# Extra Chapter 2: iHDG – Iterative Hybridized Discontinuous Galerkin method (Part 2)

This post is based on my work We continue our development of the previous work on iHDG method iHDG: An Iterative HDG Framework for Partial Differential Equations. SIAM Journal on Scientific Computing.   Video 6: Our simulations for a hyperbolic system using our new iHDG We show that the new approach has several advantages, for … Continue reading Extra Chapter 2: iHDG – Iterative Hybridized Discontinuous Galerkin method (Part 2)

# Chapter 10: On the wave turbulence theory for stratified flows in the ocean

This post is based on my paper . After the pioneering work of Garrett and Munk, the statistics of oceanic internal gravity waves has become a central subject of research in oceanography. The time evolution of the spectral energy of internal waves in the ocean can be described by a near-resonance wave turbulence equation, of … Continue reading Chapter 10: On the wave turbulence theory for stratified flows in the ocean

# Chapter 9: Wave turbulence theory for capillary water waves

This post is based on my paper Although many studies have been carried on to understand the Hasselmann-Zakharov weak turbulence equation for capillary waves since its derivation in the 60's, the question about the existence and uniqueness of solutions to the equation still remains unanswered, due to the complexity of the equation. Our work provides a … Continue reading Chapter 9: Wave turbulence theory for capillary water waves

# Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases

This post is based on my paper . At temperature $latex T$, bosons of mass $latex m$ can be regarded as quantum-mechanical wavepackets which have an extent on the order of a thermal de Broglie wavelength $latex \lambda_{dB} = \left(\frac{2 \pi \hbar^2}{m k_B T}\right)^\frac12$, where $latex k_B$ is the Boltzmann constant. The de Broglie wavelength … Continue reading Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases