arXiv subjects

Janusz Wolny

Publications and source records attributed to Janusz Wolny.

5 recordsLinked to original sources

arXiv2018

Momentum in the dynamics of variable-mass systems: classical and relativistic case

We discuss a role of a momentum vector in the description of dynamics of systems with variable mass, and show some ambiguity in expressing the 2nd Newtonian law of dynamics in terms of momentum change in time for variable-mass systems. A simple expression that the time-derivative of the momentum of the body with variable mass is equal to the net external force is not always true (only if a special frame of reference is assumed). In basic textbooks and multiple lecture notes the correct equation of motion for a variable-mass system (including relative velocities of the masses entering or leaving the body) is not sufficiently well discussed, leading to some problems with understanding the dynamics of these systems among students. We also show how the equation of motion in classical case (in translational motion) can be easily expanded to the relativistic case and discuss a motion of a relativistic rocket. For the non-relativistic case also a rotational motion is discussed. It is of course true, that most of the good literature treats the problem accurately, but some of the commonly used textbooks do not. The purpose of our letter is to pay attention to the problem of dynamics of variable-mass systems and show yet another perspective of the subject.

physics.class-ph↗

arXiv2005

An extinction rule for a class of 1D quasicrystals

We study decorated one-dimensional quasicrystal obtained by a non-standard projection of a part of two-dimensional lattice. We focus on the impact of varying relative positions of decorated sites. First, we give general expression for the structure factor. Subsequently we analyze an example of extinction rule.

cond-mat.mtrl-sci↗

arXiv2005

Physical space description of decorated quasicrystals

In this paper the systematic method of dealing with the arbitrary decorations of quasicrystals is presented. The method is founded on the average unit cell formalism and operates in the physical space only, where each decorating atom manifests itself just by an additional component of the displacement density function in the average unit cell. Such approach allows us to use almost all classical crystallography algorithms for structure refining based on experimental data and may meaningly decrease the number of parameters which have to be fit. Further help for such analysis may be the use of proposed recently average Patterson function, here applied to decorated sets. As an example we present a description of a class of decorated quasicrystals based on Sturmian sequence of two interatomic spacings: we calculate explicitly structure factor, the shape of average Patterson function and give an algorithm for pattern analysis.

cond-mat.other↗

arXiv2005

Structure factor for decorated Penrose tiling

The structure factor for arbitrary decorated Penrose tiling has been calculated in average unit cell description. Analytical expression for the structure factor has been derived in physical space. The obtained formulas can be straightforward extended to some imperfect structures, including phasons or phonons and also some other defects.

cond-mat.other↗

arXiv2005

Periodic diffraction patterns for 1D quasicrystals

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction patterns are calculated analytically both using ``cut and project'' and ``average unit cell'' methods, taking advantage of the physical space properties of the structure.

cond-mat↗