ECMI Virtual Modelling Week

Summer School - Online/Hybrid
July 5 - July 11, 2021

The course will be held online but 3 participation options are available for certain individuals:

Option 1 - online.

Option 2 - hybrid. Due to massive and continuous vaccination in Russia and resuming international air and railway service with 29 countries we offer a hybrid online/on-campus summer school option to students holding citizenship of:

the United Kingdom, Tanzania, Turkey, Switzerland, Egypt, Maldives, the United Arab Emirates, Kazakhstan, Kyrgyzstan, Republic of Korea, Cuba, Serbia, Japan, the Seychelles, Ethiopia, Vietnam, India, Qatar, Finland, Azerbaijan, Armenia, Greece, Singapore, Venezuela, Germany, Syria, Tajikistan, Uzbekistan, Sri Lanka.

You can join the online course for 250 euro (+4000 Rub for reg. fee) but come to St. Petersburg to take touristic advantages for the duration of the program and attend online classes at your dormitory/hostel.

If you choose Option 2, just apply for the online course here and inform us on your choice via email to get further instructions.

Option 3 – tailor-made. We may also arrange a tailor-made on-campus program for a group of minimum 10 students holding nationality of the countries Russia resumed international air and railway service with.

Would you like to learn more about photonics and have exciting holidays in the most beautiful city of Russia? Join this summer school!



  • Brief description

    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.

Duration: 7 days

ECTS credits: 3.0

Participation fee:

Online format: 250 Euro

Hybrid format: 250 Euro + 4000 Rub (non-refundable registration fee for the Letter of Invitation)

Participation fee includes tuition fee, study materials, field trips and cultural program.

Upon successful completion of the course students will receive hard copies of certificates with ECTS credits (mailed by post in case of the online format of the Summer School).

  • Cultural program

    Online format:*

    • - Online Pub Quiz;
    • - Online Interactive Tour to SPbPU Museum;
    • - Online broadcasting of excursion to the Hermitage museum;

    Cultural program in the Hybrid format is discussed with participants individually.

    *All of the listed above activities are planned to take place but in case any of those will have to be cancelled, an alternative event will be offered to participants.


Provided only for the Hybrid or the Tailor-made formats:

  • on campus at the university dormitory
  • off-campus at partner hostels in the city center

Details of the options and booking procedures will be discussed with each applicant individually.


Deadline for registration

Online format: June 28, 2021

Hybrid format:

- for EU- or visa-free countries nationals: June 07, 2021

- for non-EU nationals: May 03, 2021

  • Entrance requirements
    • - Basic knowledge of physics.
    • - Fluent English. All classes and extracurricular activities are carried out in English. Knowledge of the Russian language is not required.
    • - Applicants are expected to have at least 3 courses of Bachelor Degree (preferably in physical or technical sciences).

The Modelling Week 2021 will be break down by Problems

  • Problem 1. Bolted assembly optimization

    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

  • Problem 2. Hybrid Storage System for peak shifting applications

    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

  • Problem 3. Capillary moisture uptake in wood

    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

  • Problem 4. Beanstalk (or Stairway to heaven)

    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.

Professors and lecturers:

  • Scientists and industry experts experienced in the fields of optics and photonics


Summer and Winter Schools Team