STARS Laboratory’s Post

Unraveling the mystery of a circle's area with our demonstration model! Witness the visual proof that brings geometry to life. #Science #Maths #GeometryInAction #Labkafe #MathVisualized #EducationalInsights #icse #cbse

📣Colloquia Seminar: Agent-Based Optimization of Pedestrian Dynamics via Local Attraction Dr. Max Winkler Department of Mathematics, Technische Universitat Chemnitz Date/Time: 7.3.2024 - 14:30 (GMT +3) Place: Hayri Körezlioğlu Seminar Hall, IAM/METU Abstract: We study an optimization problem for pedestrian dynamics aiming at a fast evacuation of a crowd in case of an emergency situation. The forward model, the so-called Hughes model, consists of a nonlinear transport equation describing the motion of the pedestrians, coupled with an Eikonal equation whose solution provides the direction towards the next emergency exit. For an optimization of that process we add agents which are individuals of the crowds as well, but have the ability to locally attract other pedestrians. By optimizing their trajectory and attraction intensity one can avoiding e.g. the case that too many pedestrians want to squeeze through the same exit whereas other exits are rarely used, so that the evacuation might be much faster. We provide existence results and necessary optimality conditions for the resulting optimal control problem and present gradient-based optimization algorithms for a numerical computation. For the spatial discretization of the transport equation we use a finite volume scheme and show that important properties like mass-conservation and preservation of the natural bounds imposed on the pedestrian density function are retained. Furthermore, we show in numerical experiments that this optimization technique indeed leads to an improvement of an evacuation. #seminar #appliedmath #ODTÜ #METU #UME #IAM #instituteofappliedmathematics #uygulamalımatematikenstitüsü #ortadoğutekniküniversitesi #middleeasttechnicaluniversity

Had the opportunity to participate in an excellent conference in London this week - ICICT 2024. Congratulations Amit Joshi. Insightful keynotes offered by Aninda Bose, Tatiana Kalganova, Nilanjan Dey, amongst others. I had the privilege of contributing a paper and presentation titled "Sensing the Emergence of New Structure in Matter and Life and its Impact of Physics, Chemistry, and Biology, in a Light-Based Quantum Computational Model." This paper, to be published open-access by SpringerNature, explores the cosmos as a complex adaptive system (CAS) modeled as a fourfold, symmetrical, light-based, and multi-layered structure in a state of persistent quantum computation. As conditions in the CAS change this precipitates a change in the underlying mathematical model. The hypothesis is that sensing devices based on this model would naturally be more sensitive to the changing physics, chemistry, and biology of target systems. #complexsystems #quantumcomputing #technologyleadership #sensing A mirror-presentation capturing the essence of the paper is available here...https://lnkd.in/g-fqac9k

In this paper, we delve into the intricacies of the time-fractional Fornberg-Whitham equation, employing the powerful Homotopy perturbation transform method with Caputo-Fabrizio fractional derivative. Through meticulous analysis and application of fixed point theory, we establish the existence and uniqueness of solutions for this complex equation. Our research goes beyond theoretical frameworks, offering practical insights into the physical interpretation of nonlinear models through semi-analytical solutions. These solutions not only showcase the effectiveness of our proposed method but also shed light on the dynamics of atmospheric phenomena. To further enhance understanding, we present visually stunning 2D and 3D graphs of derived solutions, providing a clear depiction of their behavior under various parameter values. Join us in unraveling the mysteries of atmospheric science and nonlinear dynamics. Find more information about our research, please visit: https://lnkd.in/g6aiFHis #ESCI #mathematics #Scopus #research

🎉🚀 We are super-excited to announce that our #tLaSDI: #thermodynamics-#informed #latent #space #dynamics #identification is published online in the #CMAME journal! 📚✨ 🔗 Check it out here: https://lnkd.in/g47q3GFv 🌟 tLaSDI introduces a thermodynamics partial differential equation, i.e., #GENERIC #formalism, to model latent space dynamics. This approach creates an intriguing link between full and reduced space dynamics, relating full order dynamics with thermodynamic quantities, such as #energy and #entropy, within the latent space. 🌐🔬 For instance, we observe that the rate of increase in entropy of the latent space dynamics corresponds to the shock-forming phenomenon in Burgers' equation. This #interpretable #relationship between latent space and full order model dynamics will be pivotal in advancing the data-driven approach, serving as an indicator to switch from one phase to another as the dynamic regime changes. 🔄💡 🔍 Besides these insights, many other fascinating aspects are discussed in the paper, such as the effect of #simultaneous #training, different #loss #terms, #greedy #sampling for #generalization, and #error #analysis. 📈🧩 🔥 Pretty cool stuff! The paper is available for #free for the next 50 days, so make sure to take advantage of it! 📖💥 👏 Kudos to Jun Sur Park, Siu Wun Cheung, and Yeonjong Shin for their outstanding effort on this development! 🌟🙌 #neuralnetwork #ML #simulation #science #dynamics #ROM

