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Both collaborate with Prof. Raimund Bürger, subdirector of Center for Research in Mathematical Engineering.
Two Indian scientists conducted a stay at the Center for Research in Mathematical Engineering, CI²MA, at Universidad de Concepción: Aekta Aggarwal, professor at the Indian Institute of Management (IIM) Indore (India) and Ganesh Vaidya, currently post-doctoral researcher at Pennsylvania State University (USA) in the group of Alberto Bressan.
This visit was arranged by Raimund Bürger, sub-director of CI²MA and principal researcher of the Center for Mathematical Modelling, CMM, (FB210005) of U. de Chile, and Luis Miguel Villada, member of CI²MA, academic at the Department of Mathematics at Universidad del Bío-Bío and also an associate researcher at CMM.
“We are grateful to CMM for the funding received and especially this time for the administrative staff’s patience when selecting flight options”, Prof. Bürger said. “The visit of both has led to new directions of research, and we have identified two specific projects we will be working on in a remote collaboration in the very near future”.
During this stay, Prof. Aekta Aggarwal collaborated with Professors Bürger and Villada. “Our research interests and expertise, particularly in (nonlocal) conservation laws, discontinuous flux, and the practical applications modeled by these PDEs, significantly overlapped, making this collaboration both natural and focused,” she details.
“Over the years,” Aggarwal elaborates, “we have closely followed each other’s work and engaged in discussions and exchanges of research notes on these topics, which helped define the precise goals of this visit.”
Regarding the results of this stay, she explained that “we had enriching discussions about potential collaborations and directions for research on nonlocal conservation laws with discontinuous flux, as well as their applications to sedimentation and polydispersion models.”
“We identified several research problems that we plan to develop in the coming months,” Aggarwal adds. “This visit has opened numerous avenues for practical and sustainable applications with closed-form solutions, which we aim to achieve in the coming years.”
Regarding new scientific opportunities that could arise from this stay in Concepción, she mentioned that “the team has zeroed down on answering various fundamental research questions from systems of nonlocal conservation laws with discontinuous flux such as their well-posed-ness and efficient numerical algorithms approximating them.”
“Moreover”, she explains, “the problems have been catered to practical applications in particular, batch and continuous sedimentation of monodisperse and polydisperse mixtures. These algorithms will not only be important from the theory of PDEs but will also focus on capturing solutions which are accurate and have required physical properties of the model. The application of the models discussed and developed during this visit, could also be explored for other practical applications, other than sedimentation”.
“My academic experience has primarily focused on the theory of conservation laws, with limited exposure to developing physical models”, Aggarwal explains. “However, during this recent research visit, I had the enriching opportunity to work closely on creating physically relevant models using conservation laws”.
Meanwhile, Prof. Vaidya stated that “my interest in Prof. Bürger’s work began during my PhD, focusing initially on scalar conservation laws with discontinuous flux and more recently on nonlocal conservation laws applied to real-world phenomena such as sedimentation and polymer flooding. Thus, this visit provided a significant platform for me to learn modelling techniques and exchange the theoretical insights I have gathered over the years”.
“My visit aimed to explore the practical applications of the nonlocal conservation laws I’ve been studying, both scalar and systems, over the past years, specifically focusing on developing mathematical models for sedimentation and polydispersion”, he said and emphasized that “the objectives of our stay were successfully met as we engaged in fruitful discussions with Prof. Raimund Bürger and Prof. Luis Miguel Villada. These discussions centred around potential collaborations and future directions in the realm of nonlocal conservation laws featuring discontinuous flux, particularly in their application to sedimentation and polydispersion models”.
“The research visit was a truly enriching experience and gave us the opportunity to work closely and develop physically relevant models using conservation laws. We look forward to more such collaborations in the future”, added Prof. Vaidya, who in the context of this visit presented the talk ‘Finite Volume Schemes for Nonlocal Conservation Laws and their Error Estimates’, as part of colloquia organized by the Department of Mathematical Engineering (DIM) of UdeC.
By Iván R. Tobar Bocaz, journalist – CMM Concepción
Posted on Jul 4, 2024 in News
