arXiv subjects

Artur Kobus

Publications and source records attributed to Artur Kobus.

6 recordsLinked to original sources

arXiv2020

Hamiltonian form for general autonomous ODE systems: Low dimensional examples

Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called effectively conserved, that have dissimilar properties to traditional first integrals (e.g. differential of effectively conserved quantity being a Pfaffian form). We do not confine the discussion to physics; we consider examples from biology and chemistry, giving direct recipe for how to engage the framework in occurring problems. Perspective for future application in geometric numerical methods is given.

math-ph↗

arXiv2020

Computational enhancement of discrete gradient method

We propose new numerical approach to non-conservative dynamical systems. Our method being of low order, enhances qualitative performance of standard discrete gradient algorithm, thank to new concept of a reservoir. Paper is of explanatory character, focusing on concrete non-linear physical systems. Superiority of our new method with respect to standard discrete gradient method is observed.

math.NA↗

arXiv2019

Forced extension of GNI techniques to dissipative systems

We propose new concept of energy reservoir and effectively conserved quantity, what enables us to treat dissipative systems along the lines of the framework of Geometric Numerical Integration. Using this opportunity, we try to confirm numerically if our idea is useful. Numerical experiments show good qualitative behavior of integration technique for ODEs based on non-potential Hamiltonian formalism. It occurs that rising accurracy is a difficult task due to dissipative form of the system under scrutiny.

math.NA↗

arXiv2016

Group interpretation of the spectral parameter. The case of isothermic surfaces

It is well known that in some cases the spectral parameter has a group interpretation. We discuss in detail the case of Gauss-Codazzi equations for isothermic surfaces immersed in $E^3$. The algebra of Lie point symmetries is 4-dimensional and all these symmetries are also symmetries of the Gaus-Weingarten equations (which can be considered as so(3)-valued non-parametric linear problem). In order to obtain a non-removable spectral parameter one has to consider so(4,1)-valued linear problem which has a 3-dimensional algebra of Lie point symmetries. The missing symmetry introduces a non-removable parameter. In the second part of the paper we extend these results on the case of isothermic immersions in arbitrary multidimensional Euclidean spaces. In order to simplify calculations the problem was formulated in terms of a Clifford algebra.

nlin.SI↗

arXiv2015

On geometry of the scator space

We consider the scator space - a hypercomplex, non-distributive hyperbolic algebra introduced by Fernández-Guasti and Zaldívar. We discuss isometries of the scator space and find consequent method for treating them algebraically, along with scators themselves. It occurs that introduction of zero divisors cannot be avoided while dealing with these isometries. The scator algebra may be endowed with a nice physical interpretation, although it suffers from lack of some physically demanded important features. Despite that, there arises some open questions, e.g., whether hypothetical tachyons can be considered as usual particles possessing time-like trajectories.

math-ph↗

arXiv2015

Determination of the Riemann modulus and sheet resistivity by a six-point generalization of the van der Pauw method

Six point generalization of the van der Pauw method is presented. The method is applicable for two dimensional homogeneous systems with an isolated hole. A single measurement performed on the contacts located arbitrarily on the sample edge allows to determine the specific resistivity and a dimensionless parameter related to the hole, known as the Riemann modulus. The parameter is invariant under conformal mappings of the sample shape. The hole can be regarded as a high resistivity defect. Therefore the method can be applied for experimental determination of the sample inhomogeneity.

physics.ins-det↗