We are pleased to announce the next Community Meeting for the SIAM activity group Mathematics of Planet Earth (MPE).    It will be a Colloquium presentation on "Noise Calibration for Geophysical Fluid Dynamics Models" by Prof. Dan Crisan, Professor of Mathematics, Imperial College London, UK. It will occur on Thursday, December 21, at 11:00 a.m. EDT (23:00 CST-HK, 17.00 CEST, 15:00 UTC, 8 a.m. PDT). Please save the date!   The Zoom link for the SIAM MPE Community Meeting is https://lnkd.in/enpTGVK6 The meetings are recorded and will be made available by SIAM. The abstract of the Colloquium presentation is provided below, along with all Zoom detail information. Title: Noise Calibration for Geophysical Fluid Dynamics Models Speaker: Dr. Dan Crisan, Professor of Mathematics, Faculty of Natural Sciences, Department of Mathematics, Imperial College London, UK Abstract: Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a judicious usage in modelling fluid evolution, one needs to calibrate the amplitude of the noise to data. In this paper we address this requirement for the stochastic rotating shallow water (SRSW) model. This work is a continuation of [1], where a data assimilation methodology has been introduced for the SRSW model. The noise used in [1] was introduced as an arbitrary random phase shift in the Fourier space. This is not necessarily consistent with the uncertainty induced by a model reduction procedure. In this paper, we introduce a new method of noise calibration of the SRSW model which is compatible with the model reduction technique. The method is generic and can be applied to arbitrary stochastic parametrizations. It is also agnostic as to the source of data (real or synthetic). It is based on a principal component analysis technique to generate the eigenvectors and the eigenvalues of the covariance matrix of the stochastic parametrization. For SRSW model covered in this paper, we calibrate the noise by using the elevation variable of the model, as this is an observable easily obtainable in practical application, and use synthetic data as input for the calibration procedure. This is joint work with Alexander Lobbe, Oana Lang, Peter Jan van Leeuwen, and Roland Potthast. [1] Dan Crisan, Oana Lang, Peter Jan van Leeuwen and Roland Potthast. Bayesian inference for fluid dynamics: a case study for the stochastic rotating shallow water model. Frontiers in Applied Mathematics and Statistics, 2023.  

https://lnkd.in/gZvYu2CE Article Title: Abundant dynamical solitary waves solutions of M -fractional Oskolkov model Author(s): Badamasi Bashir Mikailu, Jafar Anafi and Shaheera Haroon* Journal: Annals of Mathematics and Physics Journal ISSN: 2689-7636 Abstract: This work uses a truncated M-fractional derivative variant of the Oskolkov model to investigate the dynamic behavior of solitary wavefronts. The methods used in this framework produce a variety of solitary waveforms, such as bright and dark solitons. A suitable choice of the free parameters is used to investigate the geometrical structures for the wave solutions, which are further characterized by stable bright periodic and soliton waves. #Nonlinearfluidequation #Solitonsolutions #Fractionalderivative #Modifiedauxiliaryequationmethod #Mathematics #Algebra #Geometry #Calculus #Probability #Statistics #NumberTheory #MathematicalAnalysis #DiscreteMathematics #LinearAlgebra #DifferentialEquations #Topology #MathematicalModeling #AppliedMathematics #ComputationalMathematics #MathematicalLogic #FunctionalAnalysis #ComplexAnalysis #NumericalAnalysis #Optimization #GraphTheory #MathematicalPhysics #Cryptography #StochasticProcesses #GameTheory

The Paradoxical Spin: Unveiling the Mystery of the Free-Space Homopolar Motor The Homopolar motor, a deceptively simple device, presents a captivating challenge to our understanding of angular momentum conservation. This essay delved into the seemingly contradictory behavior observed in a free-space Homopolar motor experiment and explored the potential explanations through the lens of mathematics and physics. https://lnkd.in/d-Z2PK6F