http://hdl.handle.net/10174/139 Sun, 05 Apr 2026 23:50:49 GMT 2026-04-05T23:50:49Z http://hdl.handle.net/10174/40565 Title: Modelling with PDEs: the example of traffic flow, a few aspects Authors: Correia, Joaquim M.C. Abstract: The lecture examines how partial differential equations are used to represent and analyse traffic dynamics. It discusses key models addressing aspects like congestion, wave propagation, and the impact of driver behaviour on traffic patterns. Sat, 31 May 2025 23:00:00 GMT http://hdl.handle.net/10174/40565 2025-05-31T23:00:00Z http://hdl.handle.net/10174/40558 Title: The Riemann problem for a model in elastoplasticity with hysteresis Authors: Correia, Joaquim M.C. Abstract: We revisit the 1-D(imensional) case of the 3-D Antman-Szymczak model for the longitudinal motion in an elastic-plastic bar [Ant, Tran]. As far as real-world applications are under consideration the model captures two main behaviour phenomena: limit “total compression”, and tension and compression yield points (elastic-plastic phase transitions, allowing for hysteresis). A major technical difficulty here is on handling the Lipschitz continuous low regularity of the so-called flux function, a consequence of the elastic-plastic phase transition, which imply discontinuous wave speeds. While in the past we solved a general class of Riemann problems for 1st order hyperbolic systems of conservation laws with Lipschitz continuous flux-functions [CLT] capturing the model under consideration we are now concerned with how to handle, directly, the common in applications 2nd order hyperbolic pdes, e.g., what if we rewrite the model as a nonlinear wave equation? Finally, a second reason to revisit this model is because of our (pre)occupation on the proper mathematical modelling of “physical phenomena”: hysteresis has a viscosity like effect, i.e., it is an interesting energy dissipative mechanism. Thu, 26 Jun 2025 23:00:00 GMT http://hdl.handle.net/10174/40558 2025-06-26T23:00:00Z http://hdl.handle.net/10174/40358 Title: Problem solving, the IMO Roadmap and Linear Algebra Authors: Correia, Joaquim M.C. Abstract: Lecture (4h=2x2h) on "Problem solving, the IMO Roadmap and Linear Algebra" at the 4th LMA Workshop Day for High-School Teachers, Academic Seminar of the Lao Mathematics Association, January 29th, 2025, Vientiane, Lao PDR Wed, 29 Jan 2025 00:00:00 GMT http://hdl.handle.net/10174/40358 2025-01-29T00:00:00Z http://hdl.handle.net/10174/40343 Title: J&J Vision Care Inc. : Manufacture of contact lenses Authors: Smith, Ann; O'Brien, David; Greenbank, Emma; Planella, Ferran Brosa; Mirnia, Javad; Almonacid, Javier; Correia, Joaquim; Moroney, Kevin; Keating, Leah; Schwarzwalder, Marc; McGuinness, Mark; Coughlan, Michael; Vynnycky, Michael; Dellar, Paul; Murphy, Sarah; Bohun, Sean; Lee, Wiliam Abstract: Optimise J&J contact lens curing process: 1) develop a mathematical model; 2) how does curing time depend on thickness.; 3) how do changes in the monomer solution affect curing time.; 4) the function of nitrogen. Thu, 22 Jun 2023 23:00:00 GMT http://hdl.handle.net/10174/40343 2023-06-22T23:00:00Z