This year for the first time we were going to host the ECMI Modelling Week in Russia. Unfortunately, the coronavirus forced us to postpone the 35th Modelling Week until next year. But this year St. Petersburg Polytechnic University will host The First ECMI Virtual Modelling Week. We are going to keep as close to traditional ECMI Modelling Week as possible. As it was scheduled, the event will take place on July 05-12, 2020.
We will start with the problem presentations. From Monday till Friday the group work will be carried out in MS Teams. And finally, the result presentation will take place on Saturday. After finishing the written report, students will get 3 ECTS credits (MW is virtual, but the credits are real).
Even some cultural program is to be included. Using Google Street View, we will have a virtual tour in St. Petersburg focused on math history of the city.
And the great news: the event will be free for ECMI students! See you in St.Petersburg MS Teams!
ECMI has been running annual Modelling Weeks for students since 1988. Students come from all over Europe to spend a week working in small multinational groups on problems which are based on real life problems. Each group is led by an ECMI instructor who introduces the problem — usually formulated in non-mathematical terms — on the first day and then helps to guide the students to a solution during the week. The students present their results to the other groups on the last day and then write up their work as a report. After finishing the report students will get 3 ECTS credits.
The main aims of the Modelling Week are to train students in Mathematical Modelling and stimulate their collaboration and communication skills, in a multinational environment. Attendance at a Modelling week is an integral part of the ECMI certificate and of many of the masters courses run at ECMI centers but many other students have also learned new skills by attending one of these very successful courses. A number of similar Modelling Weeks or Modelling Camps are organized by ECMI members each year. A full list of previous events can be found here.
Dates: July 5th to July 12th, 2020
Host University:Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia
The Modelling Week 2020 will be break down by Problems
The loosening of bolts is very dangerous phenomenon in aircraft assembly. We propose to study it by using the special assembly demonstrator developed on the base of specialized software complex for simulation of aircraft assembly process.
The assembled aircraft parts are fastened by bolts installed one-by-one. After the new bolt is installed, previously installed ones may be loosened. The compressing load is controlled in each bolt. The loosened bolts can be adjusted up to the desired load value. Due to the presence of loosening effect, the quality of contact (gap between parts) depends on the bolt installation order. The goal is to design and implement an algorithm for minimization of the assembly operations number (bolt installation and adjustment). Also the study of the effect of the bolt installation order on the residual gap change is of interest. Choosing the installation scheme that maintains as uniform gap as possible throughout the assembly operations.
Additionally the students may study the influence of fastener stiffness onto the assembly process. The model of the test junction will be provided.
Mathematical background: Calculus, Optimization methods
Energy consumption of households is not evenly distributed. To satisfy peak demand, additional CO2 intensive generators are turned on when demand peaks. To avoid peak demand from dwellings, the REDWoLF (Rethink Electricity Distribution Without Load Following) hybrid storage system is proposed, consisting of batteries, storage heaters and a water cylinder. This aims at avoiding the use of these peak generators and integrating a higher share of renewables on the Power Grid. This system is planned to be tested in 100 houses distributed in 6 pilot sites in Great Britain, Ireland and France, which are currently undergoing construction or refurbishment.
The aim is to construct based and emulate the performance of the algorithm for two consecutive days on the real datasets employing REDWoLF mathematical template and REDWoLF template code for one day run, based on the standard properties of the UK household. This would allow estimating the reduction of CO2 or if the energy is renewable a price per household. Moreover the combination of storage adds additional layer of complexity, since electrical standards and household properties vary drastically between different countries.
As a result, if time permits, the second task would be to modify the priorities for country of your choice, with the provided datasets being normalized for the chosen country.
Mathematical background: Calculus, Optimization methods
Capillary rise is a fundamental physical phenomenon that assists the water transport process in trees. Despite the obvious examples of occurrences the capillary rise phenomenon in nature (e.g. transport of fluids in plants and through the soil), the various examples of the applications of that phenomenon in the industry can also be seen, e.g. oil recovery process, dyeing of textile fabrics and inkjet printing. Due to its interesting features as well as the potential applications in industry, the mathematical models describing flow in the narrow tube are still gaining importance.
Investigation of water absorption in wood is not a trivial task due to the complex internal structure of trees. Nevertheless, a detailed analysis of a capillary rise phenomenon in conducting cells contained in a tree the trunk may provide the interesting results for various industries as well as extend our knowledge about process of water transportation in trees. The aim of this project is to deliver a mathematical model of the capillary moisture absorption in wood and to perform the analysis of the distribution of water content in the trunk. Since the absorption of water may differ for different types of trees thus the investigation of various types of wood is needed.
Mathematical background: Calculus, ODE, PDE, Fluid mechanics
The project is based on short Science Fiction novel Jack and the Beanstalk by Richard A. Lovett. The story is about a guy who climbs the tower (Beanstalk) that is 65000 kilometers high. It is said that such tower makes it possible to launch shuttles to Mars using just centrifugal force with minimal additional energy.
It is proposed to make technical audit of the project. Start with simple model: Earth as massive ball, long infinitely narrow and rigid beam with distributed mass (the Beanstalk) and space shuttle (massive dot) to be launched to Mars. Will it work? How will it affect the Earth?
Next add flexibility of the Beanstalk. What material is suitable for construction (carbon fiber, graphene)? Propose the design of the Beanstalk and make express numerical analysis of it (static loads, buckling etc.). Additionally, estimate how Earth climate can be affected by such structure.
MS Teams will be available until 10.20.2020 for discussions and preparation of reports