Gallery — Math

The viscosity of a particular fluid is an interesting parameter that plays an important role in fluid dynamics of that fluid. We chose the common household cooking item canola oil. Using a ball drop, we set out to measure viscosity at various temperatures and create a model for the viscosity of canola oil as a function of temperature, as well as an accurate measurement for viscosity at room temperature. It was found that the viscosity between 0 and 40 degrees Celsius can be approximated using an exponential function and that an estimation for viscosity at room temperature was not very difficult to obtain. The precision of this measurement was limited by uncertainty in lab equipment used to measure various quantities as well as the image analysis software we used and the limited frame-rate of our camera.

Voor huiswerkopdrachten

Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.

This paper implements Simultaneous Localization and Mapping (SLAM) technique to construct a map of a given environment. A Real Time Appearance Based Mapping (RTAB-Map) approach was taken for accomplishing this task. Initially, a 2d occupancy grid and 3d octomap was created from a provided simulated environment. Next, a personal simulated environment was created for mapping as well. In this appearance based method, a process called Loop Closure is used to determine whether a robot has seen a location before or not. In this paper, it is seen that RTAB-Map is optimized for large scale and long term SLAM by using multiple strategies to allow for loop closure to be done in real time and the results depict that it can be an excellent solution for SLAM to develop robots that can map an environment in both 2d and 3d.

Übung: Lineare Gleichungssysteme

Chapitre 2, Peip2, Polytech'Nice Sophia, sans les sch\'emas et applications sch\'ematis\'ees

CT problem set for undergraduate Medical Physics course.

Proof of a function's representation with Taylor Series

This research paper aims at exploiting efficient ways of implementing the N-Body problem. The N-Body problem, in the field of physics, predicts the movements and planets and their gravitational interactions. In this paper, the efficient execution of heavy computational work through usage of different cores in CPU and GPU is looked into; achieved by integrating the OpenMP parallelization API and the Nvidia CUDA into the code. The paper also aims at performance analysis of various algorithms used to solve the same problem. This research not only aids as an alternative to complex simulations but also for bigger data that requires work distribution and computationally expensive procedures.