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We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma…
A comprehensive analytical theory for nonlinear excitations related to horizontal (longitudinal, acoustic mode) as well as vertical (transverse, optical mode) motion of charged dust grains in a dust crystal is presented. Different types of…
This paper studies the physical-constraints-preserving (PCP) Lagrangian finite volume schemes for one- and two-dimensional special relativistic hydrodynamic (RHD) equations. First, the PCP property (i.e. preserving the positivity of the…
In this paper, we present a quantum theory for field propagation through a three dimensional dielectric when the third order dispersion and the attenuation coefficients are included. A unique Lagrangian is defined leading to the correct…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch-Schl\"{u}ter singularities, to leading order, to a single magnetic surface resonant with the…
We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
Derived geometry provides powerful tools to handle non-transverse intersections and singular moduli problems arising in geometry and theoretical physics. While derived algebraic geometry has been extensively developed, classical field…
We generalize the concept of conserving,\Phi-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamical potential in terms of fully dressed…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians…
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…
It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability…
Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…