arXiv subjects

Leon Brenig

Publications and source records attributed to Leon Brenig.

4 recordsLinked to original sources

arXiv2023

Modified Verhulst-Solow model for long-term population and economic growths

In this study, we analyze the relationship between human population growth and economic dynamics. To do so, we present a modified version of the Verhulst model and the Solow model, which together simulate population dynamics and the role of economic variables in capital accumulation. The model incorporates support and foraging functions, which participate in the dynamic relationship between population growth and the creation and destruction of carrying capacity. The validity of the model is demonstrated using empirical data.

econ.GN↗

arXiv2009

New special functions solving nonlinear autonomous dynamical systems

A general solution is found for a large class of time continuous autonomous nonlinear dynamical systems, the so-called quasi-polynomial systems. This solution is expressed in terms of a new type of special functions defined via their Taylor series. The coefficients of these Taylor series are generated by a tensor that generalizes the factorial function and has a combinatorial meaning. The existence of these functions raises the question of the relation between them and the chaotic behaviour of the solutions that may appear for the quasi-polynomial dynamical systems.

math.CA↗

arXiv2007

Is quantum mechanics based on an invariance principle?

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition to quantum mechanics. The Schroedinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wave function.

gr-qc↗

arXiv2002

On the singularities of gravity in the presence of non-minimally coupled scalar fields

We investigate the robustness of some recent results obtained for homogeneous and isotropic cosmological models with conformally coupled scalar fields. For this purpose, we investigate anisotropic homogeneous solutions of the models described by the action $$ S=\int d^4x \sqrt{-g}\left\{F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ) \right\}, $$ with general $F(ϕ)$ and $V(ϕ)$. We show that such a class of models leads generically to geometrical singularities if for some value of $ϕ$, $F(ϕ)=0$, rendering previous cosmological results obtained for the conformal coupling case highly unstable. We show that stable models can be obtained for suitable choices of $F(ϕ)$ and $V(ϕ)$. Implications for other recent results are also discussed.

gr-qc↗