Essays about: "Hyperbolic dynamics"

Found 5 essays containing the words Hyperbolic dynamics.

  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. Application of Physics-Informed Neural Networks for Galaxy Dynamics

    University essay from Linnéuniversitetet/Institutionen för fysik och elektroteknik (IFE)

    Author : Lucas Barbier; [2023]
    Keywords : ;

    Abstract : Developing efficient and accurate numerical methods to simulate dynamics of physical systems has been an everlasting challenge in computational physics. Physics-Informed Neural Networks (PINNs) are neural networks that encode laws of physics into their structure. READ MORE

  4. 3. On a novel soliton equation, its integrability properties, and its physical interpretation

    University essay from KTH/Fysik

    Author : Alexander Fagerlund; [2022]
    Keywords : Calogero-Moser systems; Conservation laws; Elliptic dynamics; Fluid dynamics; Hamiltonian mechanics; Hyperbolic dynamics; Integrability; Lax pairs; Pole ansatz; Riemann-Hilbert problems; Solitons; Bevarandelagar; Calogero-Mosersystem; Elliptisk dynamik; Fluiddynamik; Hamiltonmekanik; Hyperbolisk dynamik; Integrabilitet; Laxpar; Polansats; Riemann-Hilbertproblem; Solitoner;

    Abstract : In the present work, we introduce a never before studied soliton equation called the intermediate mixed Manakov (IMM) equation. Through a pole ansatz, we prove that the equation has N-soliton solutions with pole parameters governed by the hyperbolic Calogero-Moser system. READ MORE

  5. 4. On the dynamics of a family of critical circle endomorphisms

    University essay from KTH/Matematik (Avd.)

    Author : Nils Hemmingsson; [2019]
    Keywords : Dynamical systems; Hyperbolic dynamics; Non-uniform hyperbolicity; Lyapunov exponents; Dynamiska system; Hyperboliska system; Icke-likformig hyperbolicitet; Lyapunovexponenter;

    Abstract : In this thesis we study two seperate yet related three parameter-families of continuously differentiable maps from the unit circle to unit circle which have a single critical point. For one of the families we show that there is a set of positive measure of parameters such that there is a set of positive measure for which all points in the latter set, the derivative experiences exponential growth. READ MORE

  6. 5. Pedestrian Evacuation Modelled by a Conservation Law with a Two-inflection-point Flux Function

    University essay from Lunds universitet/Matematik LTH

    Author : Henrik Lindell; [2019]
    Keywords : Numerical analysis; Applied mathematics; Hyperbolic conservation laws; Finite volume methods; Partial differential equations; Pedestrian dynamics; Modeling; Mathematics and Statistics;

    Abstract : When designing a building one must consider safety aspects. One such aspect is that in the case of an emergency people should be able to efficiently evacuate the building. In this paper we investigate how the width-profile of a corridor leading to an exit might affect the efficiency of evacuation. READ MORE