Essays about: "integral equations"

Showing result 1 - 5 of 29 essays containing the words integral equations.

  1. 1. Investigation of soliton equations with integral operators and their dynamics

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Ruben Vikars Hall; Carl Svennerstedt; [2023]
    Keywords : Soliton; Calogero-Moser-Sutherland system; Lax pair; Hilbert transform; Szegö projection; Benjamin-Ono equation; Non-chiral Intermediate long-wave equation; Szegö equation;

    Abstract : We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. READ MORE

  3. 2. Integrability and Thermodynamics of the Gross-Neveu Model

    University essay from KTH/Fysik

    Author : Valdemar Melin; [2023]
    Keywords : Mathematical Physics; Quantum Field Theory; Bethe Ansatz; Gross-Neveu Model; Matematisk fysik; kvantfältteori; Bethe-ansatsen; Gross-Neveu-modellen;

    Abstract : The Gross-Neveu model is a quantum field theory of interacting N-flavor fermions in 1+1dimensions, with interaction term $(\bar{\psi}_f\psi_f )^2$. This model is studied using the property offactorized scattering. READ MORE

  4. 3. Implementation and study of boundary integral operators related to PDE:s in the plane

    University essay from Lunds universitet/Matematik LTH

    Author : Erik Andersson; [2023]
    Keywords : Boundary integral equation; Singular integral operator; Product integration; Close evaluation; Numerical integration; MATLAB; Mathematics and Statistics;

    Abstract : The method of solving boundary value problems of partial differential equations numerically by first reformulating the problem as a boundary integral equation has many advantages over other methods, but also some unique difficulties. Some of these difficulties stem from problems in evaluating singular or nearly singular integral operators, and solving these difficulties is an active field of research. READ MORE

  5. 4. Reinforcement Learning for Hydrobatic AUVs

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Grzegorz Woźniak; [2022]
    Keywords : Deep Reinforcement learning; Deep learning; Optimal control; Hydrobatics; Deep Reinforcement learning; Deep learning; Optimal control; Hydrobatics;

    Abstract : This master thesis focuses on developing a Reinforcement Learning (RL) controller to perform hydrobatic maneuvers on an Autonomous Underwater Vehicle (AUV) successfully. This work also aims to analyze the robustness of the RL controller, as well as provide a comparison between RL algorithms and Proportional Integral Derivative (PID) control. READ MORE

  6. 5. GPU-Accelerated Monte Carlo Geometry Processing for Gradient-Domain Methods

    University essay from Linköpings universitet/Medie- och Informationsteknik; Linköpings universitet/Tekniska fakulteten

    Author : Linus Mossberg; [2021]
    Keywords : Monte Carlo; geometry processing; partial differential equations; Poisson equation; seamless image editing; distance field; importance sampling; random walk on spheres;

    Abstract : This thesis extends the utility of the Monte Carlo approach to PDE-based methods presented in the paper Monte Carlo Geometry Processing. In particular, we implement this method on the GPU using CUDA, and investigate more viable methods of estimating the source integral when solving Poisson’s equation with intricate source terms. READ MORE