Corrected First-Order Derivative ISPH in Water Wave Simulations

First-order Formalism and Odd-derivative Actions

In this pedagogical note, we discuss obstacles to the usual Palatini formulations of gauge and gravity theories in presence of odd-derivative order, Chern-Simons, terms.

Variational Approaches To Water Wave Simulations

Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy

Combined with simultaneous approximation terms, summation-by-parts (SBP) operators o↵er a versatile and e cient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed su↵er from a loss of accuracy. While on the interior, these operators are of degree 2p...

Higher Derivative Fermionic Field Equation in the First Order Formalism

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found which extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is...

Numerical simulations of internal wave generation by convection in water.

Water's density maximum at 4°C makes it well suited to study internal gravity wave excitation by convection: an increasing temperature profile is unstable to convection below 4°C, but stably stratified above 4°C. We present numerical simulations of a waterlike fluid near its density maximum in a two-dimensional domain. We successfully model the damping of waves in the simulations using linear t...