Applied/ACMS: Difference between revisions

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*'''Where:''' 901 Van Vleck Hall
*'''Where:''' 901 Van Vleck Hall
*'''Organizers:'''  [https://math.wisc.edu/staff/fabien-maurice/ Maurice Fabien], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie],  
*'''Organizers:'''  [https://math.wisc.edu/staff/fabien-maurice/ Maurice Fabien], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie],  
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+join@g-groups.wisc.edu].
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+subscribe@g-groups.wisc.edu].


<br>   
<br>   


== Spring 2024  ==
== '''Spring 2025''' ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
! align="left" |Date
!align="left" | speaker
! align="left" |Speaker
!align="left" | title
! align="left" |Title
!align="left" | host(s)
! align="left" |Host(s)
|-
|-
| Feb 2
|Jan 31
|[https://people.math.wisc.edu/~chr/ Chris Rycroft] (UW)
|TBA
|''The reference map technique for simulating complex materials and multi-body interactions''
|
* '''Zoom:''' https://uwmadison.zoom.us/j/92068711076?pwd=dnQvOWFRb0xIRWFXaU5CWnVia0VOdz09
* '''Passcode:''' 847281
|
|
|-
|-
| Feb 9
|Feb 7
|[https://users.flatironinstitute.org/~sweady/ Scott Weady] (Flatiron Institute)
|TBA
|''Entropy methods in active suspensions''
|
|Saverio and Laurel
|
|-
|-
| Feb 16
|Feb 14
|[http://stokeslet.ucsd.edu/ David Saintillan] (UC San Diego)
|TBA
|''[[Applied/ACMS/absS24#David Saintillan (UC San Diego)|Hydrodynamics of active nematic surfaces]]''
|
|Saverio and Tom
|
|-
|-
| Feb 23
|Feb 21
|[https://cersonsky-lab.github.io/website/ Rose Cersonsky] (UW)
|TBA
|''[[Applied/ACMS/absS24#Rose Cersonsky (UW)|TBA]]''
|
|Chris
|
|-
|-
| Mar 1 [4:00pm Colloquium]
|Feb 28
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT Austin)
|TBA
|''[[Applied/ACMS/absS24#Per-Gunnar Martinsson (UT-Austin)|TBA]]''
|
|Li
|
|-
|Mar 7
|TBA
|
|
|-
|-
| Mar 8
|Mar 14
|[https://www.physics.wisc.edu/directory/jorge-rogerio/ Rogerio Jorge] (UW-Madison)
|[https://lu.seas.harvard.edu/ Yue Lu] (Harvard) '''[Colloquium]'''
|''[[Applied/ACMS/absS24#Rogerio Jorge (UW-Madison)|TBA]]''
|
|Li
|Li
|-
|-
| Mar 15
|Mar 21
|[https://www.math.purdue.edu/~qi117/personal.html/ Di Qi] (Purdue University)
|TBA
|
|
|
|Chen
|-
|-
| Mar 22
|Mar 28
|
|''Spring Break''
|
|
|
|
|-
|-
| Mar 29
|Apr 4
|Spring break
|TBA
|
|
|
|
|-
|-
| Apr 5
|Apr 11
|[https://www.jinlongwu.org/ Jinlong Wu] (UW)
|[https://meche.mit.edu/people/faculty/pierrel@mit.edu Pierre Lermusiaux] (MIT)
|''[[Applied/ACMS/absS24#Jinlong Wu (UW)|TBA]]''
|
|Saverio
|Chen
|-
|-
| Apr 12
|Apr 18
|[https://zayascaban.labs.wisc.edu/ Gabriel Zayas-Caban] (UW)
|[https://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine) '''[Colloquium]'''
|''[[Applied/ACMS/absS24#Gabriel Zayas-Caban (UW)|TBA]]''
|
|Li
|
|-
| Apr 19
|[https://www.nist.gov/people/anthony-j-kearsley Tony Kearsley] (NIST)
|''[[Applied/ACMS/absS24#Tony Kearsley (NIST)|TBA]]''
|Fabien
|-
|-
| Apr 26
|Apr 25
|[https://math.oregonstate.edu/directory/malgorzata-peszynska Malgorzata Peszynska] (Oregon State)
|[https://www-users.cse.umn.edu/~bcockbur/ Bernardo Cockburn] (Minnesota)
|''[[Applied/ACMS/absS24#Malgorzata Peszynska (Oregon State)|TBA]]''
|''Transforming stabilization into spaces''
|Fabien
| Stechmann, Fabien
|-
|-
|May 2
|[https://sylviaherbert.com/ Sylvia Herbert] (UCSD)
|
|
|
|Chen
|}
|}


== Abstracts ==
==Abstracts==
====Bernardo Cockburn (Minnesota)====
Title: Transforming stabilization into spaces


==== Chris Rycroft (UW–Madison) ====
In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.<div id="Bal"><div id="Portone"><div id="Damle"><div id="Sprague"><div id="Holmes-Cerfon"><div id="Sun"><div id="Maxian"><div id="Lavi">
Title: The reference map technique for simulating complex materials and multi-body interactions
== Archived semesters ==
 
Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented [1]. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems [2], and several examples in two and three dimensions [3] will be presented.
 
