17:00 End

PLENARY TALK ABSTRACTS

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The purpose of averaging is easy to describe. Suppose that we have a system of variables interacting with each other and moving at different scales of speed (of order 1 and of order 1/epsilon) with the fast variables `fast oscillatory’. Both slow and fast variables evolve in time according to some rules, for example solving a family of differential or stochastic differential equations. The aim is to determine whether the slow variables can be approximated by an autonomous systems of equations, called the effective dynamic, as epsilon is taken to 0 and the speed of the fast variables tends to infinity. Slow/fast systems arise from perturbations of conservation laws and breaking of symmetries.

We will discuss the latest developments in averaged dynamics, touching on recent work with M. Hairer on averaged dynamics with fractional noise (this leads to very different behaviour from the white noise case and requires new techniques).

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singularities (blowup).

Capitalizing on the above results, we can provide rigorous justification of the derivation of the Primitive Equations of planetary scale oceanic dynamics from the three-dimensional Navier-Stokes equations, for vanishing small values of the aspect ratio of the depth to horizontal width. Specifically, we can show that the Navier-Stokes equations, after being scaled appropriately by the small aspect ratio parameter of the physical domain, converge strongly to the primitive equations, globally and uniformly in time, and that the convergence rate is of the same order as the aspect ratio parameter. Furthermore, I will also consider the singular limit behavior of a tropical atmospheric model with moisture, as ε → 0, where ε > 0 is a moisture phase transition small convective adjustment relaxation time parameter.

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In this talk I will backtrack from this trend by returning to simple functional forms, motivated by physics (and somewhat justified by mathematics), but retain a key feature of the data-driven/ML approach: models must be systematically improvable. I will demonstrate how a combination of elementary ideas from analysis, approximation theory, and representation theory leads to a very competitive construction (in terms of fitting error/cost) that has a range of additional advantages, for example that it can be effectively regularised. While my talk will focus specifically on interatomic potentials, the ideas should in principle be applicable to a much wider range of particle models, and at a more conceptual level also to continuum models.

STUDENT/POSTDOC TALK ABSTRACTS

molecules

The present work considers the gaseous state of granular materials, for which, analogous to molecular gases, mathematical tools can be developed within the framework of kinetic theory. In this talk, I shall present my recent work on Grad moment method for modelling a dilute granular gaseous flow of d-dimensional smooth, identical, inelastic spheres interacting with Maxwell interaction potential—referred to as inelastic Maxwell molecules (IMM). Here d = 2 means disk flows while d = 3 means sphere flows. This work is a somewhat generalization of my previous work to arbitrary dimensions. To assess the capabilities of the derived models for IMM, the homogeneous cooling state of a freely cooling granular gas of IMM and its stability to small perturbation is studied.

Moreover, the Navier–Stokes level transport coefficients are also obtained from the moment equations and it has been found that the transport coefficients obtained in this work agree exactly with those obtained in previous studies.

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