### Bastien Grosso – Atomic structure and electronic properties of twisted Bilayer Graphene

**Supervisors:**

**Prof.**

**Oleg Yazyev**

**Description**

Moreover, the energy of the system varies if one imposes a rotation on one of the layers. Many publications have studied the twisted Bilayer for different relatively big angles but not really for small angles (smaller than one degree).

### Théo Galy-Fajou – Split-Field PML Boundaries using the Discontinuous Galerkin Method

**Supervisor: Prof. Jan Hesthaven**

Computational Mathematics and Simulation Science, MCSS, EPF, Lausanne

**Description**

Open boundaries are necessary in many computational simulation systems. To limit the domain size of the system while reproducing faithfully the real physic behaviour, especially in the case of waves simulations, special methods are needed. The first efficient solution was brought by Berenger and consist in an artificial damping material call perfectly matched layer. It has been improved since and the main method is called Split-Field Perfectly Matched Layer. In this project electromagnetic waves are simulated in a box through the recently developed Discontinuous Galerkin Method. The different parameters of the layer are investigated as well as the effect of the meshing needed for the DGM.

### Fabian Bernhard – Numerical simulation of aerosol chemistry

**Supervisor**: Prof. S. Takahama

**Description**

Within this project, a module simulating the formation of organic aerosols through absorptive partitioning has further been developed. This module can be integrated into the MCM model and extends thus its functionalities by including gas/particle partitioning for organic compounds, besides the standard gas phase reactions.

### Etienne Favre – Constructing embedded lattice rules for multivariate integration

**Description**:

### Grégoire Vionnet – Develop a solver for stationary temporal dissipative solitons in optical micro resonators

**Supervisor**: Prof. Tobias Kippenberg

Laboratory of Photonics and Quantum Measurements (K-lab), EPF, Lausanne

**Description:**

Temporal solitons are a special class of solitons that are solutions of the nonlinear AC driven Schrödinger equation and have been first identified by Russian mathematicians about 20 years ago. They are solutions of the so called (extended) Lugiato-Lefever equation (LLE) and found quite universally in nature. We recently discovered temporal dissipative solitons in optical micro resonator based frequency combs. The aim of this semester project is to numerically simulate the soliton formation. This has already been accomplished in the group using a split-step Runge-Kutta integrator on the coupled-mode equations (equivalent to the LLE) which simulates the whole dynamics. The solver developed in this project is based on the stationary extended LLE, discarding the dynamics, making the simulations much shorter. The results are compared to examples in the literature (benchmarking).

### Jonathan Giezendanner – 3D Graph-Based Formation Odor Source Localization

**Supervisors:** Prof. Alcherio Martinoli, Jorge Soares and Dr. Ali Marjovi

The Distributed Intelligent Systems and Algorithms Laboratory (DISAL), EPF, Lausanne

**Description:**

Previous efforts in DISAL have led to the development of a graph-based formation control approach to track a chemical plume to its source using ground robots.

The goal of our work is to investigate adding a 3rd dimension to the problem and the solution. Obtaining concentrations not only at ground level but also above paves the way to use the entire plume tracing solution in situations where the source is not on the same level as the robots, and where navigating in 3D space is needed (underwater, in the air, etc.).

This project will include implementation, simulation and experimentation components. The existing code will be extended and implemented in the Webots simulator, where it will be used for quickly evaluation and tuning the solution. Afterwards, the code will be ported to the new Khepera IV platform (and connected to the traversing system), and used for wind tunnel experiments using different parameters, formations and environmental conditions.

### Pablo Garcia-Amorena – Wavelet transform for fractiona operators in neural models

**Supervisors**: Prof Van De Ville Dimitri

Medical Image Processing Lab, EPF, Lausanne

**Description**:

In this work, we present a scheme to model neural responses to stimulus spike current by using the fractional derivative of a signal. Being adaptation to changes in presynaptic stimulus the goal of such a model, we introduce an approach based on the idea of short-term memory and derivative sensitivity. We

apply it to different typologies of spike trains regarding the frequency and the pattern variation. We find out multiscale properties when low-pass filtering the derivative, as well as features indicating the variation of the signal at different resolutions, encoded in the signal decomposition. The results emphasize the suitability of fractional differentiation to be integrated in a neural network scheme.

### Pierre-Olivie Guimond – Theory of Dirac fermions materials

**Supervisor**: Prof. Yazyev Oleg

Groupe Yazyev, EPF, Lausanne

**Description:**

In this project several algorithms were implemented, allowing to describe the electronic band structure of graphene in different configuration, namely for graphene layers, graphene nano-ribbons and graphene layers with defects. One can observe in the last case the magnetic effects of defects and the symmetries of the density of states. Monte-Carlo simulations were used to study behaviors of some properties of graphene, such as magnetization, at finite temperature for different mathematical nearest-neighbors models of hamiltonians. It would be interesting to further develop Monte-Carlo simulations of graphene systems with defects in order to see how it influents the electronic and magnetic properties.

### Gaël Lederrey – Collaborative Sensing and Decision Making for Intelligent Vehicle Maneuvers

**Supervisors:** Prof. Alcherio Martinoli, Milos Vasic and Iñaki Navarro

Disal, EPF, Lausanne

**Description:**

New generations of intelligent vehicles are becoming more and more developed. These kind of vehicles have very powerful resources inside, such as efficient computers, sensors and actuators. These cars can be extended on many ways such that they can reduce a lot the injuries caused by the road accidents.

One of the most dangerous maneuver on the road is the overtaking. This project deals with the implementation of collaborative sensing and decision making in this specific scenario.

At the beginning of the project, two path-following controllers have been implemented. It is an efficient way to control the vehicles on the track with predefined trajectories. Then, a lane detection algorithm has been implemented using the information received from the Lidars. This algorithm tries to place the vehicles seen by the Lidars on the right lane. Finally, a decision making algorithm has been implemented. This algorithm is used with a Finite State Machine in order to have a realistic behavior.

### Gaël Lederrey – A macrosocpic loading model for dynamic, anisotropic and congested pedestrian flows. Implementation, calibration and case study analysis

**Supervisors: **Michel Bierlaire

Transp-or, EPF, Lausanne

**Description:**

Pedestrian facilities are more and more congested. It is important to understand the modeling of pedestrian flows to assure safety and comfort. Many models have already been developed such as the social force modle and PedCTM. The problem is that either they allow for population heterogeneity or they are fast. The goal of this project is to implement a new model that has both of these characteristics.

The new model presented here is fast due to the use of a fundamental diagram. The anisotropy of this model comes from a new formulation of a fundamental diagram based on the literature, SbFD. This project gives a summary of the model and presents the new fundamental diagram.

It also compares this fundamental diagram to the state-of-the-practice, Weidmann (1992). The different parameters of the model and the fundamental diagrams are calibrated using the simulated annealing algorithm. Finally, a case study analysis on two set of experimental data is done to compare the performance of the fundamental diagrams.