# K. Kamrin, C. H. Rycroft, and J.-C. Nave, J. Mech. Phys. Solids '''60''', 1952–1969 (2012). [https://doi.org/10.1016/j.jmps.2012.06.003 <nowiki>[DOI link]</nowiki>]
# C. H. Rycroft ''et al.'', J. Fluid Mech. '''898''', A9 (2020). [https://doi.org/10.1017/jfm.2020.353 <nowiki>[DOI link]</nowiki>]
# Y. L. Lin, N. J. Derr, and C. H. Rycroft, Proc. Natl. Acad. Sci. '''119''', e2105338118 (2022). [https://doi.org/10.1073/pnas.2105338118 <nowiki>[DOI link]</nowiki>]
 
 
==== Scott Weady (Flatiron Institute) ====
 
Title: Entropy methods in active suspensions
 
Collections of active particles, such as suspensions of E. coli or mixtures of microtubules and molecular motors, can exhibit rich non-equilibrium dynamics due to a combination of activity, hydrodynamic interactions, and steric stresses. Continuum kinetic theories, which characterize the set of particle configurations through a continuous distribution function, provide a powerful framework for analyzing such systems and connecting their micro- to macroscopic dynamics. The probabilistic formulation of kinetic theories leads naturally to a characterization in terms of entropy, whether thermodynamic or information-theoretic. In equilibrium systems, entropy strictly increases and always tends towards steady state. This no longer holds in active systems, however entropy still has a convenient mathematical structure. In this talk, we use entropy methods, specifically variational principles involving the relative entropy functional, to study the nonlinear dynamics and stability of active suspensions in the context of the Doi-Saintillan-Shelley kinetic theory. We first present a class of moment closures that arise as constrained minimizers of the relative entropy, and show these closures preserve the kinetic theory's stability and entropic structure while admitting efficient numerical simulation. We then derive variational bounds on relative entropy fluctuations for apolar active suspensions that are closely related to the moment closures. These bounds provide conditions for global stability and yield estimates of time-averaged order parameters. Finally, we discuss applications of these methods to polar active suspensions.
 
 
==== David Saintillan (UC San Diego) ====
 
Title: Hydrodynamics of active nematic surfaces
 
The dynamics of biological surfaces often involves the coupling of internal active processes with in-plane orientational order and hydrodynamic flows. Such active surfaces play a key role in various biological processes, from cytokinesis to tissue morphogenesis. In this talk, I will discuss two approaches for the modeling and simulation of active nematic surfaces. In a first model, we analyze the spontaneous dynamics of a freely-suspended viscous drop with surface nematic activity and its coupling with bulk fluid mechanics. Using a spectral boundary integral solver for Stokes flow coupled with a hydrodynamic evolution equation for the nematic tensor, numerical simulations reveal a complex interplay between the flow inside and outside the drop, the surface transport of the nematic field and surface deformations, giving rise to a sequence of self-organized behaviors and symmetry-breaking phenomena of increasing complexity, consistent with experimental observations. In the second part of the talk, I will present a novel computational approach for the simulation of active nematic fluids confined to Riemannian manifolds. The fluid velocity and nematic order parameter are represented as sections of the complex line bundle of a two-manifold. Using a geometric approach based on the Levi-Civita connection, we introduce a coordinate-free discretization method that preserves the continuous local-to-global theorems in differential geometry. Furthermore, we establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. Advection of the nematic field is formulated based on the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. The proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and topology on the hydrodynamics of active nematic systems, and we illustrate its capabilities by simulating active flows on a range of surfaces of increasing complexity.
 
==== Di Qi (Purdue) ====
{{anchor|diqi}}Title: Statistical Reduced-Order Models and Random Batch Method for Complex Multiscale Systems
 
Abstract: The capability of using imperfect stochastic and statistical reduced-order models to capture key statistical features in multiscale nonlinear dynamical systems is investigated. A systematic framework is proposed using a high-order statistical closure enabling accurate prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. A new efficient ensemble forecast algorithm is developed dealing with the nonlinear multiscale coupling mechanism as a characteristic feature in high-dimensional turbulent systems. To address challenges associated with closely coupled spatio-temporal scales in turbulent states and expensive large ensemble simulation for high-dimensional complex systems, we introduce efficient computational strategies using the so-called random batch method. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the new reduced-order model in various dynamical regimes of the flow field with distinct statistical structures. Finally, the proposed model is applied for a wide range of problems in uncertainty quantification, data assimilation, and control.
 
== Future semesters ==


*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[Applied/ACMS/Fall2024|Fall 2024]]
 
*[[Applied/ACMS/Spring2024|Spring 2024]]
== Archived semesters ==
 
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]

Latest revision as of 19:31, 4 January 2025


Applied and Computational Mathematics Seminar


Spring 2025

Date Speaker Title Host(s)
Jan 31 TBA
Feb 7 TBA
Feb 14 TBA
Feb 21 TBA
Feb 28 TBA
Mar 7 TBA
Mar 14 Yue Lu (Harvard) [Colloquium] Li
Mar 21 TBA
Mar 28 Spring Break
Apr 4 TBA
Apr 11 Pierre Lermusiaux (MIT) Chen
Apr 18 Jack Xin (UC Irvine) [Colloquium]
Apr 25 Bernardo Cockburn (Minnesota) Transforming stabilization into spaces Stechmann, Fabien
May 2 Sylvia Herbert (UCSD) Chen

Abstracts

Bernardo Cockburn (Minnesota)

Title: Transforming stabilization into spaces

In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.

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