Related Experiment Video
Updated: Apr 1, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Periodic model of an LTA framework
A Mikuła1, M Król2, A Koleżyński2
1Department of Silicate Chemistry and Macromolecular Compounds, Faculty of Materials Science and Ceramics, AGH University of Science and Technology, 30 Mickiewicza Av., 30-059, Krakow, Poland. amikula@agh.edu.pl.
Abstract:
Zeolites are a group of microporous aluminosilicate frameworks with numerous applications in, for example, catalysis and ion-exchange and sorption processes. One of the most important tools for analyzing the properties of zeolite structures is vibrational spectroscopy. However, the complexity of these structures often leads to difficulties when attempting to interpret the resulting spectra, so an additional complementary tool is required: computational methods. The aim of this study was to formulate a simplified periodic model of an LTA framework containing alkali metal cations (either Li(+), Na(+), K(+), Rb(+), or Cs(+)) and to perform a set of ab initio calculations aimed at assessing the influence of these cations on the properties of the vibrational spectra of the LTA framework. Additionally, chemical bonding was analyzed by means of electron density topology analysis. Results obtained were compared with experimental spectra for alkali metal forms of zeolite A. It was found that the vibrational spectra obtained using the proposed model agree well with the corresponding experimentally derived spectra, meaning that the model can be used to analyze real spectra in detail.
More Related Videos
Related Concept Videos
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
Properties of Laplace Transform-II
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Classification of Systems-I
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

