The dynamics of laser droplet generation

We propose an experimental setup allowing for the characterization of laser droplet generation in terms of the underlying dynamics, primarily showing that the latter is deterministically chaotic by means of nonlinear time series analysis methods. In particular, we use a laser pulse to melt the end of a properly fed vertically placed metal wire. Due to the interplay of surface tension, gravity force and light-metal interaction, undulating pendant droplets are formed at the molten end, which eventually completely detach from the wire as a consequence of their increasing mass. We capture the dynamics of this process by employing a high-speed infrared camera, thereby indirectly measuring the temperature of the wire end and the pendant droplets. The time series is subsequently generated as the mean value over the pixel intensity of every infrared snapshot. Finally, we employ methods of nonlinear time series analysis to reconstruct the phase space from the observed variable and test it against determinism and stationarity. After establishing that the observed laser droplet generation is a deterministic and dynamically stationary process, we calculate the spectra of Lyapunov exponents. We obtain a positive largest Lyapunov exponent and a negative divergence, i.e., sum of all the exponents, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In addition to characterizing the dynamics of laser droplet generation, we outline industrial applications of the process and point out the significance of our findings for future attempts at mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos [supplementary material available at http://www.matjazperc.com/chaos/laser.html

Regular and chaotic vibration in a piezoelectric energy harvester

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy

Researching Fermat’s principle with GeoGebra

The following thesis presents the possibilities of using the computer software GeoGebra as an aid for verifying properties and laws when dealing with mathematical and physical problems. First, the thesis provides some basic software features of dynamic geometry. This is followed by a detail presentation of the GeoGebra software’s essential components and functions. Furthermore, possibilities of using the GeoGebra software to perform different functions are presented, as is its classroom implementation with supplying online dynamical classroom worksheets. In detail, the theoretical models of reflection and total reflection, refraction on a flat surface and refraction on a sphere are discussed. For each of the aforementioned instances, online dynamic classroom worksheets are published to help the user verify the theoretical laws in practice using the GeoGebra software

Vpliv staranja prebivalstva na potrebe po toploti na nacionalni ravni

Residential energy demands are expected to change significantly in the future with increasing electrification, energy efficiency, and improved comfort as well as climate change. While many studies have been performed into how the aforementioned influential factors could affect the energy needs of the forthcoming generations, far less are present for how population aging affects the future heating demand. The latter is particularly relevant for Europe and Slovenia as declining fertility rates and lengthening life spans give rise to the increasing ratio of the elderly. In this paper, the future residential space and water heating energy demands of the aging society in Slovenia, using a sample of geographically dispersed nursing homes as a proxy, are estimated. The results are compared against the latest EU reference scenario until 2050, whereby the adjusted estimates differ by up to 9.6 %. Thus, the study highlights the need for energy policy to be further refined and redefined to link the energy performance requirements of buildings to specific consumption characteristics of the elderly