Related papers: A Ritz variational principle for local collisionle…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…
The principle of Random Galilean Transformation (RGT) Invariance is applied to the random motion of particles in a turbulent gas to construct a kinetic equation for the transport of the particle phase space probability…
Predicting the dynamics of a thermonuclear plasma during a magnetic confinement experiment is fundamental in order to make nuclear fusion a reliable source of energy. The development of a set of equations describing the plasma evolution on…
Electrostatic Gravitational or Rayleigh-Taylor (RT) instability in an inhomogeneous magnetized multi-ions plasma with some fraction of quantum mechanical electrons. The effect of Bohm potential, temperature degeneracy and magnetic field are…
The Dimits shift, an upshift in the onset of turbulence from the linear instability threshold, caused by self-generated zonal flows, can greatly enhance the performance of magnetic confinement plasma devices. Except in simple cases, using…
The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…
Magneto-rotational instability (MRI) is an important instability mechanism for rotating flows with magnetic fields. In particular, when the strength of the magnetic field tends to zero, the stability criterion for rotating flows is…
Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behavior of a variety of space and astrophysical plasmas.…
This study comprehensively investigates fast ion-driven drift instability, extending the theory in [B. J. Kang and T. S. Hahm, Phys. Plasmas 26, 042501 (2019)]. The eigenmode equation, including the resonant contribution of passing fast…
We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally…
The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically…
The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study in three dimensions the…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
A comprehensive gyrokinetic simulation model has been implemented in the global toroidal gyrokinetic code (GTC) and verified for studying low-frequency waves and turbulence in magnetic fusion plasmas by treating all kinetic-MHD processes on…
A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre…
Gyrokinetic theory is a basis for treating magnetised plasma dynamics slower than particle gyrofrequencies where the scale of the background is larger than relevant gyroradii. The energy of field perturbations can be comparable to the…
Three fundamental variational principles used for solving elastodynamic eigenvalue problems are studied within the context of elastic wave propagation in periodic composites (phononics). We study the convergence of the eigenvalue problems…
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear…
The investigation of symmetry nonrestoration scenarios has led to a controversy, with certain nonperturbative approximation schemes giving indications in sharp disagreement with those found within conventional perturbation theory. A…