arXiv subjects
Publications and source records attributed to Andrzej Okninski.
In the present work a transition from the spin-$0$ Duffin-Kemmer-Petiau equation to the Dirac equation is described. This transformation occurs when a crossed field changes into a certain longitudinal field. An experimental setup to carry out the transition is proposed.
We study relation between the Duffin-Kemmer-Petiau algebras and some representations of Tzou algebras. Working in the setting of relativistic wave equations we reduce, via a similarity transformation, five and ten dimensional Duffin-Kemmer-Petiau algebras to three and seven dimensional Tzou algebras, respectively.
We carry out a constructive review of non-standard solutions of relativistic wave equations. Such solutions are obtained via splitting of relativistic wave equations written in spinor form. All these solutions are also solutions of the Dirac equation and are non-standard because they involve higher-order spinors. The main finding is that non-standard solutions describe decaying states.
We study the 7x7 Hagen-Hurley equations describing spin 1 particles. We split these equations, in the interacting case, into two Dirac equations with non-standard solutions. It is argued that these solutions describe decay of a virtual W boson in beta decay.
We study fermion-boson transitions. Our approach is based on the $3\times 3$ subequations of Dirac and Duffin-Kemmer-Petiau equations, which link these equations. We demonstrate that free Dirac equation can be invertibly converted to spin-$0$ Duffin-Kemmer-Petiau equation in presence of a neutrino field. We also show that in special external fields, upon assuming again existence of a neutrino (Weyl) spinor, the Dirac equation can be transformed reversibly to spin-$0$ Duffin-Kemmer-Petiau equation. We argue that such boson-fermions transitions are consistent with the main channel of pion decay.
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to the next impact, is derived. Periodic points are found and their stability is determined. The grazing manifold is computed and dynamics is approximated in its vicinity. It is shown that on the grazing manifold there are trapping as well as forbidden regions. Finally, basins of attraction are studied.
We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-Bogoliubov-Mitropolsky approach - we compute the amplitude profiles, which from mathematical point of view are algebraic curves. In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of the limiter is assumed as periodic, cubic function of time. Due to simplicity of this function analytical computations are possible. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands are created from fixed points after first period doubling in a corner-type bifurcation. Equation for the time of the next impact is solved exactly for the case of two subsequent impacts occurring in the same period of limiter's motion making analysis of chattering possible.
Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the interacting case. It is demonstrated that the Dirac equation in longitudinal external fields can be also splitted into two covariant subequations.
We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(Ω)$. In the present paper we investigate metamorphoses of the function $A(Ω)$ induced by changes of the control parameters in the case of 1:3 resonances.
We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to get the amplitude profiles $AOmega) $. Dependence of the amplitude $A$ of nonlinear resonances on the frequency $ Ω$ is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function $A(Ω) $ induced by changes of the control parameters.
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2 - cycles in a corner-type bifurcation.
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time, approximating sinusoidal motion and making analytical computations possible, is assumed as quadratic and cubic functions of time, respectively.
We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.
We study dynamics of a ball moving in gravitational field and colliding with a moving table. The motion of the limiter is assumed as periodic with piecewise constant velocity - it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity. The Poincare map, describing evolution from an impact to the next impact, is derived and scenarios of transition to chaotic dynamics are investigated analytically.
Discrete time dynamics on the SU(1,1) group is studied. It is shown that a map acting in the dual space is the stroboscopic map for a SU(1,1) Bloch equation. Exact solution of the map is used to elucidate the corresponding dynamics. It is shown that dynamics of the SU(1,1) Bloch equation in the elliptic case bears close analogy to the SU(2) Bloch dynamics.
A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.
We study internal structure of the Kemmer-Duffin-Petiau equations for spin-0 and spin-1 mesons. We demonstrate, that the Kemmer-Duffin-Petiau equations can be splitted into constituent equations, describing particles with definite mass and broken Lorentz symmetry. We also show that solutions of the three component constituent equations fulfill the Dirac equation.