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The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the presence of cylindrical symmetry is applied to a general non-vacuum case. The resulting constraints are highly non-linear and non-local in the momenta conjugate to…
This paper proposes a volumetric penalty method to simulate the boundary conditions for a non-linear hyperbolic problem. The boundary conditions are assumed to be maximally strictly dissipative on a non-characteristic boundary. This…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the…
We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We develop an exact electrostatic formulation for a finite-length conducting cylindrical shell of finite thickness separating two dielectric media with arbitrary permittivity contrast. The boundary-value problem is reduced to a coupled…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
In this paper we discuss the dynamics of the cosmological Bartnick-McKinnon analogue with $n=1$ and $\Lambda=\Lambda_{reg}(n)$ . We derive boundary conditions from energy considerations. Numerical simulations are carried out to show the…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
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The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy…
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
We calculate analytically the phase boundary for a nonequilibrium phase transition in a one-dimensional array of coupled, overdamped parametric harmonic oscillators in the limit of strong and weak spatial coupling. Our results show that the…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the…
We investigate the possibility that freely rotating cylinders with an aspect ratio $L/D=0.9$ exhibit a cubatic phase similar to the one found for a system of cut-spheres. We present theoretical arguments why a cubatic phase might occur in…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…